Social Power: A Point missed in Multi-Agent

Objective Degrees of Dependence in Social Dependence Relations Antônio Carlos da Rocha Costa1,2 and Graçaliz Pereira Dimuro1 1 Escola de Informática – Universidade Católica de Pelotas Pelotas, RS, Brazil. 2 PPGC – Universidade Federal do Rio Grande do Sul Porto Alegre, RS, Brazil {rocha,liz}@atlas.ucpel.tche.br Abstract. This paper presents a way to quantify dependence relations between agents of a multiagent system in order to introduce a measure for the degree of dependence established between them. The quantification of the dependence relations is performed on a specially defined form of reduced dependence graphs, called dependence situation graphs. The paper shows that the resulting notion of objective degree of dependence is intuitively acceptable. Given that such degrees of dependence have an objective nature, a way is presented to allow for their refinement into subjective degrees of dependence, through the consideration of subjective aspects of the dependence relationships. The paper also shows how degrees of dependence allow for a measure of the dependence that a society as a whole has on each agent that participates in it and, correlatively, a measure of the statuses and negotiation powers of the agents of such society. 1 Introduction The problem of measuring the dependence relations that arise between agents when they operate in a social context has been put forward as an important problem since at least [1], where a quantitative notion of strength of a dependence relation is proposed. The Conclusion of [7], for instance, indicated several features on which the quantification of the dependence relations could be based, such as the importance of a goal to an agent, the number of actions/resources needed to execute a plan, or the number of agents which are able to perform a needed action or to control a needed resource. In [4], dependence relations were given a quantitative evaluation on the basis of subjective notions, namely, the relative importance of goals to the agents and the cost of performing the necessary actions. We show here that the problem can be solved by appropriately quantifying the dependence situations that arise from those relations. The paper introduces a procedure for an objective quantification of dependence situations. The procedure computes degrees of dependence between agents on the basis of a specially derived form of dependence graphs – the DS-graphs (dependence situation graphs) – so that a measure of the degree of dependence of each agent on the agents that can help it to achieve its goals may be given in an easy way. The paper presents the procedure and examines some of its features. Following one of the suggestions in [7], the procedure takes into account essentially the number of agents that are able to perform each needed action, but it also takes into account the kind of dependence (AND-dependence, OR-dependence) that the structure of the dependence situation establishes between the involved agents. Thus the need for the DS-graphs, where those kinds of dependences are explicitly indicated. The resulting degrees of dependence are said to be objective because they take into account only information about the structure of the dependence situation, through the DS-graph, and do not involve subjective notions (e.g., the importance of goals). Objective degrees of dependence may be refined in many ways, according to the needs of the application where they are to be used, by weighting them with features that are relevant for the application. For instance, objective degrees of dependence may be refined by the features suggested in [7], such as the importance of a goal to an agent or the cost of the necessary resources, or by the number of resources needed to achieve the goal, or else by probability that each agent has of really performing an action when the action is necessary. Also, by summing up the objective degrees of dependence that the agents of a society have on each other, it is possible to define a measure of the dependence of the society, as a whole, on each of its agents. Correlatively, it is possible to define a measure of an agent’s status and negotiation power [2] within the society. Further more, objective degrees of dependence may be used to refine the social reasoning mechanisms that solve the problem of choosing partners for the formation of coalitions, such as the one introduced in [7, 8]. The paper is structured as follows. Section 2 summarizes the relevant ideas concerning social dependence relations and dependence situations. Section 3 reviews dependence-graphs and introduces the DS-graphs. Section 4 introduces a formal notation for DS-graphs. Section 5 defines the notion of objective degree of dependence and shows how they can be calculated on simple DS-graphs. Section 6 introduces additional concepts: objective degrees of dependence for DS-graphs containing transitive dependences and bilateral dependences; objective degrees of dependence of a society on each of its agents; a measure of an agent’s negotiation power within a society; and a way to refine objective degrees of dependence with subjective estimates. Section 7 brings the Conclusion and future work. 2 Dependence relations and dependence situations Social dependence relations are pointed out in [1] as one of the main objective reasons for the establishment of interactions between agents. Social dependence relations can be defined by: Definition 1. An agent α is said to socially depend on an agent β, with respect to an action a, for the purpose of achieving a goal g, denoted (DEP α β a g), if and only if: 1. 2. 3. 4. g is a goal of α; α cannot do a by itself; β can do a by itself; a being done by β implies g being (eventually) achieved. The definition characterizes social dependence relations as an objective feature of an agent’s behavior, in the sense that it does not depend on the agent having it represented in his mental states (beliefs, plans, etc.). Regarding the direction of the dependence, dependence relations between two agents can be classified either as unilateral or as bilateral: unilateral: ∃a, g.(DEP α β a g) ∧ ∀a′ , g ′ .¬(DEP β α a′ g ′ ) α depends on β with respect to some action a and some goal g, but there is no action and no goal with respect to which β depends on α bilateral: ∃a, g.(DEP α β a g) ∧ ∃a′ , g ′ .(DEP β α a′ g ′ ) α depends on β with respect to some action a and some goal g, and β depends on α with respect to some action a′ and some goal g ′ Regarding the goals that set the stage for the dependence, bilateral dependence relations can be classified either as mutual or as reciprocal 3 : mutual: ∃a, a′ , g.(DEP α β a g) ∧ (DEP β α a′ g) ∧ a 6= a′ α depends on β, and β depends on α, with respect to the same common goal g reciprocal: ∃a, a′ , g, g ′ .(DEP α β a g ′ ) ∧ DEP β α a′ g) ∧ a 6= a′ ∧ g 6= g ′ α depends on β, and β depends on α, with respect to different private goals Regarding the number of agents involved in a unilateral dependence, and the way their actions are combined to help achieve an agent’s goal, social dependence relations can be classified either as OR-dependence or as AND-dependence, in many ways [8]. For instance: OR-dependence, multiple partners, single goal, single action needed: (DEP α β1 a1 g) ∨ (DEP α β2 a2 g) ∨ . . . ∨ (DEP α βn an g) there are several alternative agents βi , each being able to perform an action ai that may lead an agent α to achieve the goal g AND-dependence, multiple partners, single goal, multiple actions needed: (DEP α β1 a1 g) ∧ (DEP α β2 a2 g) ∧ . . . ∧ (DEP α βn an g) there are multiple partners βi , each having to perform a different action ai to jointly lead agent α to achieve the goal g As shown in the work on the DEPNET simulator [8], however, for the purpose of quantifying dependence relations it is not necessary to take actions and plans into account: it is enough to know that agent α is dependent on agent β to achieve goal g. In case there are two or more agents that are able to help α to achieve g, it is further necessary to know just the general kind of dependence (either an AND-dependence or an OR-dependence) that arises between them and α. Such simplified picture of a dependence relation, where only agents and goals are considered, along with the types of relations connecting them, is called a dependence situation [8]. 