Probabilistic reasoning

This study aims at getting insight in the strategies employed by secondary students when they are faced with some famous probabilistic paradoxes. Four different age groups of students participated the study (48 in Grade 8, 63 in Grade 9, 53 in Grade 10 and 49 in Grade 12). All students were given the Bertrand’s Box Paradox and the Gardner’s Two Children Paradox modified in an understandable way for all age groups. The 213 written responses (answers and explanations) were analysed and categorized according to various heuristics, misconceptions and types of strategy that seemed to guide students’ choices. Differences among the various grade levels and also differences between the two problems in students’ responses of the same grade level were explored and discussed.

Abductive inference in Bayesian belief networks (BBNs) is intended as the process of generating the most probable configurations given observed evidence. When we are interested only in a subset of the network's variables, this problem is called partial abductive inference. Both problems are NP-hard and so exact computation is not always possible. In this paper, a genetic algorithm is used to perform partial abductive inference in BBNs. The main contribution is the introduction of new genetic operators designed specifically for this problem. By using these genetic operators, we try to take advantage of the calculations previously carried out, when a new individual is evaluated. The algorithm is tested using a widely used Bayesian network and a randomly generated one and then compared with a previous genetic algorithm based on classical genetic operators. From the experimental results, we conclude that the new genetic operators preserve the accuracy of the previous algorithm, and also reduce the number of operations performed during the evaluation of individuals. The performance of the genetic algorithm is, thus, improved.

Abductive inference in Bayesian belief networks (BBNs) is intended as the process of generating the most probable configurations given observed evidence. When we are interested only in a subset of the network's variables, this problem is called partial abductive inference. Both problems are NP-hard and so exact computation is not always possible. In this paper, a genetic algorithm is used to perform partial abductive inference in BBNs. The main contribution is the introduction of new genetic operators designed specifically for this problem. By using these genetic operators, we try to take advantage of the calculations previously carried out, when a new individual is evaluated. The algorithm is tested using a widely used Bayesian network and a randomly generated one and then compared with a previous genetic algorithm based on classical genetic operators. From the experimental results, we conclude that the new genetic operators preserve the accuracy of the previous algorithm, and also reduce the number of operations performed during the evaluation of individuals. The performance of the genetic algorithm is, thus, improved.

The paper addresses the problem of computing lower bounds on the optimal costs associated with each unary assignment of a value to a variable in combinatorial optimization problems. This task is instrumental in probabilistic reasoning and is also important for the development of admissible heuristic functions that can guide search algorithms for optimal solutions. The paper presents UD-MB, a new algorithm that applies the mini-bucket elimination idea [Dechter and Rish, 1997] to accomplish this task. We show empirically ...

Earth Observation (EO) data are increasingly used in policy analysis by enabling granular estimation of treatment effects. However, a challenge in EO-based causal inference lies in balancing the trade-off between capturing fine-grained individual heterogeneity and broader contextual information. This paper introduces Multi-scale Concatenation, a family of composable procedures that transform arbitrary single-scale CATE estimation algorithms into multi-scale algorithms. We benchmark the performance of Multi-scale Concatenation on a CATE estimation pipeline combining Vision Transformer (ViT) models fine-tuned on satellite images to encode images of different scales with Causal Forests to obtain the final CATE estimate. We first perform simulation studies, showing how a multi-scale approach captures multi-level dynamics that single-scale ViT models fail to capture. We then apply the multi-scale method to two randomized controlled trials (RCTs) conducted in Peru and Uganda using Landsat satellite imagery. In the RCT analysis, the Rank Average Treatment Effect Ratio (RATE Ratio) measure is employed to assess performance without ground truth individual treatment effects. Results indicate that Multi-scale Concatenation improves the performance of deep learning models in EO-based CATE estimation without the complexity of designing new multi-scale architectures for a specific use case.

Abstract: One way to address preferences in Multi-Agent negotiation scenarios, is to devise a strategy for removal of contradictions, which may arise when the preferences of all agents are put together. This paper contributes towards that goal by proposing a methodology, based on declarative diagnosis, that minimizes the losses of all agents (ie the number of preferences they have to yield in order to find a consensus) as negotiations are iterated; in other words, it will bias negotiations towards cooperation. Instead of considering explicit ...

In his Neues Organon of 1764, the mathematician and astronomer Jean-Henri Lambert [12] developed a theory of probable syllogisms, with the aim of formally describing the probabilist reasoning and then applying it to the probability of testimony, thus imparting an epistemic sense to the concept of probability. In the present text, we propose to study the principles of this theory and the difficulties it raises.

