The need to explain

How do reasoners deal with inconsistencies? James (1907) believed that the rational solution is to revise your beliefs and to do so in a minimal way. We propose an alternative: You explain the origins of an inconsistency, which has the side effect of a revision to your beliefs. This hypothesis predicts that individuals should spontaneously create explanations of inconsistencies rather than refute one of the assertions and that they should rate explanations as more probable than refutations. A pilot study showed that participants spontaneously explain inconsistencies when they are asked what follows from inconsistent premises. In three subsequent experiments, participants were asked to compare explanations of inconsistencies against minimal refutations of the inconsistent premises. In Experiment 1, participants chose which conclusion was most probable; in Experiment 2 they rank ordered the conclusions based on their probability; and in Experiment 3 they estimated the mean probability of the conclusions' occurrence. In all three studies, participants rated explanations as more probable than refutations. The results imply that individuals create explanations to resolve an inconsistency and that these explanations lead to changes in belief. Changes in belief are therefore of secondary importance to the primary goal of explanation.     

Non-Prioritized Ranked Belief Change

Traditional accounts of belief change have been criticized for placing undue emphasis on the new belief provided as input. A recent proposal to address such issues is a framework for non-prioritized belief change based on default theories (Ghose and Goebel, 1998). A novel feature of this approach is the introduction of disbeliefs alongside beliefs which allows for a view of belief contraction as independently useful, instead of just being seen as an intermediate step in the process of belief revision. This approach is, however, restrictive in assuming a linear ordering of reliability on the received inputs. In this paper, we replace the linear ordering with a preference ranking on inputs from which a total preorder on inputs can be induced. This extension brings along with it the problem of dealing with inputs of equal rank. We provide a semantic solution to this problem which contains, as a special case, AGM belief change on closed theories.     

Towards a “Sophisticated” Model of Belief Dynamics. Part I: The General Framework

It is well-known that classical models of belief are not realistic representations of human doxastic capacity; equally, models of actions involving beliefs, such as decisions based on beliefs, or changes of beliefs, suffer from a similar inaccuracies. In this paper, a general framework is presented which permits a more realistic modelling both of instantaneous states of belief, and of the operations involving them. This framework is motivated by some of the inadequacies of existing models, which it overcomes, whilst retaining technical rigour in so far as it relies on known, natural logical and mathematical notions. The companion paper (Towards a “sophisticated” model of belief dynamics. Part II) contains an application of this framework to the particular case of belief revision. Presented by Hannes Leitgeb     

Stratified Belief Bases Revision with Argumentative Inference

We propose a revision operator on a stratified belief base, i.e., a belief base that stores beliefs in different strata corresponding to the value an agent assigns to these beliefs. Furthermore, the operator will be defined as to perform the revision in such a way that information is never lost upon revision but stored in a stratum or layer containing information perceived as having a lower value. In this manner, if the revision of one layer leads to the rejection of some information to maintain consistency, instead of being withdrawn it will be kept and introduced in a different layer with lower value. Throughout this development we will follow the principle of minimal change, being one of the important principles proposed in belief change theory, particularly emphasized in the AGM model. Regarding the reasoning part from the stratified belief base, the agent will obtain the inferences using an argumentative formalism. Thus, the argumentation framework will decide which information prevails when sentences of different layers are used for entailing conflicting beliefs. We will also illustrate how inferences are changed and how the status of arguments can be modified after a revision process.     

Coherence and Conservatism in the Dynamics of Belief

In this paper I discuss the foundations of a formal theory of coherent and conservative belief change that is (a) suitable to be used as a method for constructing iterated changes of belief, (b) sensitive to the history of earlier belief changes, and (c) independent of any form of dispositional coherence. I review various ways to conceive the relationship between the beliefs actually held by an agent and her belief change strategies (that also deal with potential belief sets), show the problems they suffer from, and suggest that belief states should be represented by unary revision functions that take sequences of inputs. Three concepts of coherence implicit in current theories of belief change are distinguished: synchronic, diachronic and dispositional coherence. Diachronic coherence is essentially identified with what is known as conservatism in epistemology. The present paper elaborates on the philosophical motivation of the general framework; formal details and results are provided in a companion paper.     