3 In [1], a distinction is made between cooperation (social behavior induced by a relation of mutual dependence) and social exchange (social behavior induced by a relation of reciprocal dependence). We don’t make such distinction and use preferably the term social exchange to denote both kinds of social behaviors. Thus, the quantification procedure of dependence relations introduced below operates only on the information contained in such dependence situations, which motivates the definition of the DS-graphs, in the next section. 3 DS-graphs Dependence graphs were introduced in [9] as a generalization of dependence networks [8], for the picturing of the various dependence relations that may exist within a multiagent system. They are structures of the form DG = (Ag, Gl, P l, Ac, Ar, Ψ ) where agents Ag, goals Gl, plans P l and actions Ac are taken as nodes and are linked with each other by the arcs Ar as specified by function Ψ , thus construing the structure of the dependence relations show how agents depend on other agents to achieve goals through plans involving actions performed by those other agents. Since dependence graphs have usually quite complex structures, [9] also introduced the so-called reduced dependence graphs, where nodes representing plans are abstracted away and goals are used not as nodes, but as labels of arcs. The procedure for the quantification of dependence relations that we will introduce below requires only the information contained in the so-called dependence situations, which amounts to the immediate information content of the dependence relation expressed by the elements of the dependence graph, together with the types of dependences intervening between the agents (AND-dependences, OR-dependences). This information about type is only indirectly represented in dependence graphs, through the way actions and goals are related to plans. On the other hand, as mentioned before, the procedure abstracts away information about which plans (and actions) are involved, thus calculating degrees of dependence that are relative to an implicitly understood (e.g., currently used) set of plans. To structure such minimal information contained in dependence situations, we define the notion of a DS-graph (dependence situation graph): Definition 2. Let Ag be a set of agents and Gl be the set of goals that those agents may have. A DS-graph over Ag and Gl is a structure DS = (Ag, Gl, Ar, Lk, Ψ, ∆) such that: 1. Ar is a set of arcs, connecting either an agent to a goal or a goal to an agent; 2. Lk is a set of links, connecting subsets of arcs; 3. Ψ : Ar → (Ag × Gl) ∪ (Gl × Ag) is a function assigning either an agent and a goal or a goal and an agent to each arc, so that if Ψ (ar) = (ag, g) then arc ar indicates that agent ag has the goal g, and if Ψ (ar) = (g, ag) then arc ar indicates that goal g requires some action by agent ag in order to be achieved; 4. ∆ : Lk → ℘(Ar) is a function assigning links to sets of arcs, representing an AND-dependence between such arcs, so that ∆(l) = {ar1 , . . . , arn } iff either: (a) there are an agent ag and n goals g1 , . . . , gn such that Ψ (ar1 ) = (ag, g1 ), . . . , Ψ (arn ) = (ag, gn ) indicating that ag aims the achievement of all the goals g1 , . . . , gn ; or, (b) there are a goal g and n agents ag1 , . . . , agn such that Ψ (ar1 ) = (g, ag1 ), . . . , Ψ (arn ) = (g, agn ) indicating that g requires the involvement of all the agents in the set {ag1 , . . . , agn } in order to be achieved. Given a DS-graph: 1. if there are: a set of agents {ag0 , ag1 , . . . , agn }; a set of arcs {ar0 , ar1 , . . . , arn }; a goal g; a link l; and if it happens that Ψ (ar0 ) = (ag0 , g), and Ψ (ari ) = (g, agi ) (for 1 ≤ i ≤ n), and ∆(l) = {ar1 , . . . , arn }, then we say that agent ag0 is ANDdependent on agents ag1 , . . . , agn with respect to goal g; 2. if there are: a set of agents {ag0 , ag1 , . . . , agn }; a set of arcs {ar1 , . . . , arn , ar1′ , . . . , arn′ }; a set of goals g1 , . . . , gn ; a link l; and if it happens that Ψ (ar1 ) = (ag0 , g1 ), . . . , Ψ (arn ) = (ag0 , gn ), and Ψ (ari′ ) = (gi , ag1 ) (for 1 ≤ i ≤ n), and ∆(l) = {ar1 , . . . , arn }, then we say that agent ag0 is AND-dependent on agents ag1 , . . . , agn with respect to the goals g1 , . . . , gn ; 3. if there are: a set of agents {ag0 , ag1 , . . . , agn }; a set of arcs {ar0 , ar1 , . . . , an }; a goal g; and if it happens that Ψ (ar0 ) = (ag0 , g), and Ψ (ari ) = (g, agi ) (for 1 ≤ i ≤ n), but there is no link l such that {ar1 , . . . , arn } ⊆ ∆(l), then we say that agent ag0 is OR-dependent on agents ag1 , . . . , agn with respect to goal g; 4. if there are: a set of agents {ag0 , ag1 , . . . , agn }; a set of arcs {ar1 , . . . , arn , ar1′ , . . . , arn′ }; a set of goals g1 , . . . , gn ; and if it happens that Ψ (ar1 ) = (ag0 , g1 ), . . . , Ψ (arn ) = (ag0 , gn ), and Ψ (ari′ ) = (gi , agi ) (for 1 ≤ i ≤ n), but there is no link l such that {ar1 , . . . , arn } ⊆ ∆(l), then we say that agent ag0 is OR-dependent on agents ag1 , . . . , agn with respect to the goals g1 , . . . , gn . A1 B1 g B2 B3 A2 B4 g B5 B6 Fig. 1. Sample AND-dependence (1,2) and OR-dependence (3,4) relations for DS-graphs. Graphically, we use the convention that AND-dependence is represented by a curved link tying together the arcs involved in such dependence, while OR-dependence is represented by the absence of any such link. Figure 1 illustrates both ANDdependence (of agent A1 on agents B1 , B2 , B3 with respect to goal g1 , and of agent A2 on agent B4 , B5 , B6 with respect to goals g2 , g3 , g4 ) and OR-dependence (of agent A3 on agents B7 , B8 , B9 with respect to goal g5 , and of agent A4 on agent B10 , B11 , B12 with respect to goals g6 , g7 , g8 ). 4 A notation for DS-graphs In this section we present formal definitions that support the calculation of objective degrees of dependence in DS-graphs. We develop a notation that allows for a succinct representation of the structure of dependence situations, and that is used as the basis for the definition of the calculation procedure. 4.1 Simple dependence situations. A simple AND-dependence situation occurs in a DS-graph either when an agent is dependent on two or more agents for the realization of a single goal, or when an agent is dependent on a single agent for the realization of two or more goals. If agent α is dependent on agents β1 , β2 , . . . , βn with respect to goal g, this is denoted as (α ≺ β1 ∧ β2 ∧ . . . ∧ βn | g). If agent α is dependent on agent β with respect to goals g1 , g2 , . . . , gm , this is denoted as (α ≺ β | g1 ∧ g2 ∧ . . . ∧ gm ). A simple OR-dependence relation occurs either when an agent is dependent on two or more agents for the realization of a single goal, or when an agent is dependent on a single agent for the realization of two or more alternative goals. If agent α is dependent on agents β1 , β2 , . . . , βn with respect to goal g, this is denoted as (α ≺ β1 ∨ β2 ∨ . . . ∨ βn | g). If agent α is dependent on agent β with respect to goals g1 , g2 , . . . , gm , this is denoted as (α ≺ β | g1 ∨ g2 ∨ . . . ∨ gm ). 4.2 Composed dependence situations. A composed dependence situation occurs either when an agent is dependent on alternative sets of agents for the realization of a single goal, each set of agents being jointly capable of tackling the goal (so that the agent is OR-dependent on the various sets of agents, but AND-dependent on the agents of each set) or when a given agent is dependent on a conjunction of sets of agents, an agent in a set being able to act together with an agent in each of the other sets, in order to achieve the goal aimed by the given agent (so that the agent is AND-dependent on the various sets of agents, but OR-dependent on the agents of each set). A composed dependence situation is thus written either using a disjunctive dependence form: (α ≺ ∧i1 (βi1 ) ∨ ∧i2 (γi2 ) ∨ . . . ∨ ∧ik (δik ) | g) or using a conjunctive dependence form: (α ≺ ∨i1 (βi1 ) ∧ ∨i2 (γi2 ) ∧ . . . ∧ ∨ik (δik ) | g) 4.3 Generalized dependence situations. It may be interesting to generalize the notation for DS-graphs introduced above by extending the number of occurrences of operations ∧ and ∨, both at the agents part and at the goals part of the expression, thus including composed dependence situations as special cases. Let ⊙, ⊡ be, respectively, either the operators ∧, ∨ or the operators ∨, ∧. A generalized dependence situation is written using either an expression with a generalized conjunctive dependence form: (α ≺ ⊙i1 (⊡j1 βj1 ) ∧ ⊙i2 (⊡j2 γj2 ) ∧ . . . ∧ ⊙ik (⊡jk δjk ) | g1 ∧ g2 ∧ . . . ∧ gk ) or an expression with a generalized disjunctive dependence form: (α ≺ ⊙i1 (⊡j1 βj1 ) ∨ ⊙i2 (⊡j2 γj2 ) ∨ . . . ∨ ⊙ik (⊡jk δjk ) | g1 ∨ g2 ∨ . . . ∨ gk ) We call structured goals the goals that appear in the goals part of generalized dependence situations. Note that in the generalized dependence situations, the higher-level operators ∧ and ∨ are assumed to be non-commutative, so that a correspondence can be kept between (sets of) agents and goals. This is also the reason why the number of sets of agents that are listed and the number of goals listed should be the same. The set of generalized dependence situations expressions is denoted by GDS. 4.4 Graphical representation of generalized dependence situations. The mapping between the expressions defined above and the corresponding generalized DS-graphs is immediate. Figure 2 illustrates the generalized DS-graph corresponding to the generalized dependence situation denoted by: (A ≺ ((B1 ∧ B2 ) ∧ (B3 ∨ B4 )) ∨ (B5 ∧ B6 ) | (g1 ∧ g2 ) ∨ g3 ) g1 B1 B2 A g2 B3 B4 g3 B5 B6 Fig. 2. Sample generalized DS-graph. For the sake of space, we omit the formal definition of generalized DS-graphs. 