We present a Logic Programming framework for moral reasoning under uncertainty. It is enacted by a coherent combination of our two previously implemented systems, Evolution Prospection for decision making, and P-log for probabilistic inference. It allows computing available moral judgments via distinct kinds of prior and post preferences. In introducing various aspects of uncertainty into cases of classical trolley problem moral dilemmas, we show how they may appropriately influence moral judgments, allowing decision makers to opt for different choices, and for these to be externally appraised, even when subject to incomplete evidence, as in courts.

A contract allows to distinguish hypotheses made on a system (the guarantees) from those made on its environment (the assumptions). In this paper, we focus on models of Assume/Guarantee contracts for (stochastic) systems. We consider contracts capable of capturing reliability and availability properties of such systems. We also show that classical notions of Satisfaction and Refinement can be checked by effective methods thanks to a reduction to classical verification problems. Finally, theorems supporting compositional reasoning and enabling the scalable analysis of complex systems are also studied.

Dissertacao de Mestrado apresentada junto ao Programa de Pos-Graduacao em Desenvolvimento Regional e Meio Ambiente, Area de Concentracao em Politicas Publicas e Desenvolvimento Sustentavel para obtencao do Titulo de Mestre em Desenvolvimento Regional e Meio Ambiente.Orientador: Prof. Dr. Fabricio Moraes de Almeida

In this article we propose a Probabilistic Situation Calculus logical language to represent and reason with knowledge about dynamical worlds in which actions have uncertain effects. Two essential tasks are addressed when reasoning about change in worlds: Probabilistic Temporal Projection and Probabilistic Belief Update. Uncertain effects are modeled by dividing an action into two subparts: a deterministic input (agent produced) and a probabilistic reaction (nature produced). The probability distributions of the reactions are assumed to be known. Our logical language is an extension to Situation Calculae in the style proposed by Raymond Reiter. There are three aspects to this work. First, we extend the language to accommodate terms dealing with belief and probability. Second, we provide a operational semantics based on Randomly Timed Automata. Finally, we develop Monte-Carlo algorithms to efficiently interpret the probability and belief terms. With the framework proposed we discuss how to develop a reasoning system in Mathematica capable of performing temporal projection and belief update in the Probabilistic Situation Calculus. Finally, we present a sound basis to set rewards and observation planning.

El artículo explora el diseño de una estrategia simplificada para el uso de su vertiente lógica en dicha práctica. Luego de una introducción general a la probabilística, en la cual se opta por una concepción subjetiva de la misma, se analiza su aplicación a las inferencias judiciales que llevan de la prueba a los hechos. Seguidamente, se sugiere que, sin perjuicio del uso en ciertos contextos del teorema de Bayes, los axiomas de Kolmógorov son una plataforma prometedora para elaborar un plan de acción probabilístico para uso de los jueces. Para ello se propone una estrategia por etapas, que utiliza en forma libre algunos métodos de razonamiento sugeridos por dichos axiomas. Finalmente se realizan algunas reflexiones acerca de las posibilidades de uso y las limitaciones de la estrategia planteada.

A variety of new and powerful algorithms have been developed for image compression over the years. Among them the wavelet-based image compression schemes have gained much popularity due to their overlapping nature which reduces the blocking artifacts that are common phenomena in JPEG compression and multiresolution character which leads to superior energy compaction with high quality reconstructed images. This paper provides a detailed survey on some of the popular wavelet coding techniques such as the Embedded Zerotree Wavelet (EZW) coding, Set Partitioning in Hierarchical Tree (SPIHT) coding, the Set Partitioned Embedded Block (SPECK) Coder, and the Embedded Block Coding with Optimized Truncation (EBCOT) algorithm. Other wavelet-based coding techniques like the Wavelet Difference Reduction (WDR) and the Adaptive Scanned Wavelet Difference Reduction (ASWDR) algorithms, the Space Frequency Quantization (SFQ) algorithm, the Embedded Predictive Wavelet Image Coder (EPWIC), Compression with Reversible Embedded Wavelet (CREW), the Stack-Run (SR) coding and the recent Geometric Wavelet (GW) coding are also discussed. Based on the review, recommendations and discussions are presented for algorithm development and implementation.

