The problem of how to accommodate inconsistencies has attracted quite a number of researchers, in particular, in the area of database theory. The problem is also of concern in the study of belief change. For inconsistent beliefs are ubiquitous. However, comparatively little work has been devoted to discussing the problem in the literature of belief change. In this paper, I examine how adequate the AGM theory is as a logical framework for belief change (...) involving inconsistencies. The technique is to apply to Grove’s sphere system, a semantical representation of the AGM theory, logics that do not infer everything from contradictory premises, viz., paraconsistent logics. I use three paraconsistent logics and discuss three sphere systems that are based on them. I then examine the completeness of the postulates of the AGM theory with respect to the systems. At the end, I discuss some philosophical implications of the examination. (shrink)

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

We give a model for iterated belief change in multi-agent systems. The formal tool we use for this is a combination of modal and dynamic logic. Two core notions in our model are the expansion of the knowledge and beliefs of an agent, and the processing of new information. An expansion is defined as the change in the knowledge and beliefs of an agent when it decides to believe an incoming formula while holding on to its current (...) propositional beliefs. To prevent our agents from forming inconsistent beliefs they do not expand with every piece of information they receive. Instead, our agents remember their original beliefs and every piece of information they receive. After every receipt of information they decide which subset of the received information should be incorporated into their original beliefs. This procedure is called the processing of new information. We show that our model of belief update behaves in an intuitive way and that it is not sensitive to criticism on comparable models. (shrink)

This study examines the problem of belief revision, defined as deciding which of several initially accepted sentences to disbelieve, when new information presents a logical inconsistency with the initial set. In the first three experiments, the initial sentence set included a conditional sentence, a non‐conditional (ground) sentence, and an inferred conclusion drawn from the first two. The new information contradicted the inferred conclusion. Results indicated that conditional sentences were more readily abandoned than ground sentences, even when either choice would (...) lead to a consistent belief state, and that this preference was more pronounced when problems used natural language cover stories rather than symbols. The pattern of belief revision choices differed depending on whether the contradicted conclusion from the initial belief set had been a modus ponens or modus tollens inference. Two additional experiments examined alternative model‐theoretic definitions of minimal change to a belief state, using problems that contained multiple models of the initial belief state and of the new information that provided the contradiction. The results indicated that people did not follow any of four formal definitions of minimal change on these problems. The new information and the contradiction it offered was not, for example, used to select a particular model of the initial belief state as a way of reconciling the contradiction. The preferred revision was to retain only those initial sentences that had the same, unambiguous truth value within and across both the initial and new information sets. The study and results are presented in the context of certain logic‐based formalizations of belief revision, syntactic and model‐theoretic representations of belief states, and performance models of human deduction. Principles by which some types of sentences might be more “entrenched” than others in the face of contradiction are also discussed from the perspective of induction and theory revision. (shrink)

This study realizes belief/reliability change of a judge in a legal judgment by dynamic epistemic logic. A key feature of DEL is that possibilities in an agent’s belief can be represented by a Kripke model. This study addresses two difficulties in applying DEL to a legal case. First, since there are several methods for constructing a Kripke model, our question is how we can construct the model from a legal case. Second, since this study employs several dynamic (...) operators, our question is how we can decide which operators are to be applied for belief/reliability change of a judge. In order to solve these difficulties, we have implemented a computer system which provides two functions. First, the system can generate a Kripke model from a legal case. Second, the system provides an inconsistency solving algorithm which can automatically perform several operations in order to reduce the effort needed to decide which operators are to be applied. By our implementation, the above questions can be adequately solved. With our analysis method, six legal cases are analyzed to demonstrate our implementation. (shrink)

