Preference-based belief revision for rule-based agents

Agents which perform inferences on the basis of unreliable information need an ability to revise their beliefs if they discover an inconsistency. Such a belief revision algorithm ideally should be rational, should respect any preference ordering over the agent’s beliefs (removing less preferred beliefs where possible) and should be fast. However, while standard approaches to rational belief revision for classical reasoners allow preferences to be taken into account, they typically have quite high complexity. In this paper, we consider belief revision for agents which reason in a simpler logic than full first-order logic, namely rule-based reasoners. We show that it is possible to define a contraction operation for rule-based reasoners, which we call McAllester contraction, which satisfies all the basic Alchourrón, Gärdenfors and Makinson (AGM) postulates for contraction (apart from the recovery postulate) and at the same time can be computed in polynomial time. We prove a representation theorem for McAllester contraction with respect to the basic AGM postulates (minus recovery), and two additional postulates. We then show that our contraction operation removes a set of beliefs which is least preferred, with respect to a natural interpretation of preference. Finally, we show how McAllester contraction can be used to define a revision operation which is also polynomial time, and prove a representation theorem for the revision operation.     

Towards a theory of intention revision

Although the change of beliefs in the face of new information has been widely studied with some success, the revision of other mental states has received little attention from the theoretical perspective. In particular, intentions are widely recognised as being a key attitude for rational agents, and while several formal theories of intention have been proposed in the literature, the logic of intention revision has been hardly considered. There are several reasons for this: perhaps most importantly, intentions are very closely connected with other mental states—in particular, beliefs about the future and the abilities of the agent. So, we cannot study them in isolation. We must consider the interplay between intention revision and the revision of other mental states, which complicates the picture considerably. In this paper, we present some first steps towards a theory of intention revision. We develop a simple model of an agent’s mental states, and define intention revision operators. Using this model, we develop a logic of intention dynamics, and then investigate some of its properties.     

Executable specifications for hypothesis-based reasoning with Prolog and Constraint Handling Rules

Constraint Handling Rules (CHR) is an extension to Prolog which opens up a spectrum of hypothesis-based reasoning in logic programs without additional interpretation overhead. Abduction with integrity constraints is one example of hypothesis-based reasoning which can be implemented directly in Prolog and CHR with a straightforward use of available and efficiently implemented facilities.The present paper clarifies the semantic foundations for this way of doing abduction in CHR and Prolog as well as other examples of hypothesis-based reasoning that is possible, including assumptive logic programming, hypotheses with priority and scope, and nonmonotonic reasoning.Examples are presented as executable code so the paper may also serve the additional purpose of a practical guide for developing such programs, and it is demonstrated that the approach provides a seamless integration with existing constraint solvers.     

My beliefs about your beliefs: a case study in theory of mind and epistemic logic

We model three examples of beliefs that agents may have about other agents’ beliefs, and provide motivation for this conceptualization from the theory of mind literature. We assume a modal logical framework for modelling degrees of belief by partially ordered preference relations. In this setting, we describe that agents believe that other agents do not distinguish among their beliefs (‘no preferences’), that agents believe that the beliefs of other agents are in part as their own (‘my preferences’), and the special case that agents believe that the beliefs of other agents are exactly as their own (‘preference refinement’). This multi-agent belief interaction is frame characterizable. We provide examples for introspective agents. We investigate which of these forms of belief interaction are preserved under three common forms of belief revision.     

Nonmonotonic abductive inductive learning

Inductive Logic Programming (ILP) is concerned with the task of generalising sets of positive and negative examples with respect to background knowledge expressed as logic programs. Negation as Failure (NAF) is a key feature of logic programming which provides a means for nonmonotonic commonsense reasoning under incomplete information. But, so far, most ILP research has been aimed at Horn programs which exclude NAF, and has failed to exploit the full potential of normal programs that allow NAF. By contrast, Abductive Logic Programming (ALP), a related task concerned with explaining observations with respect to a prior theory, has been well studied and applied in the context of normal logic programs. This paper shows how ALP can be used to provide a semantics and proof procedure for nonmonotonic ILP that utilises practical methods of language and search bias to reduce the search space. This is done by lifting an existing method called Hybrid Abductive Inductive Learning (HAIL) from Horn clauses to normal logic programs. To demonstrate its potential benefits, the resulting system, called XHAIL, is applied to a process modelling case study involving a nonmonotonic temporal Event Calculus (EC).     

Perception as abduction: turning sensor data into meaningful representation

This article presents a formal theory of robot perception as a form of abduction. The theory pins down the process whereby low-level sensor data is transformed into a symbolic representation of the external world, drawing together aspects such as incompleteness, top-down information flow, active perception, attention, and sensor fusion in a unifying framework. In addition, a number of themes are identified that are common to both the engineer concerned with developing a rigorous theory of perception, such as the one on offer here, and the philosopher of mind who is exercised by questions relating to mental representation and intentionality.     