5 Calculating objective degrees of dependence in generalized DS-graphs To calculate objective degrees of dependence, a function dgr is defined, from the set of expressions of generalized dependence situations to the positive reals in the interval from 0 to 1. The calculation of the degree of dependence of an agent on other agents, with respect to a given goal, is informally defined as: – if an agent is autonomous on another agent, with respect to the given goal, its degree of dependence on that agent is assigned the value 0; – the total degree of dependence of an agent on all agents on which it is dependent, with respect to the given goal, is assigned the value 1; – if the dependence expression that characterizes the dependence situation of an agent is of a conjunctive form with k terms, and its associated degree of dependence is d, then the degree of dependence of the agent with respect to each of the terms of the dependence expression is assigned the value d; – if the dependence expression that characterizes the dependence situation of an agent is of a disjunctive form with k terms, and its associated degree of dependence is d, then the degree of dependence of the agent with respect to each of the terms of the dependence expression is assigned the value d/k. The rationale behind such informal procedure extends the one in [2]: – a conjunctive form indicates that each of its component is essential to the achievement of the involved goals, thus all such components should be valued at the same level of the involved goals; – a disjunctive form indicates that its components are alternatives that are equally able to achieve the involved goals, thus they devaluate each other and should be uniformly valued by a fraction of the value of the involved goals. This rationale gives rise to the formal definition of the function dgr: Definition 3. Let G be the structured goal of an agent α and let α be dependent on a set of other agents for the achievement of G. Then, the objective degree of dependence of α on each such agent is given by the function dgr : GDS → [0 ; 1], defined by cases as follows: 1. If G = ∧k (gk ) then dgr[(α ≺ ∧k (⊙ik (⊡jk βjk )) | G)] = 1; 2. If G = ∨k (gk ) then dgr[(α ≺ ∨k (⊙ik (⊡jk βjk )) | G)] = 1; 3. If dgr[(α ≺ ∧k (⊙ik (⊡jk βjk )) | ∧k (gk ))] = d then dgr[(α ≺ ⊙ik (⊡jk βjk ) | gk )] = d; 4. If dgr[(α ≺ ∨k (⊙ik (⊡jk βjk )) | ∨k (gk ))] = d then dgr[(α ≺ ⊙ik (⊡jk βjk ) | gk )] = d/k; 5. If dgr[(α ≺ ∧k (⊡jk βjk ) | gk )] = d then dgr[(α ≺ ⊡jk βjk | gk )] = d; 6. If dgr[(α ≺ ∨k (⊡jk βjk ) | gk )] = d then dgr[(α ≺ ⊡jk βjk | gk )] = d/k; 7. If dgr[(α ≺ ∧k βjk | gk )] = d then dgr[(α ≺ βjk | gk )] = d; 8. If dgr[(α ≺ ∨k βjk | gk )] = d then dgr[(α ≺ βjk | gk )] = d/k. The following is true about Definition 3: a) the definition provides a computable notion of degree of dependence that correspond to the two basic kinds of social dependence relations (OR-dependence, AND-dependence); b) as the notion of social dependence relation that supports them, the definition states an objective notion of degree of dependence, which is function of no subjective evaluation by the agents. 6 Additional concepts 6.1 Degrees of transitive dependences When analyzing the dependence situations between agents, it is often necessary to take into account dependence relations that go beyond the direct dependence between the agents. One form of such indirect dependence is the transitive social dependence. Transitive social dependence arises because social dependence may happen in a transitive mode: – if α depends on β with respect to some goal g, and β depends on γ w.r.t. some goal g ′ , and g ′ is instrumental to g, then α depends on γ with respect to the combined goal g • g ′ , which is implicitly adopted by α. To define degrees of dependence for transitive dependence relations, a choice has to be made regarding the operation on degrees of dependence that is induced by the transitivity of the relations of social dependence. The natural choice is multiplication: Definition 4. Let α be dependent on β with respect to goal g, and β be dependent on γ with respect to g ′ , and g ′ be instrumental do g. Then, α is said to transitively depend on γ with respect to the combined goal g • g ′ , denoted (α ≺ γ, g • g ′ ). Such transitive degree of dependence is calculated by dgr[(α ≺ γ | g • g ′ )] = dgr[(α ≺ β, g)] · dgr[(β ≺ γ, g ′ )] Definition 4 enables the calculation of degrees of dependence that takes into account dependences on agents that are far away in the overall network of social relations, and not only degrees of dependence for direct dependence relations. 6.2 Degrees of bilateral dependence The social dependence relations examined so far are said to be unilateral. When considering bilateral social dependence, a notion of degree of bilateral dependence has to be defined. The natural choice for the operation on the degrees of dependence that arise from bilateral dependences is addition: Definition 5. Let α and β be two agents such that α is dependent on β with respect to a goal g1 , and β is dependent on α with respect to a goal g2 . Then α and β are said to be bilaterally dependent on the combined goal g1 ⊗ g2 , denoted (α ≺≻ β | g1 ⊗ g2 ). Such degree of bilateral dependence is calculated by dgr[(α ≺≻ β | g1 ⊗ g2)] = dgr[(α ≺ β | g1 )] + dgr[(β ≺ α | g2 )] The following is true about Definition 5: 1. dgr[(α ≺≻ β | g1 ⊗ g2 )] = dgr[(β ≺≻ α | g1 ⊗ g2 )] = dgr[(α ≺≻ β | g2 ⊗ g1 )] 2. the definition applies both to the cases of reciprocal dependence (g1 6= g2 ) and to the cases of mutual dependence (g1 = g2 ). 6.3 Negotiation power of agents in societies Let M be a set of agents, and α a member of M . Let the subset of agents of M on which α depends be given by dep(α, M ) = {β | (α ≺ β | g) for some g ∈ Goals(α)}. Let codep(M, α) = {β ∈ dep(S, α) | (β ≺ α | g) for some g ∈ Goals(β)} be the subset of agents of M that co-depend on α, that is, the subset of agents of dep(M, α) which are themselves dependent on α. We let (α ≺ M ) denote the fact that α belongs to M and that it depends on some subset of agents of M . We let (M ≺ α) denote the fact that some subset of agents of M are co-dependent on α. The degree with which α depends on M , and the degree with which M co-depends on α, can both be calculated. We define the degree of dependence of α on M as: X dgr[(α ≺ M )] = dgr[(α ≺ β | g)] β∈dep(α,M ),g∈Goals(α) We define the degree of co-dependence of M on α as: X dgr[(M ≺ α)] = dgr[(β ≺ α | g)] β∈codep(M,α),g∈Goals(β) In [2], the degree of co-dependence of M on α is called α’s social value to M . The relation between α’s social appeal to M , and the degree of dependence that α has on M determines α’s capacity of establishing exchanges, cooperation, coalitions, etc., in M . In [2] this relation is called α’s power of negotiation in M . Formally, we may establish that the negotiation power of an agent α in a set of agent M is given by: dgr(M ≺ α) NgtPow(α, M ) = dgr(α ≺ M ) A society is a set of agents that interact in order to overcome their social dependences. As such, a society becomes itself dependent on its own agent for its normal functioning. If S is a society and α an agent of S, then dgr(M ≺ α) is the social value of α in S and, correlatively, NgtPow(α, S) is the negotiation power of α in S. 6.4 Refining objective degrees of dependence with subjective estimates Many subjective estimates of goals, actions, resources and plans can influence the way agents