Belief and Self‐consciousness

Abstract

This paper is about what is distinctive about first‐person beliefs. I discuss several sets of puzzling cases of first‐person belief. The first focus on the relation between belief and action, while the second focus on the relation of belief to subjectivity. I argue that in the absence of an explanation of the dispositional difference, individuating such beliefs more finely than truth conditions merely marks the difference. I argue that the puzzles reveal a difference in the ways that I am disposed to revise my beliefs about myself. This point develops the insight that Anscombe and others had that those of an agent’s beliefs about himself that manifest that special self‐consciousness are not based on observation, testimony or inference. The puzzles show that this kind of self‐consciousness involves, not a special kind of belief or even a special kind of self‐reference, but a special kind of belief revision policy.     

Masculinity,Femininity, and Reported Paranormal Beliefs

Previous research has found that women are more likely than men to report belief in nonmaterial paranormal phenomena (e.g., psychics). There are inconsistent findings about whether men are more likely than women to report belief in material paranormal phenomena (e.g., bigfoot/sasquatch), and no prior survey research has examined gender expression (as masculine or feminine) as it relates to paranormal beliefs. This paper asks: How do gender identity and gender expression relate to reported paranormal beliefs? It answers this question using a large sample (n = 2504) of Canadians. Femininity helps explain differences between cisgender women and men on reported beliefs about foreseeing the future and telekinesis, but less so about reported belief in ghosts. Intriguingly, reported gender atypicality is associated with reported belief in all paranormal phenomena among cisgender women and among cisgender men. The results highlight the importance of measuring gender expression for beliefs that science cannot verify.     

Grounded spatial belief revision

Beliefs frequently undergo revisions, especially when new pieces of information are true but inconsistent with current beliefs. In previous studies, we showed that linguistic asymmetries provided by relational statements, play a crucial role in spatial belief revision. Located objects (LO) are preferably revised compared to reference objects (RO), known as the LO-principle. Here we establish a connection between spatial belief revision and grounded cognition. In three experiments, we explored whether imagined physical object properties influence which object is relocated and which remains at its initial position. Participants mentally revised beliefs about the arrangements of objects which could be envisaged as light and heavy (Experiment 1), small and large (Experiment 2), or movable and immovable (Experiment 3). The results show that intrinsic object properties are differently taken into account during spatial belief revision. Object weight did not alter the LO-principle (Experiment 1), whereas object size was found to influence which object was preferably relocated (Experiment 2). Object movability did not affect relocation preferences but had an effect on relocation durations (Experiment 3). The findings support the simulation hypothesis within the grounded cognition approach and create new connections between the spatial mental model theory of reasoning and the idea of grounded cognition.     

Reapproaching Ramsey: Conditionals and Iterated Belief Change in the Spirit of AGM

According to the Ramsey Test, conditionals reflect changes of beliefs: α?>?β is accepted in a belief state iff β is accepted in the minimal revision of it that is necessary to accommodate α. Since Gärdenfors’s seminal paper of 1986, a series of impossibility theorems (“triviality theorems”) has seemed to show that the Ramsey test is not a viable analysis of conditionals if it is combined with AGM-type belief revision models. I argue that it is possible to endorse that Ramsey test for conditionals while staying true to the spirit of AGM. A main focus lies on AGM’s condition of Preservation according to which the original belief set should be fully retained after a revision by information that is consistent with it. I use concrete representations of belief states and (iterated) revisions of belief states as semantic models for (nested) conditionals. Among the four most natural qualitative models for iterated belief change, two are identified that indeed allow us to combine the Ramsey test with Preservation in the language containing only flat conditionals of the form α?>?β. It is shown, however, that Preservation for this simple language enforces a violation of Preservation for nested conditionals of the form α?>?(β?>?γ). In such languages, no two belief sets are ordered by strict subset inclusion. I argue that it has been wrong right from the start to expect that Preservation holds in languages containing nested conditionals.     

Revocable Belief Revision

Krister Segerberg proposed irrevocable belief revision, to be contrasted with standard belief revision, in a setting wherein belief of propositional formulas is modelled explicitly. This suggests that in standard belief revision is revocable: one should be able to unmake (‘revoke’) the fresh belief in the revision formula, given yet further information that contradicts it. In a dynamic epistemic logical setting for belief revision, for multiple agents, we investigate what the requirements are for revocable belief revision. By this we not merely mean recovering belief in non-modal propositions, as in the recovery principle for belief contraction, but recovering belief in modal propositions: beliefs about beliefs. These requirements are almost never met, a surprising result.     