Disasters from explosive volcanic eruptions are infrequent and experience in emergency planning and mitigation for such events remains limited. The need for urgently developing more robust methods for risk assessment and decision making in volcanic crises has become increasingly apparent as world populations continue to expand in areas of active explosive volcanism. Nowhere is this more challenging than at Vesuvius, Italy, with hundreds of thousands of people living on the flanks of one of the most dangerous volcanoes in the world. We describe how a new paradigm, evidence-based volcanology, has been applied in EXPLORIS to contribute to crisis planning and management for when the volcano enters its next state of unrest, as well as in long-term land-use planning. The analytical approach we adopted enumerates and quantifies all the processes and effects of the eruptive hazards of the volcano known to influence risk, a scientific challenge that combines field data on the vulnerability of the built environment and humans in past volcanic disasters with theoretical research on the state of the volcano, and including evidence from the field on previous eruptions as well as numerical simulation modelling of eruptive processes. Formal probabilistic reasoning under uncertainty and a decision analysis approach have provided the basis for the development of an event tree for a future range of eruption types with probability paths and hypothetical casualty outcomes for risk assessment. The most likely future eruption scenarios for emergency planning were derived from the event tree and elaborated upon from the geological and historical record. Modelling the impacts in these scenarios and quantifying the consequences for the circumvesuvian area provide realistic assessments for disaster planning and for showing the potential risk-benefit of mitigation measures, the main one being timely evacuation, but include for consideration protecting buildings against dilute, low dynamic pressure surges, and temporary roof supports in the most vulnerable buildings, as well as hardening infrastructure and lifelines. This innovative work suggests that risk-based methods could have an important role in crisis management at cities on volcanoes and small volcanic islands.

In this paper we show h o w a n umber of di erent f o r m ulations of nonmonotonic reasoning, probabilistic reasoning and design can be combined into a coherent logic-based abductive framework. This framework is based on allowing consistent assumptions to be used to prove a goal. Di erent frameworks are characterised by who chooses the assumptions, whether an adversary chooses the assumptions, nature chooses the assumptions, or one gets to choose whatever assumptions one likes.

The present article offers an approach to scientific debate called adversarial collaboration. The approach requires both parties to agree on empirical tests for resolving a dispute and to conduct these tests with the help of an arbiter. In dispute were Hertwig's claims that frequency formats eliminate conjunction effects and that the conjunction effects previously reported by Kahneman and Tversky occurred because some participants interpreted the word “and” in “bank tellers and feminists” as a union operator. Hertwig proposed two new conjunction phrases, “and are” and “who are,” that would eliminate the ambiguity. Kahneman disagreed with Hertwig's predictions for “and are,” but agreed with his predictions for “who are.” Mellers served as arbiter. Frequency formats by themselves did not eliminate conjunction effects with any of the phrases, but when filler items were removed, conjunction effects disappeared with Hertwig's phrases. Kahneman and Hertwig offer different inte...

Abstract—In abductive logic programming, abductive solutions are typically computed without attending to the abductive context. These abductive solutions can actually be reused in a different abductive context. In this paper we employ a tabling mechanism and propose a tabled abduction mechanism, that consists of a transformation from abductive normal logic programs into tabled dual programs, by tabling abductive solution entries and without requiring any meta-interpreter. Recomputation of abductive solutions for a different context ...

This work proposes the application of preferences over abductive logic programs as an appealing declarative formalism to model choice situations. In particular, both a priori and a posteriori handling of preferences between abductive extensions of a theory are addressed as complementary and essential mechanisms in a broader framework for abductive reasoning. Furthermore, both of these choice mechanisms are combined with other formalisms for decision making, like economic decision theory, resulting in theories ...

We present a Logic Programming framework for moral reasoning under uncertainty. It is enacted by a coherent combination of our two previously implemented systems, Evolution Prospection for decision making, and P-log for probabilistic inference. It allows computing available moral judgments via distinct kinds of prior and post preferences. In introducing various aspects of uncertainty into cases of classical trolley problem moral dilemmas, we show how they may appropriately influence moral judgments, allowing decision makers to opt for different choices, and for these to be externally appraised, even when subject to incomplete evidence, as in courts.