Reasoning and change over inconsistent knowledge bases is of utmost relevance in areas like medicine and law. Argumentation may bring the possibility to cope with both problems. Firstly, by constructing an argumentation framework from the inconsistent KB, we can decide whether to accept or reject a certain claim through the interplay among arguments and counterarguments. Secondly, by handling dynamics of arguments of the AF, we might deal with the dynamics of knowledge of the underlying inconsistent KB. (...) Dynamics of arguments has recently attracted attention and although some approaches have been proposed, a full axiomatization within the theory of belief revision was still missing. A revision arises when we want the argumentation semantics to accept an argument. Argument Theory Change encloses the revision operators that modify the AF by analyzing dialectical trees—arguments as nodes and attacks as edges—as the adopted argumentation semantics. In this article, we present a simple approach to ATC based on propositional KBs. This allows to manage change of inconsistent KBs by relying upon classical belief revision, although contrary to it, consistency restoration of the KB is avoided. Subsequently, a set of rationality postulates adapted to argumentation is given, and finally, the proposed model of change is related to the postulates through the corresponding representation theorem. Though we focus on propositional logic, the results can be easily extended to more expressive formalisms such as first-order logic and description logics, to handle evolution of ontologies. (shrink)

Isaac Levi has claimed that our reliance on the testimony of others, and on the testimony of the senses, commonly produces inconsistency in our set of full beliefs. This happens if what is reported is inconsistent with what we believe to be the case. Drawing on a conception of the role of beliefs in inquiry going back to Dewey, Levi has maintained that the inconsistent belief corpus is a state of ``epistemic hell'': it is useless as a (...) basis for inquiry and deliberation. As he has also noticed, the compatibility of these two elements of his pragmatist epistemology could be called into question. For if inconsistency means hell, how can it ever be rational to enter that state, and on what basis could we attempt to regain consistency? Levi, nonetheless, has tried to show that the conflict is only apparent and that no changes of his theory are necessary. In the main part of the paper I argue, by contrast, that his attempts to reconcile these components of his view are unsuccessful.The conflict is real andthus presents a genuine threat to Deweyan pragmatism, as understood by Levi. After an attempt to pinpoint exactly where the source of the problem lies, I explore some possibilities for how to come to grips with it. I conclude that Levi can keep his fundamental thesis concerning the role of beliefs in inquiry and deliberation, provided that he (i) gives up the view that the agent can legitimately escape from inconsistency, and (ii) modifies his account of prediction alias deliberate expansion by acknowledging a third desideratum, besides probability and informational value, namely, not to cause permanent breakdown further down the line of inquiry. The result is a position which is more similar to Peter Gärdenfors's than is Levi's original theory, while retaining the basic insights of the latter. (shrink)

Consistency is usually seen as one of the hallmarks and a cardinal virtue of moral theory, as well as of any defensible real-life moral perspective. In everyday life a consistent set of moral beliefs is conductive to moral clarity, communicability, responsibility and responsiveness. But this is just one side of the story. In this paper I argue that inconsistency, properly understood, is a productive and constructive aspect of both moral philosophy and our moral lives. After an introductory glance at Ralf (...) Waldo Emerson and Hannah Arendt, the argument proceeds in three main steps. First, I discuss the philosophical importance of paying heed to inconsistencies in our moral lives, which often are prematurely pruned from moral philosophy. Second, I discuss the positive moral roles of inconsistency in terms of responsiveness to different situations, values, needs and concerns that call upon our attention in everyday life. Third, I argue that moral inconsistencies contribute to the necessary adaptability of our moral understandings to changing conditions. Fourth, in the place of a conclusion, I revisit the issue of consistency, clarity and accountability. (shrink)