perceive their dependences on other agents: importance, cost, preferences, emotional reactions, cultural biases, etc., all make the degrees of dependence depart in many ways from the values that can be objectively calculated by the procedure defined above. Thus, we must define a means to allow the objective degrees of dependence to be refined by the subjective estimates of those various aspects of a dependence situation. In a dependence situation, the object agent is the agent whose dependence is being analyzed, while a third part agent is an agent on which the object agent depends [8]. The subjective factors that may influence the determination of a degree of dependence are due either to the object agent (importance of goals, preferences among goals, etc.) or to the third part agents (costs of actions, probability of action execution, etc.). In a DS-graph, the subjective factors due to the object agents should label the arcs connecting the object agents to the goals in concern, while the third part agent factors should label the arcs connecting the goals with the third part agents. We thus extend definition 3: Definition 6. Let the wi ∈ [0 ; 1]. Then, the weighted objective degree of dependence wdgr : GDS → [0 ; 1] is defined by cases as follows: 1. If G = ∧k (wk · gk ) then dgr[(α ≺ ∧k (⊙ik (⊡jk (wjk · βjk ))) | G)] = 1; 2. If G = ∨k (wk · gk ) then dgr[(α ≺ ∨k (⊙ik (⊡jk (wjk · βjk ))) | G)] = 1; 3. If dgr[(α ≺ ∧k (⊙ik (⊡jk (wjk · βjk ))) | ∧k (wk · gk ))] = d then dgr[(α ≺ ⊙ik (⊡jk (wjk · βjk )) | wk · gk )] = d; 4. If dgr[(α ≺ ∨k (⊙ik (⊡jk (wjk · βjk ))) | ∨k (wk · gk ))] = d then dgr[(α ≺ ⊙ik (⊡jk (wjk · βjk )) | wk · gk )] = d/k; 5. If dgr[(α ≺ ∧k (⊡jk (wjk · βjk )) | wk · gk )] = d then dgr[(α ≺ ⊡jk (wjk · βjk ) | gk )] = wk · d; 6. If dgr[(α ≺ ∨k (⊡jk (wjk · βjk )) | wk · gk )] = d then dgr[(α ≺ ⊡jk (wjk · βjk ) | gk )] = (wk · d)/k; 7. If dgr[(α ≺ ∧k (wjk · βjk ) | gk )] = d then dgr[(α ≺ βjk | gk )] = wjk · d; 8. If dgr[(α ≺ ∨k (wjk · βjk ) | gk )] = d then dgr[(α ≺ βjk | gk )] = (wjk · d)/k. In this way, the objective degrees of dependence that we defined above clearly show their roles as reference values, upon which subjective factors may operate to modulate the objective evaluations with subjective ones. 7 Conclusion This paper introduced degrees of dependence in dependence relations, whose calculations involve only objective notions, that is, notions that do not depend on the beliefs and preferences of the agents involved in those relations. It stated the basic properties of objective degrees of dependence. Many lines of work may derive from the results presented here. It is necessary to better explore the possible ways objective degrees of dependence may be combined with subjective estimates, so that the dynamic evolution of the exchanges during the functioning of the organization, and the effective behaviors of the agents, can be considered in the moment of calculating the degrees of dependence. It is necessary to consider in which ways degrees of dependence can be used as criteria in social reasoning mechanisms concerned with the formation of coalitions ( [4] proposed one such way, for utility-based subjective degrees of dependence). For this to profitable, however, it is also necessary to develop a theoretical account of the deep relations that seem to exist between the theory of dependence relations [1] and the theory of social exchange values [5, 6, 3], showing how degrees of dependence and exchange values may jointly enrich the explanations of the higher level social notions that can be derived from social dependence, like influence, power, trust, etc. Acknowledgements: The authors thank Cristiano Castelfranchi for the remarks on a previously wrong presentation of the transitivity of dependence relations, and for calling our attention to the importance of connecting the work with the notion of negotiation power. To an anonymous referee, for the suggestion that degrees of dependence could be refined by the probability of the partner agents really performing needed actions. References 1. C. Castelfranchi, M. Miceli and A. Cesta. Dependence Relations among Autonomous Agents. In: E. Werner and Y. Demazeau (eds.), Decentralized A.I.-3. Elsevier, Amsterdam, 1992. p.215–227. 2. C. Castelfranchi and R. Conte. The Dynamics of Dependence Networks and Power Relations in Open Multiagent Systems. In: Proc. COOP’96 – Second International Conference on the Design of Cooperative Systems, Juan-les-Pins, France, June, 12-14. INRIA SophiaAntipolis, 1996. p.125-137. 3. A. C. R. Costa and G. P. Dimuro. Systems of Exchange Values as Tools for Multiagent Organizations. Journal of the Brazilian Computer Society, Special Edition on Multiagent Organizations (J. Sichman, O. Boissier, C. Castelfranchi, V. Dignum, eds.), 2005. 4. N. David, J. S. Sichman and H. Coelho. Agent-Based Social Simulation with Coalitions in Social Reasoning. Proc. 2nd. International Workshop on Multi-Agent Based Simulation (MABS’00), Boston, USA. In: P. Davidsson and S. Moss eds. Multi-Agent Based Simulation, Lecture Notes in Artificial Intelligence, vol. 1979. Springer-Verlag, Berlin, 2000. 5. J. Piaget. Sociological Studies. Routlege, London, 1995. 6. M. R. Rodrigues, A. C. R. Costa, and R. Bordini. A System of Exchange Values to Support Social Interactions in Artificial Societes. In: Proceeding of the Second International Conference on Autonomous Agnets and Multiagents Systems, AAMAS 2003, Melbourne, pages 81–88, 2003. 7. J. S. Sichman and Y. Demazeau. On Social Reasoning in Multi-Agent Systems. Revista Iberoamericana de Inteligencia Artificial, vol. 13, Verano, pages 68–84, 2001. Available online at http://tornado.dia.fi.upm.es/caepia/numeros/13/sichman.pdf 8. J. S. Sichman, R. Conte, C. Castelfranchi and Y. Demazeau. A Social Reasoning Mechanism Based on Dependence Networks. In: A. G. Cohn (ed.) Proceedings of the 11th. European Conference on Artificial Intelligence, Baffins Lane, England: John Wiley & Sons, 1994. 9. J. S. Sichman and R. Conte. Multi-agent Dependence by Dependence Graphs. 2002. In: Proc. 1st International Joint Conference on Autonomous Agents and Multi-Agent Systems – AAMAS’02. pages 483-492, Bologna, Italy, July 2002. 

Practical "Permission": Dependence, Power, and Social Commitment Cristiano Castelfranchi Istituto di Psicologia del CNR* Unit of AI & Cognitive Modelling Roma, v. Marx 15 - 00137 Roma - ITALY cris@pscs2.irmkant.rm.cnr.it Extended Abstract - Preliminary version Premise The analytic enquiry of deontic modalities (obligatory, permitted, etc.) has been developed before and independently of the logic modelling of mental attitudes, of cognitive agent architecture, and of social interaction; it taken place following the blue print of non-deontic modalities (necessary; possible). We might consider this kind of approach and this use of the logic as basically anti-mentalistic: one tries to define, formalise, and to reason about obligation and permission substantially ignoring the mind of the involved agents. Thus, traditional treatment of deontic modalities is very problematic for a cognitive scientist. Let me explain why. As a cognitive scientist aimed at providing cognitive models of social relations and interactions (Conte e Castelfr), I will claim that: • There cannot be any obligation or permission that are not relative to, impinging on, some Agent -more precisely some Cognitive Agent. Why there could not be obligations/permissions for non-cognitive Agents? which is the special, intrinsic relation between deontic modality and cognition? • There cannot be any obligation or permission for non-social, standing alone, Agent. Why this? which is the special, intrinsic relation between deontic modality and sociality? In my view, current treatment by deontic logic does not help us to answer these crucial questions. • Obligations and permissions are just relative to actions i.e. to the behaviour of a cognitive agent (a behaviour based on beliefs and directed by goals). * This research has been supported by the ModelAge. EEC Project. I would like to thank Rosaria Conte with whom I developped in years many reflections obout norms and cognition. There cannot be obligations/permissions on mere word states and events unless as results of an action of some agent. Obligation and permission are addressed to a mind, and although pointing to a behaviour they are implicitly referring to mental attitudes. More than this: obligations and permissions are relations between minds and can be fully understood only on this perspective 1 1 . In this paper I will attempt to analyse permission in terms of a cognitive-social relation between two agents: • If something is "permitted", it is permitted to somebody (y), by somebody (x). I will analyse some basic aspects of the social relation between x and y and of their mind. In particular, I will search for elements of Dependence relations, power, goal adoption, and Social Commitment, as ingredient of the notion of "permitted" and of the Permission relation between x and y. I think that current developments in AI, philosophy, and logics relative to mental attitudes, rational action, agent architecture (especially BDI models: for ex. Ingrand & Pollack ; Rao & Georgeff, 91; Bell, 95; ), and Multi-Agent Systems, will allow the expression of the mental and relational core of this notion. In this preliminary exploration I will adopt a naive attitude, substantially ignoring the rich and subtle philosophical literature on the topic (mainly on legal, institutional form of permission), just reacting to some basic and consolidated notions, trying to build up on a sociocognitive ground this ontology. I will not propose any formalisation, but just point out some aspects that should be formalised. 