Primeiramente agradeço a minha mãe, Aliete, quem sempre me incentivou e apoiou nas decisões importantes e que nunca mediu esforços em investir na minha educação, possibilitando assim que eu concluísse o mestrado numa instituição pública de ensino superior, passando a constituir um grupo reduzido de pessoas em nosso país. Ao meu orientador, Paulo Aristarco Pagliosa, que não só conduziu o trabalho com precisão e dedicação, muitas vezes extrapolando suas obrigações como professor, mas também tornou as horas difíceis e exaustivas em momentos mais amenos e agradáveis, deixo aqui o meu mais sincero apreço e admiração. Aos professores e funcionários do Departamento de Computação e Estatística da Universidade Federal de Mato Grosso do Sul, agradeço pela atenção com que sempre me receberam e presteza com que me auxiliaram ao longo dessa jornada. Resumo Braz, C.C.M. Objetos Inteligentes Baseados em CLP para Aplicações Científicas. Campo Grande, 2004. Dissertação (Mestrado)-Universidade Federal de Mato Grosso do Sul. A programação lógica com restrições (constraint logic programming, ou CLP)é uma classe de linguagens de programação baseada na programação lógica e programação com restrições. Descende de estudos emáreas diversas como inteligência artificial, linguagens de programação e otimização combinatorial e cada vez mais vem sendo utilizada para modelar e resolver muitos problemas reais complexos. O objetivo deste trabalhoé propor, validar e implementar um conceito de objeto inteligente baseado em CLP. Um objeto inteligente engloba dados, métodos e também conhecimento declarativo e mecanismos de inferência, os quais permitem a este utilizar seu conhecimento a fim de produzir comportamentos inteligentes. Este conhecimentoé formulado através de regras CLP que estão associadas a um objeto na forma de pseudo-métodos declarados na classe do objeto. Esta integração respeita as características principais da orientação a objetos-encapsulamento, herança e polimorfismo-, resultando em aplicações nas quais a computação se dá em um universo constituído por objetos que trocam mensagens entre si. Dessa forma, o controle das ações nãoé exercido por um mecanismo de inferência central, mas sim pelo fluxo comum de mensagens em aplicações orientadas a objetos. Com isso, a modelagem e a implementação de sistemas complexos que necessitem fazer uso das técnicas introduzidas pela CLP podem continuar sendo baseadas no paradigma da orientação a objetos. Os benefícios sâo reusabilidade, manutenabilidade, legibilidade e eficiênica que podem ser alcançados em programas que utilizam este paradigma, além de tornar, para os engenheiros de sistemas, mais intuitiva e natural a absorção desta técnica de inteligência artificial.

Primeiramente agradeço a minha mãe, Aliete, quem sempre me incentivou e apoiou nas decisões importantes e que nunca mediu esforços em investir na minha educação, possibilitando assim que eu concluísse o mestrado numa instituição pública de ensino superior, passando a constituir um grupo reduzido de pessoas em nosso país. Ao meu orientador, Paulo Aristarco Pagliosa, que não só conduziu o trabalho com precisão e dedicação, muitas vezes extrapolando suas obrigações como professor, mas também tornou as horas difíceis e exaustivas em momentos mais amenos e agradáveis, deixo aqui o meu mais sincero apreço e admiração. Aos professores e funcionários do Departamento de Computação e Estatística da Universidade Federal de Mato Grosso do Sul, agradeço pela atenção com que sempre me receberam e presteza com que me auxiliaram ao longo dessa jornada. Resumo Braz, C.C.M. Objetos Inteligentes Baseados em CLP para Aplicações Científicas. Campo Grande, 2004. Dissertação (Mestrado)-Universidade Federal de Mato Grosso do Sul. A programação lógica com restrições (constraint logic programming, ou CLP)é uma classe de linguagens de programação baseada na programação lógica e programação com restrições. Descende de estudos emáreas diversas como inteligência artificial, linguagens de programação e otimização combinatorial e cada vez mais vem sendo utilizada para modelar e resolver muitos problemas reais complexos. O objetivo deste trabalhoé propor, validar e implementar um conceito de objeto inteligente baseado em CLP. Um objeto inteligente engloba dados, métodos e também conhecimento declarativo e mecanismos de inferência, os quais permitem a este utilizar seu conhecimento a fim de produzir comportamentos inteligentes. Este conhecimentoé formulado através de regras CLP que estão associadas a um objeto na forma de pseudo-métodos declarados na classe do objeto. Esta integração respeita as características principais da orientação a objetos-encapsulamento, herança e polimorfismo-, resultando em aplicações nas quais a computação se dá em um universo constituído por objetos que trocam mensagens entre si. Dessa forma, o controle das ações nãoé exercido por um mecanismo de inferência central, mas sim pelo fluxo comum de mensagens em aplicações orientadas a objetos. Com isso, a modelagem e a implementação de sistemas complexos que necessitem fazer uso das técnicas introduzidas pela CLP podem continuar sendo baseadas no paradigma da orientação a objetos. Os benefícios sâo reusabilidade, manutenabilidade, legibilidade e eficiênica que podem ser alcançados em programas que utilizam este paradigma, além de tornar, para os engenheiros de sistemas, mais intuitiva e natural a absorção desta técnica de inteligência artificial.

