Belief Revision (Computer Science)

Can science tell us what’s objectively true? Or is it merely a clever way to cure doubt – to give us something to believe in, whether it’s true or not? In this essay, I look at the pragmatist account of science expounded by Charles Sanders Peirce in his 1877 essay, ‘The Fixation of Belief’. Against Peirce, I argue that science does not come naturally to our species, nor does the doubting open-mindedness upon which its practice relies. To the extent that science is successful in ‘curing’ doubt, it’s because it tracks the real state of the world; and I argue that Peirce himself – his pragmatist narrative notwithstanding – is implicitly committed to this view as well.

One sense of 'imagination' that matters in epistemology has the word mean 'reality-oriented mental simulation' (ROMS): we suppose that something is the case; develop the supposition by importing background knowledge and beliefs; and check what is true in the imagined scenario.
What is the logic of ROMS? Imagination has a reputation for being logically anarchic. In particular, it's hyperintensional: we can imagine A without imagining a necessarily equivalent B. This work considers a Principle of Equivalence in Imagination which, if accepted, will limit the anarchy: when A and B are equivalent in imagination, one will imagine the same things after supposing either in ROMS.
What is equivalence in imagination? It is suggested that it's cognitive equivalence. A and B are cognitively equivalent for one when they play the same role in one's cognitive life: whatever one understands, concludes, etc., given either, one does, given the other. ROMS is logically modelled via variably strict modals. Two formal semantics are proposed for them: one uses possible worlds plus an algebra of topics; the other resorts to impossible worlds. The two deal with equivalence in imagination in subtly different ways.

A Topic-Sensitive Intentional Modal (TSIM) is a two-place, variably strict modal with an aboutness or topicality constraint, of the form ‘X^φψ’ (read: ‘Given φ, the agent X’s that ψ’, X being some mental state or act). TSIMs do nice things for mainstream and formal epistemology, belief revision theory, and mental simulation theory. I present a basic formal semantics for TSIMs and explore three readings of ‘X^φψ’ one gets by imposing different constraints on their truth conditions: (1) as expressing knowability relative to information (‘Given total information φ, one is in the position to know that ψ’), inspired by Dretske’s view that what one can know depends on the available (empirical) information; (2) as a mental simulation operator (‘In mental simulation starting with input φ, one imagines that ψ’) capturing features of mainstream mental simulation theories, like that of Nichols and Stich; (3) as a hyperintensional belief revision operator (‘After (statically) revising by φ, one believes that ψ’), reducing the idealization of cognitive agents one finds in standard doxastic logics and AGM. I close by mentioning developments of TSIM theory currently in progress.

The single most important statement that can be made with regard to the logical status of human and physical geographical reasoning is that it belongs to the class of non-monotonic reasoning. In other words,  geographical reasoning is defeasible (i.e. earlier drawn conclusions can be defeated by the addition of new facts, some of which are generated by the very application of our ideas outside academe) and non-demonstrative (i.e. our beliefs about reality cannot be demonstrated once and for ever; we must do with building provisional arguments based on the current weight of the evidence, which itself changes with the times). Indeed, unlike mathematics, which is a closed world of formalisms that relies heavily on deduction, demonstration, and proof, geography studies and attempts to improve the real, messy world out there. Because that wild, unruly world is always in a process of becoming, the conclusions drawn yesterday may have to be abandoned today, and so on, without end in sight. The core virtue of geographical reasoning is not certainty, but adaptability. As the world changes, so do geography’s entertained beliefs about how to improve it. The point we are trying to make is that an alternative window into the nature of geographical reasoning, besides the one provided by the discipline’s key concepts, offers an opening toward the more subtle problematic of the mechanisms by which the updating of geographical beliefs operate.

I present a possible worlds semantics for a hyperintensional belief revision operator, which reduces the logical idealization of cognitive agents affecting similar operators in doxastic and epistemic logics, as well as in standard AGM belief revision theory. (Revised) belief states are not closed under classical logical consequence; revising by inconsistent information does not perforce lead to trivialization; and revision can be subject to ‘framing effects’: logically or necessarily equivalent contents can lead to different revisions. Such results are obtained without resorting to non-classical logics, or to non-normal or impossible worlds semantics. The framework combines, instead, a standard semantics for propositional S5 with a simple mereology of contents.