Minimal Belief Change and the Pareto Principle

This paper analyzes the notion of a minimal belief change that incorporates new information. I apply the fundamental decision-theoretic principle of Pareto-optimality to derive a notion of minimal belief change, for two different representations of belief: First, for beliefs represented by a theory – a deductively closed set of sentences or propositions – and second for beliefs represented by an axiomatic base for a theory. Three postulates exactly characterize Pareto-minimal revisions of theories, yielding a weaker set of constraints than the standard AGM postulates. The Levi identity characterizes Pareto-minimal revisions of belief bases: a change of belief base is Pareto-minimal if and only if the change satisfies the Levi identity (for “maxichoice” contraction operators). Thus for belief bases, Pareto-minimality imposes constraints that the AGM postulates do not. The Ramsey test is a well-known way of establishing connections between belief revision postulates and axioms for conditionals (“if p, then q”). Pareto-minimal theory change corresponds exactly to three characteristic axioms of counterfactual systems: a theory revision operator that satisfies the Ramsey test validates these axioms if and only if the revision operator is Pareto-minimal. This revised version was published online in June 2006 with corrections to the Cover Date.     

Scientific reasoning in a real‐world context: The effect of prior belief and outcome on children's hypothesis‐testing strategies

The impact of event outcome and prior belief on scientific reasoning was investigated within a real‐world oral health context. Participants (N= 144; ranging from 3 to 11 years) were given hypothesis‐testing tasks and asked to explain their answers. Participants were presented with information that was either consistent or inconsistent with their own beliefs. Each task consisted of scenarios in which the outcome was either good or bad oral health. When the information was belief consistent and the outcome was good, or when the information was belief inconsistent and the outcome was bad, children were more likely to choose scientifically appropriate tests of the stated hypothesis (i.e. manipulate only one variable). Evidence‐based explanations were associated with scientifically appropriate choices in the good‐outcome, belief‐inconsistent scenario and the belief‐consistent, bad‐outcome scenario. Participants' performance on these tasks is explained by considering the plausibility of causal variables. A control of variables strategy was used to test hypotheses in cases in which the evidence was consistent with participants' beliefs and knowledge of causal mechanisms. In contrast, when the evidence was inconsistent with participants' beliefs, children chose to manipulate behaviours likely to lead to a positive health outcome. These findings demonstrate that context and prior knowledge interact to play an important role in children's scientific reasoning.     

Keep Changing Your Beliefs, Aiming for the Truth

We investigate the process of truth-seeking by iterated belief revision with higher-level doxastic information. We elaborate further on the main results in Baltag and Smets (Proceedings of TARK, 2009a, Proceedings of WOLLIC’09 LNAI 5514, 2009b), applying them to the issue of convergence to truth. We study the conditions under which the belief revision induced by a series of truthful iterated upgrades eventually stabilizes on true beliefs. We give two different conditions ensuring that beliefs converge to “full” (complete) truth, as well as a condition ensuring only that they converge to true (but not necessarily complete) beliefs.     

Preface Writers are Consistent

The preface paradox does not show that it can be rational to have inconsistent beliefs, because preface writers do not have inconsistent beliefs. I argue, first, that a fully satisfactory solution to the preface paradox would have it that the preface writer's beliefs are consistent. The case here is on basic intuitive grounds, not the consequence of a theory of rationality or of belief. Second, I point out that there is an independently motivated theory of belief – sensitivism – which allows such a solution. I sketch a sensitivist account of the preface writer's (consistent) doxastic state.     

Bounded Revision: Two-Dimensional Belief Change Between Conservative and Moderate Revision

This paper presents the model of ‘bounded revision’ that is based on two-dimensional revision functions taking as arguments pairs consisting of an input sentence and a reference sentence. The key idea is that the input sentence is accepted as far as (and just a little further than) the reference sentence is ‘cotenable’ with it. Bounded revision satisfies the AGM axioms as well as the Same Beliefs Condition (SBC) saying that the set of beliefs accepted after the revision does not depend on the reference sentence (although the posterior belief state does depend on it). Bounded revision satisfies the Darwiche–Pearl (DP) axioms for iterated belief change. If the reference sentence is fixed to be a tautology or a contradiction, two well-known one-dimensional revision operations result. Bounded revision thus naturally fills the space between conservative revision (also known as natural revision) and moderate revision (also known as lexicographic revision). I compare this approach to the two-dimensional model of ‘revision by comparison’ investigated by Fermé and Rott (Artif Intell 157:5–47, 2004) that satisfies neither the SBC nor the DP axioms. I conclude that two-dimensional revision operations add substantially to the expressive power of qualitative approaches that do not make use of numbers as measures of degrees of belief.     