Probabilistic dynamic belief revision

We investigate the discrete (finite) case of the Popper–Renyi theory of conditional probability, introducing discrete conditional probabilistic models for knowledge and conditional belief, and comparing them with the more standard plausibility models. We also consider a related notion, that of safe belief, which is a weak (non-negatively introspective) type of “knowledge”. We develop a probabilistic version of this concept (“degree of safety”) and we analyze its role in games. We completely axiomatize the logic of conditional belief, knowledge and safe belief over conditional probabilistic models. We develop a theory of probabilistic dynamic belief revision, introducing probabilistic “action models” and proposing a notion of probabilistic update product, that comes together with appropriate reduction laws.     

Learning from examples does not prevent order effects in belief revision

A common finding is that information order influences belief revision (e.g., Hogarth & Einhorn, 1992 Hogarth, R. M. and Einhorn, H. J. 1992. Order effects in belief updating: The belief-adjustment model. Cognitive Psychology, 24: 1–55. [Crossref], [Web of Science ®] , [Google Scholar]). We tested personal experience as a possible mitigator. In three experiments participants experienced the probabilistic relationship between pieces of information and object category through a series of trials where they assigned objects (planes) into one of two possible categories (hostile or commercial), given two sequentially presented pieces of probabilistic information (route and ID), and then they had to indicate their belief about the object category before feedback. The results generally confirm the predictions from the Hogarth and Einhorn model. Participants showed a recency effect in their belief revision. Extending previous model evaluations the results indicate that the model predictions also hold for classification decisions, and for pieces of information that vary in their diagnostic values. Personal experience does not appear to prevent order effects in classification decisions based on sequentially presented pieces of information and in belief revision.     

Iterated revision and minimal change of conditional beliefs

We describe a model of iterated belief revision that extends the AGM theory of revision to account for the effect of a revision on the conditional beliefs of an agent. In particular, this model ensures that an agent makes as few changes as possible to the conditional component of its belief set. Adopting the Ramsey test, minimal conditional revision provides acceptance conditions for arbitrary right-nested conditionals. We show that problem of determining acceptance of any such nested conditional can be reduced to acceptance tests for unnested conditionals. Thus, iterated revision can be accomplished in a virtual manner, using uniterated revision.     

Updating: A psychologically basic situation of probability revision

The Bayesian model has been used in psychology as the standard reference for the study of probability revision. In the first part of this paper we show that this traditional choice restricts the scope of the experimental investigation of revision to a stable universe. This is the case of a situation that, technically, is known as focusing. We argue that it is essential for a better understanding of human probability revision to consider another situation called updating (Katsuno & Mendelzon, 1992 Katsuno, A. and Mendelzon, A. 1992. “On the difference between updating a knowledge base and revising it”. In Belief revision, Edited by: Gärdenfors, P. 183–203. Cambridge, , UK: Cambridge University Press. [Crossref] , [Google Scholar]), in which the universe is evolving. In that case the structure of the universe has definitely been transformed and the revision message conveys information on the resulting universe. The second part of the paper presents four experiments based on the Monty Hall puzzle that aim to show that updating is a natural frame for individuals to revise their beliefs.     

Determining the environment: a modal logic for closed interaction

The aim of the work is to provide a language to reason about Closed Interactions, i.e. all those situations in which the outcomes of an interaction can be determined by the agents themselves and in which the environment cannot interfere with they are able to determine. We will see that two different interpretations can be given of this restriction, both stemming from Pauly Representation Theorem. We will identify such restrictions and axiomatize their logic. We will apply the formal tools to reason about games and their regulation.     

Modal Deduction in Second-Order Logic and Set Theory - II

In this paper, we generalize the set-theoretic translation method for poly-modal logic introduced in [11] to extended modal logics. Instead of devising an ad-hoc translation for each logic, we develop a general framework within which a number of extended modal logics can be dealt with. We first extend the basic set-theoretic translation method to weak monadic second-order logic through a suitable change in the underlying set theory that connects up in interesting ways with constructibility; then, we show how to tailor such a translation to work with specific cases of extended modal logics.     

Cognitive behaviour therapy for eating disorders: a "transdiagnostic" theory and treatment

This paper is concerned with the psychopathological processes that account for the persistence of severe eating disorders. Two separate but interrelated lines of argument are developed. One is that the leading evidence-based theory of the maintenance of eating disorders, the cognitive behavioural theory of bulimia nervosa, should be extended in its focus to embrace four additional maintaining mechanisms. Specifically, we propose that in certain patients one or more of four additional maintaining processes interact with the core eating disorder maintaining mechanisms and that when this occurs it is an obstacle to change. The additional maintaining processes concern the influence of clinical perfectionism, core low self-esteem, mood intolerance and interpersonal difficulties. The second line of argument is that in the case of eating disorders shared, but distinctive, clinical features tend to be maintained by similar psychopathological processes. Accordingly, we suggest that common mechanisms are involved in the persistence of bulimia nervosa, anorexia nervosa and the atypical eating disorders. Together, these two lines of argument lead us to propose a new transdiagnostic theory of the maintenance of the full range of eating disorders, a theory which embraces a broader range of maintaining mechanisms than the current theory concerning bulimia nervosa. In the final sections of the paper we describe a transdiagnostic treatment derived from the new theory, and we consider in principle the broader relevance of transdiagnostic theories of maintenance.     