Is information always true? According to some authors, including Dretske, Grice, Barwise, and recently, Floridi, who has defended the Veridicality Thesis, the answer is positive. For, on Floridi’s view, there is an intimate relation between information and knowledge, which is always true. It is argued in this article that information used in inferential knowledge can, nevertheless, be false, thereby showing that the Veridicality thesis is false.

The abilities of detecting contradictions and rearranging the
cognitive space in order to cope with them are important to be embedded in
the BDI architecture of an agent acting in a complex and dynamic world.
However, to be accomplished in a multi-agent environment, "belief revision"
must depart considerably from its original definitions. According to us, the
main changes should be the following ones:
1. replacing the "priority to the incoming information principle" with the
"recoverability principle": any previously believed piece of information must
belong to the current cognitive state whenever it is possible
2. dealing not just with pieces of information but with couples <source,
information>, since the reliability of the source affects the credibility of the
information and vice-versa.
The "belief-function" formalism is here accepted as a simple and intuitive
way to transfer the sources' reliability to the information's credibility.

Dynamics pertaining to learning from the actions of others are modeled with focus on a running example, showing how we may come to conclusions regarding an ontic fact solely by observing others act on their beliefs regarding the fact in question. The tools used are elements from dynamic epistemic logic, with the addition of decision and interpretation rules, allowing local, rule-based choice and reasoning about such.

New in the probability theory and eventology theory, the concept of Kopula (eventological copula) is introduced. The theorem on the characterization of the sets of events by Kopula is proved, which serves as the eventological pre-image of the well-known Sclar's theorem on copulas (1959). The Kopulas of doublets and triplets of events are given, as well as of some N-sets of events. For further development of this topic, see my later works: https://www.academia.edu/34390291/, https://www.academia.edu/34373279/, https://www.academia.edu/34357251/

Keywords: eventology, probability, Kolmogorov event, event, set of events, Kopula (eventological copula), Kopula characterizing a set of events.

If you are interested in my work, and you have the opportunity to provide financial support for the publication of my book "Theory of experience and of chance as a theory of being," I ask you to use my PayPal account: paypal.me/EventologyTheory

In this paper we present a brief overview of belief change, a research area concerned with the question of how a rational agent ought to change its mind in the face of new, possibly conflicting, information. We limit ourselves to logic-based belief change, with a particular emphasis on classical propositional logic as the underlying logic in which beliefs are to be represented. Our intention is to provide the reader with a basic introduction to the work done in this area over the past 30 years. In doing so we hope to sketch the main historical results, provide appropriate pointers to further references, and discuss some current developments. We trust that this will spur on the interested reader to learn more about the topic, and perhaps to join us in the further development of this exciting field of research.

While propositional doxastic attitudes , like knowledge and belief, capture an agent's opinion about certain propositions, her attitudes towards sources of information express her opinion about the reliability (or trustwor-thiness) of those sources. If an agent trusts a witness, then she will, within certain limits, tend to accept his testimony as veridical. But if she considers the witness to be a notorious liar, she may come to believe the opposite of what he tells her. In this paper, we put such attitudes towards sources (or dynamic (doxastic) attitudes) center stage, and formalize them as belief-revision strategies: policies governing how an agent changess her beliefs whenever new information from a certain (type of) source is received. We present a semantic, qualitative modelling of this notion and investigate its properties .

Abduction was first introduced by the philosopher C.S. Peirce in the epistemological context of scientific discovery. It was more recently analyzed in Artificial Intelligence, especially with respect to diagnosis analysis or ordinary reasoning. These two fields share a common view of abduction as a general process of hypotheses formation. More precisely, abduction is conceived as a kind of reverse explanation where a hypothesis H can be abduced from facts E if H is a "good explanation" of E. The paper aims at giving a general logical picture of abduction which could be used in both fields.

The logic of uncertainty is not the logic of experience and as well as it is not the logic of chance. It is the logic of experience and chance. Experience and chance are two inseparable poles. These are two dual reflections of one essence, which is called co∼event. The theory of experience and chance is the theory of co∼events. To study the co∼events, it is not enough to study the experience and to study the chance. For this, it is necessary to study the experience and chance as a single entire, a co∼event. In other words, it is necessary to study their interaction within a co∼event. The new co∼event axiomatics and the theory of co∼events following from it were created precisely for these purposes. In this work, I am going to demonstrate the effectiveness of the new theory of co∼events in a studying the logic of uncertainty. I will do this by the example of a co∼event splitting of the logic of the Bayesian scheme, which has a long history of fierce debates between Bayesionists and frequentists. I hope the logic of the theory of experience and chance will make its modest contribution to the application of these old dual debaters.