Logical dynamics of belief change in the community

In this paper we explore the relationship between norms of belief revision that may be adopted by members of a community and the resulting dynamic properties of the distribution of beliefs across that community. We show that at a qualitative level many aspects of social belief change can be obtained from a very simple model, which we call ‘threshold influence’. In particular, we focus on the question of what makes the beliefs of a community stable under various dynamical situations. We also consider refinements and alternatives to the ‘threshold’ model, the most significant of which is to consider changes to plausibility judgements rather than mere beliefs. We show first that some such change is mandated by difficult problems with belief-based dynamics related to the need to decide on an order in which different beliefs are considered. Secondly, we show that the resulting plausibility-based account results in a deterministic dynamical system that is non-deterministic at the level of beliefs.     

Belief Revision And Epistemology

Postulational approaches attempt to understand the dynamics of belief revision by appealing to no more than the set of beliefs held by an agent and the logical relations between them. It is argued there that such an approach cannot work. A proper account of belief revision must also appeal to the arguments supporting beliefs, and recognize that those arguments can be defeasible. If we begin with a mature epistemological theory that accommodates this, it can be seen that the belief revision operators on which the postulational theories are based are ill-defined. It is further argued that there is no way to repair the definitions so as to retain the spirit of those theory. Belief revision is better studied from within an independently motivated epistemological theory.     

The need to explain

How do reasoners deal with inconsistencies? James (1907) believed that the rational solution is to revise your beliefs and to do so in a minimal way. We propose an alternative: You explain the origins of an inconsistency, which has the side effect of a revision to your beliefs. This hypothesis predicts that individuals should spontaneously create explanations of inconsistencies rather than refute one of the assertions and that they should rate explanations as more probable than refutations. A pilot study showed that participants spontaneously explain inconsistencies when they are asked what follows from inconsistent premises. In three subsequent experiments, participants were asked to compare explanations of inconsistencies against minimal refutations of the inconsistent premises. In Experiment 1, participants chose which conclusion was most probable; in Experiment 2 they rank ordered the conclusions based on their probability; and in Experiment 3 they estimated the mean probability of the conclusions' occurrence. In all three studies, participants rated explanations as more probable than refutations. The results imply that individuals create explanations to resolve an inconsistency and that these explanations lead to changes in belief. Changes in belief are therefore of secondary importance to the primary goal of explanation.     

Gricean Belief Change

One of the standard principles of rationality guiding traditional accounts of belief change is the principle of minimal change: a reasoner's belief corpus should be modified in a minimal fashion when assimilating new information. This rationality principle has stood belief change in good stead. However, it does not deal properly with all belief change scenarios. We introduce a novel account of belief change motivated by one of Grice's maxims of conversational implicature: the reasoner's belief corpus is modified in a minimal fashion to assimilate exactly the new information. In this form of belief change, when the reasoner revises by new information p ∨ q their belief corpus is modified so that p∨q is believed but stronger propositions like p∧q are not, no matter what beliefs are in the reasoner's initial corpus. We term this conservative belief change since the revised belief corpus is a conservative extension of the original belief corpus given the new information.     

Diagnostic reasoning with circumstantial evidence

Individuals often evaluate hypotheses about the cause of particular events on the basis of circumstantial evidence. This article describes a quantitative model of belief revision with circumstantial evidence. The model assumes that subjects revise belief on the basis of a cascaded reasoning process that combines beliefs about three premises—the association of a clue and a possible cause, and forward and backward implications of the clue—to revise belief in a causal hypothesis. Subjects in three experiments solved fictional murder mysteries, reporting on each trial a subset of the beliefs specified by the model. Experiment 1 demonstrates that the model provides a good account of the reasoning process, over several contexts in which clues are evaluated. Subjects appear to develop causal models that affect the interpretation of clues. Experiment 2 provides further evidence on the development of causal models and compares the present model with a model based on Bayes' theorem. Experiment 3 is a control experiment which demonstrates that the belief assessments used in Experiments 1 and 2 do not alter the process of belief revision. Tests of subjects' memory for suspect-clue associations provide further support for the hypothesis that subjects develop causal models of the true cause and demonstrate the contrast between reasoning with currently available information and retrospective access to the facts on which belief revision is based. The present view is compared with other theories of causal thinking and belief revision.