1. Permission is not the absence of prohibition It should be clear, on the basis of previous claims that and why I cannot accept the well established analysis that reduces the Permission to do a to the negation of the Obligation of omitting a (if is not prohibited is permitted) (for ex. Ross). This is absurd. Permission is something that is "given" to somebody, and he "has". It is a social action and relation. It cannot just consist of the absence of a prohibition, of an obligation to abstain from a. It is not a lack of some constraint, or of some restrictive authority: it is the presence of a positive act and relation of an agent (x) towards another agent (y). If Robinson is living on a desert rock in the ocean, and nobody prohibits and prevents him from using any part of the island as he likes, he is not "permitted" to do so. Only if there are other agents, with a specific attitude and relation Robinson might be "permitted" to do something. If I'm walking around and breathing, I do not got the "permission" of breathing just because there is nobody (and no law) ordering of not breathing. Before starting this analysis about what is involved when "x permits to y to do a" (PERMIT x y a), it is important to stress the fact that I'm not analysing the normative or even the legal or institutional permission (Jones, ). I'm analysing "permission" in faceto-face, everyday interactions among agents not endowed with special roles. I think that interpersonal or practical permission is both the conceptual and the practical forerunner of the normative and institutional permission. I claim that the understanding the former is a necessary, though non-sufficient condition for understanding the latter. At the end of the paper I will say something about the Interpersonal Normative Permission, 1 In several languages the meaning of the verb "to permit" is broader than that of the noun "permission" and of the locution "to give the permission". For example it is possible to say that a physical agent "permitted" to a behavioural agent to do something ("rain did not permit John..."). In this use "to permit" is related to "prevent" not to "prohibit". I will consider only the meaning of "to permit" that is in some sense opposed to "to prohibit" and is close to "to give the permission". contrasting it with the Interpersonal Practical Permission. I will say nothing about the Institutional Permission (a complex form of the Normative one): I basically agree with Jones and Sergot' analysis, although I think that their formal apparatus (deontic logic) is not able to express the underlying cognitive and social relations that I describe for the Practical Permission and that I claim to hold also in the other forms of Permission. My working examples of interpersonal practical permission are the following ones: (1) y intends to enter a room, in the middle of the door there is x; y asks x "could you let me pass, please" and y answers "please" moving away. (2) two children on a beach are writing on the sand with some pipes used as pens. x's pipe is good, y's pipe is not good at all. x puts aside his pipe and y asks him: "may I use that?" "yes, but later you give me it back". 2. Permission presupposes Dependence-Power relations Let's now start to analyse the basic aspects of this social relation between x and y, and of their mind. In particular, I will search for elements of Dependence relations, power, goal adoption, and Social Commitment, as ingredient of the notion of "permitted" and of the Permission relation between x and y. (PERMIT x y a) implies -or better presupposes- that y is dependent on x as for her possible goal G of executing a. x cannot permit y something that he cannot prevent y from2 2. 1 The dependence theory Below, I will describe a theory of dependence as presented in [Sichman et al. (1994)] on the basis of a pre-existing model developed by Castelfranchi et al. [(1992; Conte & Castelfranchi, 1995) Our model We claim that social agents are plunged into a network of social relationships. The focus is on the agents' mental states, namely their goals. Social networks are here seen as patterns of relationships holding among the goals and actions of a given set of agents. The most fundamental relationship among agents' goals and actions is social dependence [(Castelfranchi et al., 1992)], where one agent needs the action of another to achieve one of her goals. The three basic notions of the social dependence theory are social market, dependence relation and dependence situation. We will present here only the first two; the last one is available in [(Sichman et al., 1994)]. The social market We will call a social market, or a market for short, any aggregate of agents where the value of a single agent's resources depend on the wants and needs of the others. In other words, in a social market, agents reach their goals thanks to what they have to “sell”. The general principle for achieving one's goals is that you-have-what-I-need-and-Ihave-what-you-need. The social market consists of a data structure composed by: (a) the set of goals each agent wants to achieve, (b) the set of actions she is able to perform, 2 At the institutional/legal level of course practical impossibility is not enough. The action could be practically executable by y, but not morally or legally executable without x's consensus. So, y continues to be dependent on x, but not for the execution of the practical action a, but for the execution of the institutional/ regular action a' that requires as a condition the permission of x. y dependence on x is institutionally, normatively created (see ch. 5). (c) the set of resources she controls and (d) the set of plans she has. A plan consists of a sequence of actions with its associated resources needed to accomplish them. However, an agent may have a plan whose actions or resources do not necessarily belong to her own set of actions or resources, and therefore she may depend on others in order to carry on a certain plan, and achieve a certain goal. An entry corresponding to an agent ag j has respectively: - the set of goals, - actions, - resources and - plans the external observer believes ag j has3 . By, resources, we mean, concrete objects that may be required by performing actions. For the time being, we will conceive of resources as both non-consumable and re-usable (for example a pair of scissors is a resource for cutting a piece of cloth). In future development of the model, both constraints will actually be dropped. Dependence relations Using the external description defined above, we define the notions of autonomy and dependence as follows . An agent agi is a-autonomous (action autonomous) for a given goal gk , according to a set of plans Pqk if there is a plan that achieves this goal in this set and every action appearing in this plan belongs to her own set of actions A(agi ). In other terms, an agent is a-autonomous if she is endowed with all the actions involved in at least one of the plans that achieves her goal: if her set of plans is non-empty, but none of those plans is exhausted by her actions, the agent is not a-autonomous. Analogously, we define the notion of r-autonomy (resource autonomy). Finally, an agent agi is s-autonomous (social autonomous) if she is both a-autonomous and rautonomous for this