Keywords: Eventology, event, probability, probability theory, Kolmogorov’s axiomatics, experience, chance, cause, consequence, co∼event, set of co∼events, bra-event, set of bra-events, ket-event, set of ket-events, believability, certainty, believability theory, certainty theory, theory of co∼events, theory of experience and chance, co∼event dualism, co∼event axiomatics, logic of uncertainty, logic of experience and chance, logic of cause and consequence, logic of the past and the future, Bayesian scheme.

It has been established that methods of belief merging suitable for the aim of truthlikeness do not necessarily conform to standard belief merging frameworks. Following on from this work, this brief note considers how integrity constraints would work for belief merging in a truthlikeness context.

Paraconsistent Belief Revision based on a formal consistency operator (in portuguese)

Belief Revision studies how rational agents change their beliefs when they receive new information. The AGM system, most influential work in this area of study investigated by Alchourrón, Gärdenfors and Makinson, postulates rationality criteria for different types of belief change and provides explicit constructions for them -- the equivalence between the postulates and operations is called representation theorem. Recent studies show how the AGM paradigm can be compliant with different non-classical logics, which is called the AGM-compliance -- this is the case of the paraconsistent logics family we analyze in this thesis, the Logics of Formal Inconsistency (LFIs).

Despite the AGM-compliance, when a new logic is taken into account its underlying rationality must be understood and its language should be used. In that way new constructions are proposed, which actually captures the intuition of LFIs -- what we call the AGMo system. Thus, we provide a new interpretation for these logics, more in line with formal epistemology. In an alternative approach, by considering the AGM-compliance, we show how the AGM results can be directly applied to LFIs -- resulting the AGMp system. In both approaches, we prove the corresponding representation theorems where needed.

Key-words: belief revision, non-classical logics, formal epistemology, paraconsistent logic, theory dynamics, logical consistency, logical contradicition.


Resumo

A Revisão de Crenças estuda como agentes racionais mudam suas crenças ao receberem novas informações. O sistema AGM, trabalho mais influente desta área apresentado por Alchourrón, Gärdenfors e Makinson, postula critérios de racionalidade para os diferentes tipos de mudança de crenças e oferece construções explícitas para tais -- a equivalência entre os postulados e operações é chamado de teroema da representação. Trabalhos recentes mostram como o paradigma AGM pode ser compatível com diferentes lógicas não-clássicas, o que é chamado de AGM-compatibilidade -- este é o caso da família de lógicas paraconsistentes que analisamos, as Lógicas da Inconsistência Formal (LFIs, da sigla em inglês).

A despeito da AGM-compatibilidade, ao se partir de uma nova lógica sua racionalidade subjacente deve ser entendida e sua linguagem deve ser efetivamente usada. Propomos assim novas construções que de fato capturam a intuição presente na LFIs -- é o que chamamos de sistema AGMo. Com isso, possibilitamos a estas lógicas uma nova interpretação, na esteira da epistemologia formal. Em uma abordagem alternativa, ao se partir da AGM-compatibilidade os resultados AGM podem ser diretamente aplicados às LFIs -- o que chamamos de sistema AGMp. Em ambas abordagens, provamos os respectivos teoremas da representação sempre que necessário.

Palavras-chave: revisão de crenças, lógicas não-clássicas, epistemologia formal, lógica paraconsistente, dinâmica de teorias, consistência lógica, contradição lógica.