Las relaciones que planteamos no son solo de decimales random, sino de extensiones decimales que tienen una relación escalar basada en el 100, el 10 y el 1 (y el 0). Al mismo tiempo, encontramos relaciones kolmogorovianas como la indiferencia o paradoja de no poder conocer o determinar si 1 o 0 es decidible o no, de si 0 y 1 en términos probabilísticos, similar a las ecuaciones simultáneas que dan como resultado 1 y 0, y una paradoja que es consistente y no contradictoria, ya que no es simétrica absolutamente (es decir, que no es inversamente proporcional). No es inversamente proporcional porque, a pesar de la relación entre probabilidad y remanente, aquí se extraen distintas magnitudes probabilísticas, y además que dan indistintamente 0 y 1, que significa que son indecidibles. De este modo, como el reverso o anverso de la ley de números grandes, se encuentra una superposición cuántica o equivalente a qbits, donde se podrían desmenuzar los qbits en estados mixtos y viceversa, distintos de spins de ½, y que completarían la cuántica en la dirección de la crítica de la EPR, pero también yendo más allá de la solución de la EPR misma, confirmando a Einstein en su definición de la cuántica como incompleta. Es decir: una cuántica no-micrológica, sino macro y para poblaciones y conjuntos de sampleos, no solo valores individuales micro.

We present a unified logical framework for representing and reasoning about both probability quantitative and qualitative preferences in probability answer set programming [Saad and Pontelli, 2006; Saad, 2006; Saad, 2007a], called probability answer set optimization programs. The proposed framework is vital to allow defining probability quantitative preferences over the possible outcomes of qualitative preferences. We show the application of probability answer set optimization programs to a variant of the well-known nurse restoring problem [Bard and Purnomo, 2005], called the nurse restoring with probability preferences problem. To the best of our knowledge, this development is the first to consider a logical framework for reasoning about probability quantitative preferences, in general, and reasoning about both probability quantitative and qualitative preferences in particular.

We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore how probabilistic reasoning under coherence is related to model-theoretic probabilistic reasoning and to default reasoning in System ¢. In particular, we show that the notions of g-coherence and of g-coherent entailment can be expressed by combining notions in model-theoretic probabilistic logic with concepts from default reasoning. Moreover, we show that probabilistic reasoning under coherence is a generalization of default reasoning in System ¢. That is, we provide a new probabilistic semantics for System ¢ , which neither uses infinitesimal probabilities nor atomic bound (or big-stepped) probabilities. These results also provide new algorithms for probabilistic reasoning under coherence and for default reasoning in System ¢ , and they give new insight into default reasoning with conditional objects.

In this paper we first recall some notions and results on the coherence-based probabilistic treatment of uncertainty. Then, we deepen some probabilistic aspects in nonmonotonic reasoning, by generalizing OR, CM, and Cut rules. We also illustrate the degradation of these inference rules when the number of premises increases. Finally, we show that the lower bounds obtained when applying OR and Quasi-Conjunction inference rules coincide, respectively, with Hamacher and Lukasiewicz t-norms; the upper bounds in both rules coincide with Hamacher t-conorm.

We make a probabilistic analysis related to some inference rules which play an important role in nonmonotonic reasoning. In a coherence-based setting, we study the extensions of a probability assessment defined on n conditional events to their quasi conjunction, and by exploiting duality, to their quasi disjunction. The lower and upper bounds coincide with some well known t-norms and t-conorms: minimum, product, Lukasiewicz, and Hamacher t-norms and their dual t-conorms. On this basis we obtain Quasi And and Quasi Or rules. These are rules for which any finite family of conditional events p-entails the associated quasi conjunction and quasi disjunction. We examine some cases of logical dependencies, and we study the relations among coherence, inclusion for conditional events, and pentailment. We also consider the Or rule, where quasi conjunction and quasi disjunction of premises coincide with the conclusion. We analyze further aspects of quasi conjunction and quasi disjunction, by computing probabilistic bounds on premises from bounds on conclusions. Finally, we consider biconditional events, and we introduce the notion of an n-conditional event. Then we give a probabilistic interpretation for a generalized Loop rule. In an appendix we provide explicit expressions for the Hamacher t-norm and t-conorm in the unitary hypercube.

