Belief Revision Research Articles

An Epistemological Study of Theory Change

Belief Revision is a well-established field of research that deals with how agents rationally change their minds in the face of new information. The milestone of Belief Revision is a general and versatile formal framework introduced by Alchourrón, Gärdenfors and Makinson, known as the AGM paradigm, which has been, to this date, the dominant model within the field. A main shortcoming of the AGM paradigm, as originally proposed, is its lack of any guidelines for relevant change. To remedy this weakness, Parikh proposed a relevance-sensitive axiom, which applies on splittable theories; i.e., theories that can be divided into syntax-disjoint compartments. The aim of this article is to provide an epistemological interpretation of the dynamics (revision) of splittable theories, from the perspective of Kuhn's inuential work on the evolution of scientific knowledge, through the consideration of principal belief-change scenarios. The whole study establishes a conceptual bridge between rational belief revision and traditional philosophy of science, which sheds light on the application of formal epistemological tools on the dynamics of knowledge.

How narrative transportation in movies affects audiences' positive word-of-mouth: The mediating role of emotion.

On the basis of the cognitive–affective–behavioral model, this study investigated the effects of narrative transportation in movies on audience emotion and positive word-of-mouth (PWOM). To the best of the authors’ knowledge, this is the first study to explore the effects of the multidimensionality of narrative transportation on the multidimensionality of emotion. In this study, narrative transportation was divided into dimensions of empathy, immersion, and belief revision, and emotion was divided into pleasure and arousal. To explore the relationship between narrative transportation, emotions, and PWOM, the participants, comprising individuals with movie watching experience, completed a questionnaire on the movie that had left the deepest impression on them. The responses were analyzed through structural equation modeling. Empathy, immersion, and belief revision were significantly and positively associated with pleasure and arousal, which positively correlated with PWOM. The relationship between empathy or immersion and PWOM was partially mediated by pleasure and arousal, whereas pleasure and arousal fully mediated the association between belief revision and PWOM. Practical suggestions for filmmakers were derived from the present findings.

The similarity-updating model of probability judgment and belief revision.

People often take nondiagnostic information into account when revising their beliefs. A probability judgment decreases due to nondiagnostic information represents the well-established "dilution effect" observed in many domains. Surprisingly, the opposite of the dilution effect called the "confirmation effect" has also been observed frequently. The present work provides a unified cognitive model that allows both effects to be explained simultaneously. The suggested similarity-updating model incorporates two psychological components: first, a similarity-based judgment inspired by categorization research, and second, a weighting-and-adding process with an adjustment following a similarity-based confirmation mechanism. Four experimental studies demonstrate the model's predictive accuracy for probability judgments and belief revision. The participants received a sample of information from one of two options and had to judge from which option the information came. The similarity-updating model predicts that the probability judgment is a function of the similarity of the sample to the options. When one is presented with a new sample, the previous probability judgment is updated with a second probability judgment by taking a weighted average of the two and adjusting the result according to a similarity-based confirmation. The model describes people's probability judgments well and outcompetes a Bayesian cognitive model and an alternative probability-theory-plus-noise model. The similarity-updating model accounts for several qualitative findings, namely, dilution effects, confirmation effects, order effects, and the finding that probability judgments are invariant to sample size. In sum, the similarity-updating model provides a plausible account of human probability judgment and belief revision. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

An Algorithm to Belief Revision and to Verify Consistency of a Knowledge Base

The belief revision process involves several problems considered hard. One of the crucial problems is how to represent to the knowledge base K to consider, as well as how to represent and to add new information , which may even be contradictory to the knowledge base. In this work, both the knowledge base and the new information are in conjunctive normal form. Each clause of a conjunctive normal form is encoded by a string consisting of: 0, 1, *, representing the falsifying assignments of the clause. To use the falsifying assignments of the clauses allows to perform efficiently different logical operators among conjunctive forms. Our belief revision process (K * ) between conjunctive forms is based on solving first the propositional inference, i.e. K = . Based on to count falsifying assignments represented by tertiary chains, an algorithmic proposal is made that allows to determine in a practical way, when (K E ( K * )) is inconsistent. Finally, the time-complexity analysis of our algorithmic proposal is carried out.