Finding MAPs using strongly equivalent high order recurrent symmetric connectionist networks

Belief revision is the problem of finding the most plausible explanation for an observed set of evidences. It has many applications in various scientific domains like natural language understanding, medical diagnosis and computational biology. Bayesian Networks (BN) is an important probabilistic graphical formalism widely used for belief revision tasks. In BN, belief revision can be achieved by finding the maximum a posteriori (MAP) assignment. Finding MAP is an NP-Hard problem. In previous work, we showed how to find the MAP assignment in BN using High Order Recurrent Neural Networks (HORN) through an intermediate representation of Cost-Based Abduction. This method eliminates the need to explicitly construct the energy function in two steps, objective and constraints. This paper builds on that previous work by providing the theoretical foundation and proving that the resultant HORN used to find MAP is strongly equivalent to the original BN it tries to solve.     

Basic Infobase Change

Generalisations of theory change involving arbitrary sets of wffs instead of belief sets have become known as base change. In one view, a base should be thought of as providing more structure to its generated belief set, and can be used to determine the theory change operation associated with a base change operation. In this paper we extend a proposal along these lines by Meyer et al. We take an infobase as a finite sequence of wffs, with each element in the sequence being seen as an independently obtained bit of information, and define appropriate infobase change operations. The associated theory change operations satisfy the AGM postulates for theory change. Since an infobase change operation produces a new infobase, it allows for iterated infobase change. We measure iterated infobase change against the postulates proposed by Darwiche et al. and Lehmann.     

时间序列关系推理研究概述

时间序列关系推理是对事件发生的先后顺序关系的推理,是日常生活思维的重要方面。已有的研究关注3类推理问题,探查了不同任务变式下成人时间序列关系推理过程和推理策略,研究结果多支持心理模型理论。未来的研究应探明3类问题的性质,从心理逻辑理论的角度深化策略的研究结果,进一步揭示推理的机制。     

Hermeneutics and theory of mind

In contemporary philosophy and psychology there is an ongoing debate around the concept of theory of mind. Theory of mind concerns our ability to understand another person. The two approaches that dominate the debate are “Theory Theory” (TT) and “Simulation Theory” (ST). This paper explores the connection between theory of mind and hermeneutics. Although both speak of the nature of understanding, and the way we gain and organize our knowledge of others, certain aspects of Schleiermacher’s hermeneutics reflect a theory approach, long before TT itself was developed. In contrast, Dilthey’s hermeneutics reflects a simulation approach. In contrast to both of these approaches, I propose a contextual theory, as a parallel to Gadamer’s work in hermeneutics, and as a view that offers the basis for an important critique of both TT and ST.

冲突情境下幼儿的选择性信任和信念修正

幼儿如何选择性地采信他人提供的信息、获取知识, 是幼儿社会认知发展研究的重要问题。除客观的信息内容外, 信息传递者的特征也影响幼儿的选择性信任。另外, 在不确定情境下, 他人证言与幼儿已有信念可能存在冲突, 在二者冲突的情境下, 幼儿是否可以采信他人的证言, 并最终改变幼儿的已有判断是以往研究忽略的问题。本研究考察了当母亲证言与幼儿已有信念冲突时, 不同程度的冲突情境(面对不同比例的合成动物时)对幼儿选择性信任和信念修正的影响。研究采用冲突信息源范式, 向74名4~6岁幼儿呈现对不同比例合成动物(50%-50%任务 vs 75%-25%任务)命名的证言, 考察幼儿对信息提供者的询问意愿、对证言的信任情况和在证言前后对合成动物的判断(信念修正)。信息提供的一方为母亲(提供相似度低的动物名称), 另一方为陌生人(提供相似度高的动物名称)。结果发现, 幼儿的选择性信任和信念修正受到母亲证言与已有信念冲突程度的影响。在低冲突情境下, 幼儿对母亲证言的询问意愿和外显信任均高于高冲突情境。幼儿的信念修正存在年龄差异, 在低冲突情境下, 年长幼儿比年幼幼儿更倾向于改变已有信念, 在高冲突情境下, 年长的幼儿比年幼幼儿更不愿意改变已有信念。本研究结果表明, 当母亲的证言与幼儿已有信念冲突时, 中国幼儿可以区分不同程度的冲突情境, 并且可以根据冲突的程度进行选择性信任和信念修正。