We generalize, by a progressive procedure, the notions of conjunction and disjunction of two conditional events to the case of n conditional events. In our coherence-based approach, conjunctions and disjunctions are suitable conditional random quantities. We define the notion of negation, by verifying De Morgan's Laws. We also show that conjunction and disjunction satisfy the associative and commutative properties, and a monotonicity property. Then, we give some results on coherence of prevision assessments for some families of compounded conditionals; in particular we examine the Fréchet-Hoeffding bounds. Moreover, we study the reverse probabilistic inference from the conjunction C n+1 of n+1 conditional events to the family {C n , E n+1 |H n+1 }. We consider the relation with the notion of quasi-conjunction and we examine in detail the coherence of the prevision assessments related with the conjunction of three conditional events. Based on conjunction, we also give a characterization of p-consistency and of p-entailment, with applications to several inference rules in probabilistic nonmonotonic reasoning. Finally, we examine some non p-valid inference rules; then, we illustrate by an example two methods which allow to suitably modify non p-valid inference rules in order to get inferences which are p-valid.

Modus ponens (\emph{from $A$ and "if $A$ then $C$" infer $C$}, short: MP) is one of the most basic inference rules. The probabilistic MP allows for managing uncertainty by transmitting assigned uncertainties from the premises to the conclusion (i.e., from $P(A)$ and $P(C|A)$ infer $P(C)$). In this paper, we generalize the probabilistic MP by replacing $A$ by the conditional event $A|H$. The resulting inference rule involves iterated conditionals (formalized by conditional random quantities) and propagates previsions from the premises to the conclusion. Interestingly, the propagation rules for the lower and the upper bounds on the conclusion of the generalized probabilistic MP coincide with the respective bounds on the conclusion for the (non-nested) probabilistic MP.

We study in the setting of probabilistic default reasoning under coherence the quasi conjunction, which is a basic notion for defining consistency of conditional knowledge bases, and the Goodman & Nguyen inclusion relation for conditional events. We deepen two results given in a previous paper: the first result concerns p-entailment from a finite family F of conditional events to the quasi conjunction C(S), for each nonempty subset S of F; the second result analyzes the equivalence between p-entailment from F and p-entailment from C(S), where S is some nonempty subset of F. We also characterize p-entailment by some alternative theorems. Finally, we deepen the connections between p-entailment and inclusion relation, by introducing for a pair (F, E|H) the class of the subsets S of F such that C(S) implies E|H. This class is additive and has a greatest element which can be determined by applying a suitable algorithm.

We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore how probabilistic reasoning under coherence is related to model-theoretic probabilistic reasoning and to default reasoning in System ¢. In particular, we show that the notions of g-coherence and of g-coherent entailment can be expressed by combining notions in model-theoretic probabilistic logic with concepts from default reasoning. Moreover, we show that probabilistic reasoning under coherence is a generalization of default reasoning in System ¢. That is, we provide a new probabilistic semantics for System ¢ , which neither uses infinitesimal probabilities nor atomic bound (or big-stepped) probabilities. These results also provide new algorithms for probabilistic reasoning under coherence and for default reasoning in System ¢ , and they give new insight into default reasoning with conditional objects.

In this paper we first recall some notions and results on the coherence-based probabilistic treatment of uncertainty. Then, we deepen some probabilistic aspects in nonmonotonic reasoning, by generalizing OR, CM, and Cut rules. We also illustrate the degradation of these inference rules when the number of premises increases. Finally, we show that the lower bounds obtained when applying OR and Quasi-Conjunction inference rules coincide, respectively, with Hamacher and Lukasiewicz t-norms; the upper bounds in both rules coincide with Hamacher t-conorm.

We make a probabilistic analysis related to some inference rules which play an important role in nonmonotonic reasoning. In a coherence-based setting, we study the extensions of a probability assessment defined on n conditional events to their quasi conjunction, and by exploiting duality, to their quasi disjunction. The lower and upper bounds coincide with some well known t-norms and t-conorms: minimum, product, Lukasiewicz, and Hamacher t-norms and their dual t-conorms. On this basis we obtain Quasi And and Quasi Or rules. These are rules for which any finite family of conditional events p-entails the associated quasi conjunction and quasi disjunction. We examine some cases of logical dependencies, and we study the relations among coherence, inclusion for conditional events, and pentailment. We also consider the Or rule, where quasi conjunction and quasi disjunction of premises coincide with the conclusion. We analyze further aspects of quasi conjunction and quasi disjunction, by computing probabilistic bounds on premises from bounds on conclusions. Finally, we consider biconditional events, and we introduce the notion of an n-conditional event. Then we give a probabilistic interpretation for a generalized Loop rule. In an appendix we provide explicit expressions for the Hamacher t-norm and t-conorm in the unitary hypercube.