goal. On the other hand, if an agent does not have all the actions (or resources) to achieve a given goal, according to a set of plans, she may depend on the others for this goal. agi a-depends (action-depends) on another agent ag j for a given goal gk , according to a set of plans Pqk if agi has gk in her set of goals, she is not a-autonomous for gk and there is a plan in Pqk that achieves gk where at least one action used in this plan is in ag j 's set of actions A(ag j ) . An agent In a similar way, we have defined the notion of r-dependence (resource-dependence). Finally, an agent agi s-depends (social-depends) on another agent ag j if she either a-depends or rdepends on this latter. Social Dependence, Power and Permission When y is asking x for a permission (for example of passing or of using something), she is believing that x is able and in position of preventing her from doing what she needs. So, y is asking x of "let her doing". In fact, if y depends on x, x got some social power over y [Castel 90] 3 For the formal expression of our model, see Sichman et al. (1994). (S-DEP y x a g) (POWER-over x y g) x has the power of (CAN) allowing, favouring y in achieving g, and the power of preventing her from this. We call this form of social power "power over" the other (more precisely: over the goal of the other), and also "rewarding power" since x has the power of giving y positive (goal achievement) or negative (goal frustration) rewards. In the permission relation (asking/receiving-giving permission) there is a mutual belief of x and y about y's dependence on x and x's power over y, as for a given goal of y. A good formalization of this power relation and than of PERMIT would require a formal definition of PREVENT (ex.[Ortiz] and of LET as a form of doing [(Porn)]). Notice that there is not true "let something happen" if there is not (a belief about) the power of preventing it or at least of attempting to prevent it.. 2.1. Permission and Practical Possibility (why "weak" Dependence is weak) One might object that in many cases y might have the practical possibility of doing what she wants, of obtaining what she needs from x, without asking for something. Thus she is not really dependent on x. For example in (1) or in (2) y might be much stronger than x and could just push aside x's or take away x's pipe. In this cases, that are normally conceptualised as "weak dependence" [(Jennings, )] the problem is the correct identification of the goal y is depending on x for. In "weak dependence" notion, y could, is able to do a, but he "prefers" to rely on x, to exploit x's help/action. In my view this notion is quite superficial. In a deeper analysis one should express the fact that if y "prefers" x's help, this means that there is more utility in this choice: in other words, y will achieve more goals (for example the same result of doing by himself plus saving time and effort). Now, as for the achievement of this more global, compound goal he is strictly depending on x. In other terms, when y is said to be "weakly" dependent on x for goal g, this means that in fact he is depending on x for a compound goal G, g is just a part of, while he is not depending on x as for g; therefore, that he (of course) prefers to achieve the entire G than just g (if the cost of using x does not exceed the utility of G - g). The same holds in permission: when y is asking/waiting for a permission for a given action a when apparently she has the practical possibility (CAN) of doing a, this means that the real goal of y, she is depending on x for, is not simply the successful execution of a, but this plus other results that need x (passive) help. For example, she has the goal of doing a without being impolite or aggressive, or doing a without fighting or arguing with x. In order to achieve this global goal y is dependent on x and needs x's permission. Also the action she will execute is not trivially "the same action a", since this action will produce different results in different conditions. 2.2. Physical Obstacles, Conflict and Prohibition Since in many cases x is not materially creating obstacles to y's action, but just could do so, since normally x has just to let y doing a, why should y need x's permission? It is necessary that y believes that there is a possible intention, motive, reason in x for opposing to her action. So, the fact that x CAN obstacle y, his power, is a necessary but insufficient condition for a permission relation. Also x's "willingness" [(Miceli, Cesta, )] is important. Precisely, x is supposed to have the possible goal that y does not do a. y is searching for x's agreement, consensus. Apparently x's disagreement, conflictual attitudes, is consider by y an obstacle to her activity. Either x has the power of materially, physically preventing y from doing a, and (although at the moment there are no physical obstacles) y worries about x's putting such obstacles; or, x's mental attitude is per se important for y and creates an obstacle. In both cases the intention of x, his willingness of not creating obstacles, is the real matter. Of course, y will have the goal that something will NOT happen, only if there is some reason to suspect that it might be so: there is some reasons why x might have the goal of contrasting y (in Normative Permission for example x's rights on a - see §.5). Cognitive agent can be prevented from doing something just influencing them via communication. Prohibition is in fact a way of preventing, of blocking, just based on influence. More precisely, x makes y aware of x's conflictual goal: "I don't want that you do a" ("my goal is opposite to your goal; I have the goal that you don't have/pursue your goal") [(Castelfranchi, 1996)]. And he communicates this in order to change y's mind, in order y does not do a. This is an Interpersonal Prohibition, an Imperative of not doing something (based just on personal social power). So to prohibit is aimed at preventing, and is a form and a way of preventing. How the awareness of x's opposite goal is an obstacle for y's action? As we said, either it is just the announcement/prediction of future physical obstacles, or is an impeachment per se. In this case clearly enough the real goal of y is not only that of doing a, but that of doing a with the agreement of x, without disappointing x (this can derive from several reasons: affect, respect, politeness, norms, etc.). In conclusion, when y asks/needs x's permission she is trying to avoid x's opposition, either material, practical opposition or merely hostile attitudes (goal): in both cases in fact is interested in x's mental attitudes; and there is some reason to expect possible opposition by x. 2.3. Permission empowers The identification of dependence-power ground of permission explains why permission is power for y: it gives power to y. In fact, y's possibilities are augmented. Before and without x's permission (a form of passive help) y has not the power of doinga (or of G), she CANNOT a; after and thanks to x's permission she CAN. In traditional treatment of permission this effect was described but it is not explained. It is just postulated and seems quite unexplainable and by magic. Consider for example Lewis's semantic for command and permission in his Master/Slave game, and the opposite effects of command and permission on the "sphere of permissibility" [(Lewis, 1979)]. The problem, in my view, is why a command is a contraction, a restriction of the set of y's possible behaviours, and on the contrary a permission is an expansion on the preexisting set of possible behaviour. My trivial explanation is that permission expand y's powers when prescription (and prohibition) restrict them, and that this is due to y's dependence from x, and to x's power over y. If x prescribes something to y and has the power of influencing y [(Castelfranchi, 1990)] which is based (especially for prohibition) on his power over y, y's behavioural alternatives are reduced to one, and in any case y has not power of doing something else without violating x's prescription. If x permits something to y (y was depending on x) the sphere of y's powers is larger: now she can achieve what was impossible before 4 . 