A Characterization of Probability-based Dichotomous Belief Revision

This article investigates the properties of multistate top revision, a dichotomous (AGM-style) model of belief revision that is based on an underlying model of probability revision. A proposition is included in the belief set if and only if its probability is either 1 or infinitesimally close to 1. Infinitesimal probabilities are used to keep track of propositions that are currently considered to have negligible probability, so that they are available if future information makes them more plausible. Multistate top revision satisfies a slightly modified version of the set of basic and supplementary AGM postulates, except the inclusion and success postulates. This result shows that hyperreal probabilities can provide us with efficient tools for overcoming the well known difficulties in combining dichotomous and probabilistic models of belief change.

Local Belief Dynamics in Network Knowledge Bases

People are becoming increasingly more connected to each other as social networks continue to grow both in number and variety, and this is true for autonomous software agents as well. Taking them as a collection, such social platforms can be seen as one complex network with many different types of relations, different degrees of strength for each relation, and a wide range of information on each node. In this context, social media posts made by users are reflections of the content of their own individual (or local) knowledge bases; modeling how knowledge flows over the network—or how this can possibly occur—is therefore of great interest from a knowledge representation and reasoning perspective. In this article, we provide a formal introduction to the network knowledge base model, and then focus on the problem of how a single agent’s knowledge base changes when exposed to a stream of news items coming from other members of the network. We do so by taking the classical belief revision approach of first proposing desirable properties for how such a local operation should be carried out (theoretical characterization), arriving at three different families of local operators, exploring concrete algorithms (algorithmic characterization) for two of the families, and proving properties about the relationship between the two characterizations (representation theorem). One of the most important differences between our approach and the classical models of belief revision is that in our case the input is more complex, containing additional information about each piece of information.

Conciliatory Views on Peer Disagreement and the Order of Evidence Acquisition

Abstract The evidence that we get from peer disagreement is especially problematic from a Bayesian point of view since the belief revision caused by a piece of such evidence cannot be modelled along the lines of Bayesian conditionalisation. This paper explains how exactly this problem arises, what features of peer disagreements are responsible for it, and what lessons should be drawn for both the analysis of peer disagreements and Bayesian conditionalisation as a model of evidence acquisition. In particular, it is pointed out that the same characteristic of evidence from disagreement that explains the problems with Bayesian conditionalisation also suggests an interpretation of suspension of belief in terms of imprecise probabilities.

Conflict-Based Belief Revision Operators in Possibilistic Logic

In this paper, we investigate belief revision in possibilistic logic, which is a weighted logic proposed to deal with incomplete and uncertain information. Existing revision operators in possibilistic logic are restricted in the sense that the input information can only be a formula instead of a possibilistic knowledge base which is a set of weighted formulas. To break this restriction, we consider weighted prime implicants of a possibilistic knowledge base and use them to define novel revision operators in possibilistic logic. Intuitively, a weighted prime implicant of a possibilistic knowledge base is a logically weakest possibilistic term (i.e., a set of weighted literals) that can entail the knowledge base. We first show that the existing definition of a weighted prime implicant is problematic and need a modification. To define a revision operator using weighted prime implicants, we face two problems. The first problem is that we need to define the notion of a conflict set between two weighted prime implicants of two possibilistic knowledge bases to achieve minimal change. The second problem is that we need to define the disjunction of possibilistic terms. We solve these problems and define two conflict-based revision operators in possibilistic logic. We then adapt the well-known postulates for revision proposed by Katsuno and Mendelzon and show that our revision operators satisfy four of the basic adapted postulates and satisfy two others in some special cases.