Standard belief change assumes an underlying logic containing full classical propositional logic. However, there are good reasons for considering belief change in less expressive logics as well. In this paper we build on recent investigations by Delgrande on contraction for Horn logic. We show that the standard basic form of contraction, partial meet, is too strong in the Horn case. This result stands in contrast to Delgrande’s conjecture that orderly maxichoice is the appropriate form of contraction for Horn logic. We then define a more appropriate notion of basic contraction for the Horn case, influenced by the convexity property holding for full propositional logic and which we refer to as infra contraction. The main contribution of this work is a result which shows that the construction method for Horn contraction for belief sets based on our infra remainder sets corresponds exactly to Hansson’s classical kernel contraction for belief sets, when restricted to Horn logic. This result is obtained via a detour through contraction for belief bases. We prove that kernel contraction for belief bases produces precisely the same results as the belief base version of infra contraction. The use of belief bases to obtain this result provides evidence for the conjecture that Horn belief change is best viewed as a ‘hybrid’ version of belief set change and belief base change. One of the consequences of the link with base contraction is the provision of a representation result for Horn contraction for belief sets in which a version of the Core-retainment postulate features.

In this paper we propose a geometric approach to the theory of evidence based on convex geometric interpretations of its two key notions of belief function and Dempster's sum. On one side, we analyze the geometry of belief functions as points of a polytope in the Cartesian space called belief space, and discuss the intimate relationship between basic probability assignment and convex combination. On the other side, we study the global geometry of Dempster's rule by describing its action on those convex combinations. By proving that Dempster's sum and convex closure commute we become able to depict the geometric structure of conditional subspaces, i.e. sets of belief functions conditioned by a given function b. Natural applications of these geometric methods to classical problems like probabilistic approximation and canonical decomposition are outlined.

Judgment-aggregation theory has always focused on the attainment of rational collective judgments. But so far, rationality has been understood in static terms: as "coherence" of judgments at a given time, understood as consistency, completeness, and/or deductive closure. By contrast, this paper discusses whether collective judgments can be dynamically rational, so that they change rationally in response to new information. Formally, a judgment aggregation rule is dynamically rational with respect to a given revision operator if, whenever all individuals revise their judgments in light of some information (a learnt proposition), then the new aggregate judgments are the old ones revised in light of this information, i.e., aggregation and revision commute. We prove a general impossibility theorem: if the propositions on the agenda are sufficiently interconnected, no judgment aggregation rule with standard properties is dynamically rational with respect to any revision operator satisfying some mild conditions (familiar from belief revision theory). Our theorem is the dynamic-rationality analogue of some well-known impossibility theorems for static rationality. We also explore how dynamic rationality might be achieved by relaxing some of the conditions on the aggregation rule and/or the revision operator.

When the circumstances are good, people can follow other people's theories and world views with an almost uncanny precision and are able to adapt their own world views and the meaning of terms they use with ease. How is this possible? Some authors have suggested topic continuity as a way of (partly) explaining why terminological disagreements remain substantive and not merely about words when different theories and world views are changing or are changed. In this talk, I lay out the ‘Tracking View’ of topic continuity and argue that it fares better than other accounts. However, I also argue that topic continuity is not needed for a philosophical justification of the potential fruitfulness of particular endeavours of Conceptual Engineering (Cappelen 2018) and Conceptual Ethics (Burgess & Plunkett 2013ab). Metalinguistic disagreements about a term can - and usually will - be substantive even when there is a good case to be made that the underlying background theories or world views are about different topics. If that is true, then a lack of topic continuity cannot be used as an argument against ameliorative projects.

We present a semantic analysis of the Ramsey test, pointing out its deep underlying flaw: the tension between the " static " nature of AGM revision (which was originally tailored for revision of only purely ontic beliefs, and can be applied to higher-order beliefs only if given a " backwards-looking " interpretation) and the fact that, semantically speaking, any Ramsey conditional must be a modal operator (more precisely, a dynamic-epistemic one). Thus, a belief about a Ramsey conditional is in fact a higher-order belief, hence the AGM revision postulates are not applicable to it, except in their " backwards-looking " interpretation. But that interpretation is consistent only with a restricted (weak) version of Ramsey's test (in-applicable to already revised theories). The solution out of the conundrum is twofold: either accept only the weak Ramsey test; or replace the AGM revision operator * by a truly " dynamic " revision operator ⊗, which will not satisfy the AGM axioms, but will do something better: it will " keep up with reality " , correctly describing revision with higher-order beliefs.

We present a complete, decidable logic for reasoning about a notion of completely trustworthy ("conclusive") evidence and its relations to justifiable (implicit) belief and knowledge, as well as to their explicit justifications. This logic makes use of a number of evidence-related notions such as availability, admissibility, and "goodness" of a piece of evidence, and is based on an innovative modification of the Fitting semantics for Artemov's Justification Logic designed to preempt Gettier-type counterexamples. We combine this with ideas from belief revision and awareness logics to provide an account for explicitly justified (defeasible) knowledge based on conclusive evidence that addresses the problem of (logical) omniscience.