Ian and Dick first connected in 1987, when Dick delivered a paper at the Law and Society Conference. Ian was just finishing his first year of teaching, and he hadn't yet overcome the kind of anxiety that caused him to tremble at the prospect of asking a question. Not only was Dick open and gentle in his response, but soon after the conference Ian received from him a letter of encouragement. Ian was floored by his letter because Dick, unbidden, had also included comments on a draft article of Ian's. That e-mail began a long-distance relationship that was immensely helpful to a young scholar. Over the decades, Dick and Ian mailed and e-mailed comments on over a dozen drafts of each other's writings, Though they never taught at the same school in the same semester, Ian nonetheless felt like Dick was one of his closest colleagues. Their academic havruta not only predates e-mail, it predates WordPerfect and Word-as those first comments were composed on the XyWrite wordprocessing software. No one else comes close to taking the time to have written as many or as high-quality comments on Ian's drafts. Dick has been a role model not only on the typed page, but also in the way he has carried himself in seminars, both while presenting and in the audience. Dick speaks softly but carries a collaborative and constructive stick. His ready smile is emblematic of his warmth. Just bringing to mind memories of Dick in seminar or talking over coffee lifts one's spirits. Of course, even very good academics can be acerbic and annoying. As with the Tsar, one sometimes wants to bless and keep them. .. far away, Not so Dick Craswell. He is proof that you can be a serious, respected scholar, and be universally admired. Even in the boisterous milieu of the University of Chicago seminar, he was a calming presence. There is a balm in Gilead. Richard Craswell. THE RULE OF PROBABILITIES havior and constrain judicial decisionmaking.2 Dick's analysis of how consumers might mistakenly update their prior beliefs after a corrective advertising order 3 is a close analogy to our claim that unguided juries are likely to mistakenly update in response to incomplete statistical DNA evidence.

This paper describes an approach to integrate complex modeling experience into a decision support framework for non-point source pollution modeling of a watershed. The approach employs probabilistic reasoning techniques and derives probability distributions from previous model simulations. Thus, the sensitivity of a given model to its inputs is captured in such a way that the system can be used to find solutions to management problems through the application of probabilistic inference. A graphical probability model is a visual formalism encoding random variables and relationships between random variables as nodes and directed links in a graph. In our model, the nodes represent individual parameters for each of the fields in a watershed. Directed links connect correlated nodes, such as nodes representing the management practice in a field to nodes representing soil loss rates. The directed links Ž between the nodes in the probability model follow the drainage network of the watershed. The relationships or. Ž. links between the nodes are quantified via two methods. The first method integrates data cases derived from Ž. Monte Carlo simulation of a non-point source NPS pollution model. In the second method, deterministic functions defined in the NPS model are used to specify the relationships. The Monte Carlo simulations are performed to include the influence of parametric uncertainty on model results. The network for an entire watershed is complex with a large number of nodes, therefore, a spatial analysisrvisualization tool was developed for interacting with the large probability model.

Each year it has become more and more difficult for healthcare providers to determine if a patient has a pathology related to the vertebral column. There is great potential to become more efficient and effective in terms of quality of care provided to patients through the use of automated systems. However, in many cases automated systems can allow for misclassification and force providers to have to review more causes than necessary. In this study, we analyzed methods to increase the True Positives and lower the False Positives while comparing them against stateof-the-art techniques in the biomedical community. We found that by applying the studied techniques of a data-driven model, the benefits to healthcare providers are significant and align with the methodologies and techniques utilized in the current research community.