Tracking probabilistic truths: a logic for statistical learning

We propose a new model for forming and revising beliefs about unknown probabilities. To go beyond what is known with certainty and represent the agent’s beliefs about probability, we consider a plausibility map, associating to each possible distribution a plausibility ranking. Beliefs are defined as in Belief Revision Theory, in terms of truth in the most plausible worlds (or more generally, truth in all the worlds that are plausible enough). We consider two forms of conditioning or belief update, corresponding to the acquisition of two types of information: (1) learning observable evidence obtained by repeated sampling from the unknown distribution; and (2) learning higher-order information about the distribution. The first changes only the plausibility map (via a ‘plausibilistic’ version of Bayes’ Rule), but leaves the given set of possible distributions essentially unchanged; the second rules out some distributions, thus shrinking the set of possibilities, without changing their plausibility ordering.. We look at stability of beliefs under either of these types of learning, defining two related notions (safe belief and statistical knowledge), as well as a measure of the verisimilitude of a given plausibility model. We prove a number of convergence results, showing how our agent’s beliefs track the true probability after repeated sampling, and how she eventually gains in a sense (statistical) knowledge of that true probability. Finally, we sketch the contours of a dynamic doxastic logic for statistical learning.

Modelling supra-classical logic in a Boltzmann neural network: I representation

Abstract This paper looks at the representation of supra-classical, non-monotonic (SCNM) logic by an artificial neural network. It identifies the features of defeasiblity in this logic related to inference in the context of common-sense reasoning. It considers the machine characteristics that make a representation possible, with reference to previous literature. We describe a theoretical environment for investigating the representation and provide experimental evidence confirming that a Boltzmann machine is a suitable network representation. A Boltzmann machine can learn an input distribution corresponding to a preference relation and explicitly retrieve appropriate model states, constituting one-to-many mappings, entailed by the uncertain information contained in a premiss. The place of the Boltzmann machine in knowledge representation is discussed. In future papers, this neural network model of SCNM logic will serve as an experimental gateway for exploration of typicality and belief revision.

Computational Errors and Suspension in a PWK Epistemic Agent

Abstract In a computational program there can be two kinds of errors: (i) critical errors and (ii) non-critical errors. A critical error stops the program in a global way, which means the error cannot be fixed in the subsequent computation process. A non-critical error partially stops the computation program, and the error can be fixed in the subsequent computation process. We argue that two kinds of errors correspond to two kinds of suspension and can be modeled using Paraconsistent Weak Kleene ($ {\textsf{PWK}}$) belief revision theory, with the help of a new interpretation of the third value of $ {\textsf{PWK}}$, that is, off-topic. According to this new interpretation, if a proposition obtains the third value $\textbf{u}$, it means it is off-topic. Within our framework of $ {\textsf{PWK}}$ belief revision theory, we will show that a non-critical error corresponds to a non-critical suspension and that a critical error corresponds to a critical suspension.

Expressivism, Inferentialism and the Simulation Game

Expressivism, Inferentialism and the Simulation Game

Interpolating causal mechanisms: The paradox of knowing more.

Causal knowledge is not static; it is constantly modified based on new evidence. The present set of seven experiments explores 1 important case of causal belief revision that has been neglected in research so far: causal interpolations. A simple prototypic case of an interpolation is a situation in which we initially have knowledge about a causal relation or a positive covariation between 2 variables but later become interested in the mechanism linking these 2 variables. Our key finding is that the interpolation of mechanism variables tends to be misrepresented, which leads to the paradox of knowing more: The more people know about a mechanism, the weaker they tend to find the probabilistic relation between the 2 variables (i.e., weakening effect). Indeed, in all our experiments we found that, despite identical learning data about 2 variables, the probability linking the 2 variables was judged higher when follow-up research showed that the 2 variables were assumed to be directly causally linked (i.e., C→E) than when participants were instructed that the causal relation is in fact mediated by a variable representing a component of the mechanism (M; i.e., C→M→E). Our explanation of the weakening effect is that people often confuse discoveries of preexisting but unknown mechanisms with situations in which new variables are being added to a previously simpler causal model, thus violating causal stability assumptions in natural kind domains. The experiments test several implications of this hypothesis. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