This paper argues that there is a conflict between two theses held by John McDowell, namely i) the claim that we are under a standing obligation to revise our beliefs if reflection demands it; and ii) the view that veridical experience is a mode of direct access to the world. Since (i) puts no bounds on what would constitute reasonable doubt, it invites skeptical concerns which overthrow (ii). Conversely, since (ii) says that there are some experiences which we are entitled to trust, it undermines the prescriptive scope of (i). Drawing on C. S. Peirce’s distinction between genuine and contrived doubt, I maintain that critical revisions of beliefs should be triggered only by unwanted disruptions of habits, thereby restoring unity between McDowell’s two theses.

We present a logic of conditional doxastic actions, obtained by incorporating ideas from belief revision theory into the usual dynamic logic of epistemic actions. We do this by extending to actions the setting of epistemic plausibility models, developed in Baltag and Smets (2006) for representing (static) conditional beliefs. We introduce
a natural extension of the notion of update product from Baltag and Moss (2004) to plausibility models.

In this paper two systems of AGM-like Paraconsistent Belief Revision
are overviewed, both defined over Logics of Formal Inconsistency
(LFIs) due to the possibility of defining a formal consistency
operator within these logics.

The AGM° system is strongly based on this operator and internalize the
notion of formal consistency in the explicit constructions and
postulates. Alternatively, the AGMp system uses the AGM-compliance of
LFIs and thus assumes a wider notion of paraconsistency – not
necessarily related to the notion of formal consistency.

There are many methods to perform iris biometric identification
systems, but all of them have a problem: the presence of noises in
the image of the eye (eyelid, eyelashes, etc...). To remove it many
authors apply appropriate preprocessing to the image, but
unfortunately this yields losses of information. Our work aims at
correctly recognizing the subject also in presence of high rates of
noise. The basic idea is that of partitioning the image of iris into 8
not-interleaved segments of the same size. Each segment is given
to a Neural Network (LVQ network) which generates prototypes
with a high resistance to noise. Notwithstanding this, the 8 LVQ
nets may still disagree in identifying the subject. In this paper we
apply a method developed by the “belief revision” community to
identify conflicts and rearrange the degrees of reliability of each
expert (the LVQ nets) through a Bayesian algorithm. This
estimated ranking of reliability is useful to take the final decision.
Our work has produced an interesting 91.67 % of positive
identification on Test set.

On the basis of impossibility results on probability, belief revision, and conditionals, it is argued that conditional beliefs differ from beliefs in conditionals qua mental states. Once this is established, it will be pointed out in what sense conditional beliefs are still conditional, even though they may lack conditional contents, and why it is permissible to still regard them as beliefs, although they are not beliefs in conditionals. Along the way, the main logical, dispositional, representational, and normative properties of conditional beliefs are studied, and it is explained how the failure of not distinguishing conditional beliefs from beliefs in conditionals can lead philosophical and empirical theories astray.

Two systems of belief change based on paraconsistent logics are introduced in this paper by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic that extends classical logic such that the law of excluded middle holds w.r.t. the paraconsis-tent negation. The second one, AGM•, is specifically designed for para-consistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator which allows to recover all the classical inferences. Besides the three usual operations over belief sets, namely expansion, contraction and revision (which is obtained from contraction by the Levi identity), the underlying paraconsistent logic allows us to define additional operations involving (non-explosive) contradictions. Thus, it is defined external revision (which is obtained from contraction by the reverse Levi identity), consolidation and semi-revision, all of them over belief sets. It is worth noting that the latter operations, introduced by S. Hansson, involve the temporary acceptance of contradictory beliefs, and so they were originally defined only for belief bases. Unlike to previous proposals in the literature, only defined for specific paraconsistent logics, the present approach can be applied to a general class of paracon-sistent logics which are supraclassical, thus preserving the spirit of AGM. Moreover, representation theorems w.r.t. constructions based on selection functions are obtained for all the operations. Final version (all rights reserved to Oxford University Press): TESTA, R. R.; CONIGLIO, M. E.; RIBEIRO, M. M. AGM-like paraconsistent belief change.