Fusion refers to the combination of two or more probability assignments to pieces of evidence that support the same hypotheses. The probability assignments usually result from different inference paths in reasoning and are, in general, different. Given a set of probability assignments for evidence to be fused, it is well known that certain constraints, called consistent bounds, must be satisfied. These bounds arise from the theory of probability and define an admissible domain for the fused evidence. However, because the bounds are, in general, interactive, a general methodology for computing the admissible domain other than a brute-force numerical approach (linear programming) is lacking. This paper examines the role of interaction in evidence fusion and demonstrates the effect of interaction on the fused evidence. A simple case consisting of one hypothesis supported by two pieces of evidence is considered, and the interactive bounds and admissible domain are derived analytically. In particular, the effect of different dependency assumptions on the consistent bounds is derived to show that the assumption of conditional dependence can lead to inconsistencies under certain circumstances, that is, the fused evidence lies outside the admissible domain. Uncertain evidence expressed in the form of bounds is not very useful in practice because the bounds tend to become large as the uncertainty is cascaded from one level to another in inferencing. Point evidence may be more helpful. Three suggestions for obtaining consistent point estimates from the consistent bounds are presented, and numerical examples are given.

This work proposes the application of preferences over abductive logic programs as an appealing declarative formalism to model choice situations. In particular, both a priori and a posteriori handling of preferences between abductive extensions of a theory are addressed as complementary and essential mechanisms in a broader framework for abductive reasoning. Furthermore, both of these choice mechanisms are combined with other formalisms for decision making, like economic decision theory, resulting in theories ...

Continuous constraint reasoning assumes the uncertainty of numerical variables within given bounds and propagates such knowledge through a network of constraints, reducing the uncertainty. In some problems there is also information about the plausibility distribution of values within such bounds. However, the classical constraint framework cannot accommodate that information. This paper describes how the continuous constraint programming paradigm may be extended, in order to accommodate some probabilistic considerations, bridging the gap between the pure interval-based approach, that does not consider likelihoods, and the pure stochastic approach, that does not guarantee the safety of the obtained results.

System dynamics is naturally expressed by means of differential equations. Despite their expressive power, they are difficult to reason about and to make decisions upon, given their non‐linearity and the important effects that the uncertainty on data may cause. In contrast with traditional numerical simulations that may only provide a likelihood of the results obtained, we propose a constraint reasoning framework that enables safe decision support despite data uncertainty. The approach is illustrated in the tuning of drug design and in an epidemiological study. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

This special issue of the IfColog Journal of Logics and their Applications "Frontiers of Abduction" is based on a selection of papers concerning abduction that are situated at the crossroad of logic, epistemology, and cognitive science. The status of abduction-that Hintikka considered the fundamental problem of contemporary epistemology [7]-is very controversial. When dealing with abductive reasoning, misinterpretations and equivocations are common. What are the differences between abduction and induction? What are the differences between abduction and the well-known hypothetico-deductive method? What did Peirce mean when he considered abduction a kind of inference? Does abduction involve only the generation of hypotheses or their evaluation too? Are the criteria for the best explanation in abductive reasoning epistemic, or pragmatic, or both? How many kinds of abduction are there? The papers presented in this issue aim at increasing knowledge-logical, cognitive, epistemological-about creative and expert inferences. Analyzing various reasoning and modeling practices provides a way of specifying the nature of some abductive reasoning processes. Following [12; 14] we have to distinguish between sentential, model-based, and manipulative abduction. In the past decades many attempts have been made to model abduction by developing some formal tools in order to illustrate its computational properties and the relationships with the different forms of deductive reasoning (see, for example, [4]). Some of these formal models of abductive reasoning are based on the theory of the epistemic state of an agent [3], where the epistemic state of an individual is modeled as a consistent set of beliefs that can change by expansion and contraction (belief revision framework). These formal tools, often related to the tradition of nonmonotonic logic, logic programming, semantic tableaux, dynamic and adaptive logic, etc., are usually devoted to illustrating sentential abduction and present some limitations [13]. It may be said that the traditional logical accounts of abduction certainly illustrate much of what is important in abductive reasoning, especially the objective of selecting a set of hypotheses (diagnoses, causes) that are able to dispense good (preferred) explanations of data (observations), but fail in accounting for many cases of explanations occurring in science or in everyday reasoning. The logical papers

Education is an area where innovation moves slowly. In this study, we will propose a framework with a novel approach that will support the development of a multi-interactive chatbot's system for an educational area using AIML 2.0. e system will facilitate the students for their learning towards an outcome-based education domain. e proposed framework will be composed of a user module which consists of user and user interface, chat agents module which will respond to the user query, chatbot KB which will act as the brain for the chatbot system, and socket system for establishing the communication link. Finally, the proposed system will be evaluated using a confusion matrix. e multichatbot communication system will support text-based dialogues on a limited set of questions related to education. However, the system will be implemented in java. e outcomes of this research will be useful for the education sector where these intelligent systems will help the students in schools, universities, and other training scenarios.