No Evidence for the Involvement of Cognitive Immunisation in Updating Beliefs About the Self in Three Non-Clinical Samples

BackgroundCognitive immunisation against disconfirmatory evidence (i.e., devaluing expectation-disconfirming information through cognitive mechanisms) has recently been discussed as an obstacle to the revision of dysfunctional beliefs in mental disorders such as depression. Yet, it is unclear whether cognitive immunisation is also involved in belief updating in non-clinical samples.MethodsUsing a three-group modulation protocol (promotion vs. inhibition of cognitive immunisation vs. control group), we examined how cognitive immunisation influences belief updating in response to performance feedback in three non-clinical samples. In Experiments 1 (N = 99) and 2 (N = 93), participants received unexpectedly negative feedback, whereas participants from Experiment 3 (N = 118) received unexpectedly positive feedback. Depressive symptoms and dispositional optimism were examined as additional predictors of belief updating.ResultsIn all experiments, participants adjusted their expectations in line with the feedback received, but this effect was not influenced by the cognitive immunisation manipulation. In Experiment 3, expectation change remained stable over 2 weeks. Depressive symptoms were associated with a reduced integration of positive feedback, but not with an increased sensitivity to negative feedback.ConclusionsWhereas previous research has shown that cognitive immunisation contributes to persistent beliefs in clinical populations, the present findings suggest that it does not affect belief updating in non-clinical samples.

A general multi-agent epistemic planner based on higher-order belief change

In recent years, multi-agent epistemic planning has received attention from both dynamic logic and planning communities. Existing implementations of multi-agent epistemic planning are based on compilation into classical planning and suffer from various limitations, such as generating only linear plans, restriction to public actions, and incapability to handle disjunctive beliefs. In this paper, we consider centralized multi-agent epistemic planning from the viewpoint of a third person who coordinates all the agents to achieve the goal. We treat contingent planning, resulting in nonlinear plans. We model private actions and hence handle beliefs, formalized with the multi-agent KD45 logic. We handle static propositional common knowledge, which we call constraints. For such planning settings, we propose a general representation framework where the initial knowledge base (KB) and the goal, the preconditions and effects of actions can be arbitrary KD45n formulas, and the solution is an action tree branching on sensing results. In this framework, the progression of KBs w.r.t. actions is achieved through the operation of belief revision or update on KD45n formulas, that is, higher-order belief revision or update. To support efficient reasoning and progression, we make use of a normal form for KD45n called alternating cover disjunctive formulas (ACDFs). We propose reasoning, revision and update algorithms for ACDFs. Based on these algorithms, adapting the PrAO algorithm for contingent planning from the literature, we implemented a multi-agent epistemic planner called MEPK. Our experimental results show the viability of our approach.

Structured argumentation dynamics

This paper develops a logical theory that unifies all three standard types of argumentative attack in AI, namely rebutting, undercutting and undermining attacks. We build on default justification logic that already represents undercutting and rebutting attacks, and we add undermining attacks. Intuitively, undermining does not target default inference, as undercutting, or default conclusion, as rebutting, but rather attacks an argument’s premise as a starting point for default reasoning. In default justification logic, reasoning starts from a set of premises, which is then extended by conclusions that hold by default. We argue that modeling undermining defeaters in the view of default theories requires changing the set of premises upon receiving new information. To model changes to premises, we give a dynamic aspect to default justification logic by using the techniques from the logic of belief revision. More specifically, undermining is modeled with belief revision operations that include contracting a set of premises, that is, removing some information from it. The novel combination of default reasoning and belief revision in justification logic enriches both approaches to reasoning under uncertainty. By the end of the paper, we show some important aspects of defeasible argumentation in which our logic compares favorably to structured argumentation frameworks.