3. Permission as a form of Social Goal-Adoption (passive help) When (PERMIT x y a), doing a should be a possible goal of y: either an active goal y is considering (desire) or pursuing by a plan (intention), or a goal that x believes that y might/will activate and pursue. If (x believes that) y does not want a, he cannot permit y a. 4 To be more clear, I think that to Prescribe/Command and to Permit are not symmetric. They are quite different: Command reduces possible y's behaviours only if y's accept it (goal-adoption), although it automatically contracts permitted behaviours (it is true that if something is prohibited is not permitted). Permission expands automatically both permitted actions and possible actions. This is due to the fact that Permission is just based on the power-over (dependence) while Prohibition is based on the power-of-influencing that pass through some decision of y. For this reason for example the following dialogue is pragmatically and logically inconsistent: Daughter: "I don't want to marry dot. Smith!!!" Father: "Well, I give you my permission (of marry him)".5 More precisely, if (PERMIT x y a) necessarily x does not believe that y will never have such a goal (for the time the permission is referred to): Not (BEL x (Not Eventually (GOAL y a))) in fact, the father could perfectly answer: Father: "Anyway, in case you change your mind, I give you my permission". a is not necessarily a current, active and pursued goal of y. When y is "permitted" to do a, is up to her, and x leaves to her, the decision about doing a or not, and this decision is autonomous and free: no prescription of x is involved in this decision: if y likes to do a, she can; or better as for x she can: x will not attempt to contrast or prohibit her doing so. Notice that (PERMIT x y a) constraints the class of the agent y: such an agent should be autonomous, able to deciding about, pursuing its own goals, and basing this pursuit on its beliefs 6. Since in permitting a has to be a goal of y, permitting a x is adopting a goal of y, he is helping y to achieve her goal. But consider that this is a special form of goal adoption and help, a quite passive form: to abstain from opposing. Social Goal-Adoption (Castelfranchi 90 e 91) is when an agent adopts a goal because and until (he believes that) is a goal of another agent. Or better (since this definition could cover also some form of imitation), the agent has the goal that the other agent achieves 7 /satisfies her goal [(Conte e Castelfr; Mic Cesta; Haddadi, 1996)] (GOAL x (OBTAIN y g)) where (OBTAIN y g) =def (GOAL y g) (KNOW y g)8 5 Notice that on the contrary the father could perfectly say: Father: "Well, I order you to marry him!" This shows on my view that it is false that to give an command (prescription, obkigation) implies to give the permission. Command might presuppose that y does not want to, when permission presupposes that a is a (potential, possible) goal of y. Only a subpart of the ingredients of giving a permission is implied by giving an order. In particular, in commands x, having accepted (required) y action (S-Commitment to x to do a) is conversely SociallyCommitted to y to want y doing a and to not oppose to this. I have also other problems with deontic logic assumption. For eample from the cognitive point of view it is possible to permitt impossible things (things that x believes impossible): this is y's problem. Of course this makes x's help very limited and literal. While it irrational to prescribe impossible things, because it is x's matter to satisfy the goal he is prescribing. Either the real intend aeffect (goal) is not what he prescribes (but some side effect) or the prescription is irrational. 6 I feel quite contradictory to define a notion of "permission" relative to a slave agent that is so slave that commands are automatically accepted and necessarely true. This kind of agent is not autonomous, has no personal will, does not decide whether obey or not to his master; thus it is meaningless to give him "permissions" that presupposes some autonomous desires and goals in the agent! If an agent can be permitted to do something and then has his own goals, he cannot automatically execute commands: he will take some decision of obeing or refusing them. 7 In helping and goal adoption the awareness of y is not necessary, and also y's pursuit of her goal is not necessary. x help might be spontaneous and total (doing everithing necessary for realizing g for y). This is why the predicate ACHIEVE perhaps is too strong (Haddadi, 1996). 8 This definition too is not completely satisfactory. In fact, in the definition of OBTAIN, (GOAL y g) should be just presupposed: (GOAL x (OBTAIN y g)) shouldn't imply that (GOAL x (GOAL y g)). There is an active help when in order to make the other achieve/satisfy her goal, x has to plan and execute some action; there is a passive help when to allow y achieving her goal y has just to abstain from doing something: he has just to let something to happen. In case that x is in fact already creating obstacles to y's action, in giving the permission he is also committing himself to actively remove such obstacles (like in the example 1). Passive goal-adoption is implied by permission but is broader than permission. Not all cases of passive goal-adoption are permission. Consider in example (2) that y, ignoring that the pipe on the sand is related to x (close to x, discovered and used by x) just takes and uses it, and suppose that x notices this and decide to let y do. Is x's behaviour a permission? Not at all. This is just passive help: x could obstacle y, but decides to consent, let, permit, allow y's action. x's action is also a social action (Conte e Castelfranchi, 1995), but not sufficient to characterise a Permission relation, although just practical and interpersonal (non-normative and non-institutional). In this example y is not aware of x's decision and "help", and even of her dependence on x; x has not the goal that y knows about his decision; y has not the goal of x deciding of not opposing, and of letting her know about his decision; x is not adopting both y's goal of doing a, and also y's goal that x does not oppose to her and that x let her know about his decision. On the contrary, all this is necessary in Permission: mutual believes, communication, and x letting y know about his adoptive intention. In short, Permission is a form of promise. 4. Permission as Social-Commitment As said above, in giving his permission x is not only adopting y's possible goal of doing a, but is also adopting y's goal of this adoption (permission) and of communicating (letting her know about this adoption). The goal of y of having the permission normally is explicitly communicated (request for permission), but it could be of course also an implicit expectation. What exactly y is waiting from x, is a "promise" of not opposing, contrasting her. The promised action (active or passive) might either be immediately executed or delayed: it depends on if/when y will pursue her goal (in example 1 and 2 for example it is immediate). More generally what y expects is a Social-Commitment by x (S-COMMIT x y g). 4.1. What is a S-Commitment Social Commitment, is not just personal commitment to a give intention: it is a social relation. More precisely [(Castelfranchi, 1995)]: (a) a social Commitment is a form of "Goal Adoption". In other terms: x is committed to y to do a, if y is interested in a. The result of a is a goal of y;for this reason, y has the goal that x does a. Thus we should include in the formal definition of S-Commitment the fact that (S-COMM x y a z) implies that (GOAL y (DOES x a)) . b) If x is S-Committed to y, then y can (is entitled to): - control if x does what he "promised"; - exact/require that he does it; - complain/protest with x if he doesn't do a; - (in some cases) make good his losses (pledges, compensations, retaliations,. ) x and y mutually know that x intends to do a and that this is y 's goal, and that as for a y has specific rights on x (y is entitled by x to a). One should introduce a relation of "entitlement" between x and y meaning that y has the rights of controlling a, of exacting a, of protesting (and punishing), in other words, x is S-Committed to y to not oppose to these rights of y (in such a way, x "acknowledges" these rights of y ). Not all the adoptions of a goal of y by x imply a S-Commitment of x to y. What else is required? First, the Mutual Knowledge I already mentioned. Second, y 's agreement ! In fact, if x has just the I-Commitment to favour one of y 's goals, this is not sufficient (even if there is common awareness): y should "accept" this. In other words, she decided, she is I-Committed to achieve her goal by means of x's action. This acceptance is known by x, there is an agreement. Then, the S-Commitment of x implies a SCommitment of y to x to accept x's action (y doesn't refuse, doesn't protest, doesn't say "who told y ou!", ...). Without such (often implicit) agreement (which is a reciprocal SCommitment) no true S-Commitment of x to y has been established. As I said the very act of committing oneself to someone else is a "rights-producing" act: before the S-Commitment, before the "promise", y has no rights over x, y is not entitled (by x) to exact this action. After the S-Commitment it exists such a new and crucial social relation: y has some rights on x, she is entitled by the very act of Commitment on x's part. What I just said implies also that if x is S-Committed to y, he has a duty, an obligation, he ought to do what he is Committed to 9 . So, when x is committed, a is more than an Intention of x, it is a special kind of goal, more cogent. The more cogent and normative nature of S-Commitment explains why abandoning a Joint Intention or plan, a coalition or a team is not so simple as dropping a private Intention. In fact, one cannot exit a S-Commitment in the same way one can exit a private Commitment. 