JOWO, ‘The Joint Ontology Workshops—Episode I: The Argentine Winter of Ontology’, was held for the first time in Buenos Aires, at the 24th International Joint Conference on Artificial Intelligence – IJCAI 2015. Its mission is to join forces of the diverse communities interested in building, reasoning with, and ap- plying formalised ontologies in the wide spectrum of Artificial Intelligence theory and applications.
The present edition of JOWO 2015 collocated four workshops that cover a broad spectrum of contemporary ontology research ranging from philosophical founda- tions to theoretical investigations of reasoning problems to a variety of AI appli- cations of ontologies. JOWO included
OntoLP1 Workshop on Ontologies and logic programming for query answering; OntoChange2 Workshop on Belief Change and Non Monotonic Reasoning in Ontologies and Databases;
WoMO3 Ninth International Workshop on Modular Ontologies; FOfAI4 Workshop on Formal Ontologies for Artificial Intelligence.

The AGM model is the most remarkable framework for modeling belief revision. However, it is not perfect in all aspects. Paraconsistent belief revision, multi-agent belief revision and non-prioritized belief revision are three different extensions to AGM to address three important criticisms applied to it. In this article, we propose a framework based on AGM that takes a position in each of these categories. Also, we discuss some features of our framework and study the satisfiability of AGM postulates in this new context. KEYWORDS belief revision, the AGM model, multi-source belief revision, non-prioritized belief revision, para-consistent belief revision, the logic PAC

We investigate the logical and conceptual connections between abductive reasoning construed as a process of belief change, on the one hand, and truth approximation, construed as increasing (estimated) verisimilitude, on the other. We introduce the notion of '(verisimilitude-guided) abductive belief change' and discuss under what conditions abductively changing our theories or beliefs does lead them closer to the truth, and hence tracks truth approximation conceived as the main aim of inquiry. The consequences of our analysis for some recent discussions concerning belief revision aiming at truth approximation and inference to the best explanation are also highlighted.

We present a complete, decidable logic for reasoning about a notion of completely trustworthy (" conclusive ") evidence and its relations to justifiable (implicit) belief and knowledge, as well as to their explicit justifications. This logic makes use of a number of evidence-related notions such as availability, admissibility, and " goodness " of a piece of evidence, and is based on an innovative modification of the Fitting semantics for Artemov's Justification Logic designed to preempt Gettier-type counterexamples. We combine this with ideas from belief revision and awareness logics to provide an account for explicitly justified (defeasible) knowledge based on conclusive evidence that addresses the problem of (logical) omniscience.

The merging/fusion of belief/data collections in propositional logic form is a topic that has received due attention within the domains of database and AI research. A distinction can be made between two types of scenarios to which the process of merging can be applied. In the first type, the collections represent preferences, such as the voting choices of a group of people, that need to be aggregated so as to give a consistent result that in some way best represents the collective judgement of the group. In the second type, the collections represent factual data that is to be aggregated with an aim of obtaining a result that maximises factual correctness. After introducing a general framework for belief merging via some prominent literature on the topic, this paper then introduces and considers a method for belief merging with the second type of scenario in mind. Its suitability is corroborated by demonstrating how it can be seen as a special case of a merging procedure that combines aggregation of probabilities and maximisation of expected truthlikeness.

In this paper we discuss the semantics and properties of the relative belief transform, a probability transformation of belief functions closely related to the classical plausibility transform. We discuss its rationale in both the probability-bound and Shafer's interpretations of belief functions. Even though the resulting probability (as it is the case for the plausibility transform) is not consistent with the original belief function, an interesting rationale in terms of optimal strategies in a non-cooperative game can be given in the probability-bound interpretation to both relative belief and plausibility of singletons. On the other hand, we prove that relative belief commutes with Dempster's orthogonal sum, meets a number of properties which are the duals of those met by the relative plausibility of singletons, and commutes with convex closure in a similar way to Dempster's rule. This supports the argument that relative plausibility and belief transform are indeed naturally associated with the D-S framework, and highlights a classification of probability transformations in two families, according to the operator they relate to. Finally, we point out that relative belief is only a member of a class of \relative mass" mappings, which can be interpreted as low-cost proxies for both plausibility and pignistic transforms.