Do Stronger Wise‐Thinking Dispositions Facilitate Auditors' Objective Evaluation of Evidence When Assessing and Addressing Fraud Risk?*

ABSTRACTThe objective evaluation of evidence is imperative for audit effectiveness and the proper exercise of professional skepticism. However, numerous studies suggest that auditors fail to evaluate evidence objectively when assessing or addressing the risk of material misstatement due to fraud. We develop theory to predict that auditors do evaluate evidence objectively but only when they have stronger wise‐thinking dispositions (WTDs), a construct that is new to the audit literature. We define WTDs as the tendency of individuals to naturally engage in the balanced revision of beliefs and doubts about target phenomena by thinking openly and reflectively about evidence. We report prediction‐consistent results from two experiments that measure the strength of participants' WTDs and manipulate whether the underlying evidence is less or more indicative of fraud. The experimental results also document that auditors vary considerably in WTD strength and collectively demonstrate the reproducibility of audit judgment‐quality benefits of stronger WTDs. We further validate the WTD construct in auditing using confirmatory bi‐factor analyses to show that it has one higher‐order general factor along with several subfactors. Overall, our theory and results advance the literature by identifying WTDs as a determinant of auditors' ability to objectively evaluate evidence. In addition, our findings have implications for standard setters and audit firms as quality control standards and audit working paper review processes might benefit from revisions that take into account that auditors do not objectively evaluate evidence unless they have stronger WTDs.

How negative mood hinders belief updating in depression: results from two experimental studies.

In two experimental studies, we tested the hypothesis that negative mood would hinder the revision of negative beliefs in response to unexpectedly positive information in depression, whereas positive mood was expected to enhance belief updating. In study 1 (N = 101), we used a subclinical sample to compare the film-based induction of sad v. happy mood with a distraction control group. Subsequently, participants underwent a well-established paradigm to examine intra-individual changes in performance-related expectations after unexpectedly positive performance feedback. In study 2, we applied the belief-updating task from study 1 to an inpatient sample (N = 81) and induced sad v. happy mood via film-clips v. recall of autobiographic events. The results of study 1 showed no significant group differences in belief updating; the severity of depressive symptoms was a negative predictor of belief revision, though, and there was a non-significant trend suggesting that the presence of sad mood hindered belief updating in the subgroup of participants with a diagnosed depressive episode. Study 2 revealed that participants updated their expectations significantly less in line with positive feedback when they underwent the induction of negative mood prior to feedback, relative to positive mood. By indicating that the presence of negative mood can hinder the revision of negative beliefs in clinically depressed people, our findings suggest that learning from new experiences can be hampered if state negative mood is activated. Thus, interventions relying on learning from novel positive experiences should aim at reducing state negative mood in depression.

Belief-Driven Pathfinding through Personalized Map Abstraction

We investigate the case of belief-driven pathfinding (BDP) according to which characters hold a personalized account of a dynamic changing game-world. BDP is concerned with maintaining and revising a set of beliefs that persists over time as a character navigates to subsequent target destinations. This allows for a differentiation among characters with different observations in the game and can provide better believability. We present BGCA*, a practical BDP approach that is based on (i) decomposing the map into regions, (ii) using personalized beliefs per character about the connectivity of regions, and (iii) employing a regular pathfinding component as a service. We evaluate BGCA* in terms of computational effort and precision wrt a regular solver over several benchmark maps. Our results motivate a simple belief revision strategy that induces small overhead and amortizes effort spent toward precision.

Conceptual Learning and Local Incommensurability: A Dynamic Logic Approach

In recent decades, the logical study of rational belief dynamics has played an increasingly important role in philosophy. However, the dynamics of concepts such as conceptual learning received comparatively little attention within this debate. This is problematic insofar as the occurrence of conceptual change (especially in the sciences) has been an influential argument against a merely logical analysis of beliefs. Especially Kuhn’s ideas about the incommensurability, i.e., untranslatability, of succeeding theories seem to stand in the way of logical reconstruction. This paper investigates conceptual change as model-changing operations similar to belief revision and relates it to the notion of incommensurability. I consider several versions of conceptual change and discuss their influences on the expressive power, translatability and the potential arising of incommensurability. The paper concludes with a discussion of animal taxonomy in Aristotle’s and Linnaeus’s work.