4.2. S-Commitment in Permission Giving his permission, x is S-Committing himself to y to not opposing to y doing a. In case for example that x gave the permission but later -when y is doing a- he makes opposition, complains, or argues, y can with reasons protest for x's attitudes, saying: "But you gave me the permission!!". In fact, trough the permission y acquired some rights of doing a without x opposition, and x, because of his assent, acquired some duties of not creating obstacles. The same is true for removing personal obstacles. In example (1), x cannot answer "yes" (permission) while remaining to block the way out. This behaviour is not coherent: saying "yes" x promised of letting y to pass, and implicitly of removing his obstacle. Like in any S-Commitment relation x is adopting some goals of y, and y on her turn is acknowledging her dependence on x and delegating to x an helping action (either passive or active). It seems to me that all the basic ingredients of S-Commitment are there in a Permission relation. Of course not any S-Commitment is Practical Permission. Something more is needed. In simple S-Commitment y is asking/delegating an action/goal to x, and x is doing something for y; in Practical Permission x lets y doing an action, and he is just requested 9 Such creation of interpersonal obligations and rights through S-Commitments (‘microdeontics’) will require a general approach to deontics that allows contradictions among deontic contexts and hierarchical levels (in this direction, see e.g. [Jones & Porn 1985]). For example, a killer gets an obligation to his instigator to murder somebody, but, from the point of view of the society such an obligation is in contrast with a prohibition (law) and with a much stronger obligation. to consent, and is committed to not prohibit or contrast (and in case, to eliminate obstacles depending on him) 10. Introducing S-Commitment we introduce some Normative stuff also in the merely Practical Permission. In fact we know that Social Commitment act is an act that create some rights (and complementary duties). It is an open problem whether this creation of rights is merely interpersonal and "natural", or it presupposes some social system and social norms (for example about promise keeping). I'm trying to explore the first alternative as long as possible, trying to let norms and laws emerge from interactions (and minds) -bottom up- and not only putting them from the top (society) impinging on the agents. 5. Towards Normative Permission: x's rights, entitlement and authority Many readers might consider my notion of Practical Permission, just based on dependence and practical power, too poor, lacking some more "normative" stuff. They might consider insufficiently deontic the Social-Commitment relation (promise) between x and y. I acknowledge that what I described is the basic and weakest form of interpersonal permission. Even in the very trivial examples I used some other important ingredients emerge, and I untowardly bypassed them. In particular, father-doughtier example is, to be honest, a clear example of more "institutional" permission, based on some form of "authority"; and also in children example there is something more. Precisely what I put aside in this example was the fact that in some sense x "owns" his pipe (by some sort of natural right), he has some "title" on it, and that y acknowledges this rights and titles, and is asking for the permission because she aknowledges this and does not want to violate x's rights. The reasons why I ignored this features are first methodological: because I claim that there is a basic nucleus in the notion of permission which is only enriched but not eliminated by the notion of x rights and y's recognition of them; second, there are practical reasons. To study permission based on rights and authority is more complex than to study this poorer form of practical permission. But of course this is just on step. So, in the great majority of permission episodes (and in a more specific notion of permission) there is mutual belief between x and y about the fact that x is entitled to prohibit y from using a resource he "owns" or from doing something. Thus the obstacles that x could oppose to y action are not only practical or dispositional but also normative obstacles. We know that x could block (or disturb) y's goal not only with some practical action (fighting, concealing or destroying a resource, etc.) but simply by prohibiting y's action. And x could be in position for prohibiting it not just in a weak sense (just expressing his opposite goal), but in a stronger normative sense. There is a normative prohibition when the expressed prescription is not just the individual personal will of x, but is a norm [(Conte, Caste)]. In this case y's action would import the violation of some normative prescription related to x's will. x will in some way creates a norm ("authority" is nothing but this capability). As I said, there is a poor form of practical Prescription/Prohibition as there is a poor form of permission. If x is able to block y, to prevent y from entering a room or a way, and he declares to y his goal that y does not pass trough, his intention to block her, and declares this in order to induce y to not enter, x is practically "prohibiting" to y to entering (independently of any rights). There is an imperative of not doing something. Of course this prescription is not a Norm. Under which condition x will is creating an instanciated norm for y? This is the problem. In conclusion, one should distinguish between Normative Permission/Prohibition/Prescription and non-normative but just personal and practical 10 This is different from legal permission (law) by authority, that is a more complex and 3 terms relationship between three agents: x (the authority) gives the permission to y and give a complementary prohibition to z about contrasting y's permitted behaviour. x prescribe to z to acknowledge y's rights. Permission/Prohibition/Prescription. I tried to analyse the latter claiming that there is a common core, and with the purpose of describing the social-interactive basis of the emergence of normative notions and relations. In order to fully understand the notion of permission also at the normative and institutional level, the analysis of normative prescription and adoption (Conte, ; Conte) and of rights [(xxx)] is needed. To sum up In sum, face-to-face permission is a social relation between two agents x and y relative to a possible intentional action a of y. It implies: • that y depends on x as for a (and x having power over y as for a); • that x adopts y's goal (although in a passive form: not preventing it); • that there is a social commitment of x to y to not contrasting y It creates rights for y and correspondent obligations for x. It empowers y. It requires also some either explicit or implicit communication (to ask for/ to give) since is based on mutual beliefs between x and y about the previous conditions. References [1] J. Bell. Changing Attitudes. In [x] pp. 40-55 [2] Bratman,M.E., Israel, D.J., Pollack, M.E. 1988. Plans and resource-bounded practical reasoning. Computational Intelligence 4: 349-55. [3] C. Castelfranchi, Social power: A missed point in DAI, MA and HCI. In Decentralized AI, Y. Demazeau and J.P. Mueller (eds.),49-62. North-Holland, Elsevier.1990. 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