The main contribution of this dissertation is the development of a hyperintensional semantics for belief revision and a corresponding system of dynamic doxastic logic, with the intention of addressing various aspects of over-idealisation and the logical omniscience problem which repeatedly occurs in the literature on belief dynamics. The models introduced in Chapter 2 make up the core of this dissertation. The starting point in the development of these models is shifting the representational focus of doxastic models from (...) class='Hi'>belief sets to collections of information, and defining changes of beliefs as artifacts of changes of information. In this way, the current work is aimed at achieving a flexible and less idealised account of belief representation and belief change. This is done by accommodating object-linguistic belief change operators within a state-semantics for information dynamics, which results in suggesting a non-monotonic, hyperintensional and inconsistency tolerant belief dynamics. A number of important themes concerning belief dynamics result from these models, such as hyperintensionality, inconsistency-tolerance and deductive closure. In the rest of this dissertation, these themes are investigated in more detail, with the exception of Chapter 6. In particular, Chapter 3 aims for locating this work in the hyperintensionality literature, by presenting a comparative survey of various accounts of hyperintensional belief change, besides a brief history of the debate about hyperintensional meaning. Various comparison points arise from the analysis of these accounts, in particular between possible worlds and state-semantics representations of hyperintensional belief revision, which are discussed in detail in Section 3.3. The latter themes mentioned above, namely inconsistency-tolerance and deductive closure are first investigated under the umbrella of fragmentation of belief states. The debate on fragmented beliefs is focused on the requirements of deductive closure and consistency imposed on belief sets, and how these lead to the problem of logical omniscience. The review of the literature shows various modeling solutions to the problem, Chapter 4 is then aimed at locating the current work in this literature. The issue of inconsistency-tolerance reoccurs in Chapter 5, in relation to consistency-sensitive epistemic modalities. In this part of the dissertation, two new epistemic modalities are investigated. A consistency-sensitive evidence modality picks out the consistent parts of an otherwise inconsistent collection of information, by distinguishing trusted sources of information. A consistency-sensitive safe belief modality then determines a set of persistent beliefs based on evidence. While the models introduced here are heavily inspired by the presentation in Chapter 2, they exhibit various differences due to the choice of the underlying semantics. Finally, Chapter 6 steers the discussion towards another direction. Here, the models developed in Chapter 2 are reinterpreted and applied to represent a special form of conceptual change. The aim of this application is to suggest these models as a bridging component between theories of belief revision and of scientific change. In particular, it is proposed that a belief-revision-like system can be used to mirror radical types of conceptual change that might occur as part of scientific revolutions. It is not surprising that belief revision and scientific theory revision are strikingly similar, given that both can be understood as corpus of information and inferences (or hypothesis). The parallel between the two is manifested in this chapter, also by the translation of belief revision postulates into rationality postulates for conceptual change in Section 6.4. (shrink)

The empirical study of belief is emerging at a rapid clip, uniting work from all corners of cognitive science. Reliance on belief in understanding and predicting behavior is widespread. Examples can be found, inter alia, in the placebo, attribution theory, theory of mind, and comparative psychological literatures. Research on belief also provides evidence for robust generalizations, including about how we fix, store, and change our beliefs. Evidence supports the existence of a Spinozan system of belief (...) fixation: one that is automatic and independent of belief rejection. Independent research supports the existence of a system of fragmented belief storage: one that relies on large numbers of causally isolated, context-sensitive stores of belief in memory. Finally, empirical and observational data support at least two systems of belief change. One system adheres, mostly, to epistemological norms of updating; the other, the psychological immune system, functions to guard our most centrally held beliefs from potential inconsistency with newly formed beliefs. Refining our under- standing of these systems can shed light on pressing real-world issues, such as how fake news, propaganda, and brainwashing exploit our psychology of belief, and how best to construct our modern informational world. (shrink)

There is a principle in things, about which we cannot be deceived, but must always, on the contrary, recognize the truth – viz. that the same thing cannot at one and the same time be and not be": with these words of the Metaphysics, Aristotle introduced the Law of Non-Contradiction, which was to become the most authoritative principle in the history of Western thought. However, things have recently changed, and nowadays various philosophers, called dialetheists, claim that this Law does not (...) hold unrestrictedly – that in peculiar circumstances the same thing may at the same time be and not be, and contradictions may obtain in the world. This book opens with an examination of the famous logical paradoxes that appear to speak on behalf of contradictions (e.g., the Liar paradox, the set-theoretic paradoxes such as Cantor’s and Russell’s), and of the reasons for the failure of the standard attempts to solve them. It provides, then, an introduction to paraconsistent logics – non-classical logics in which the admission of contradictions does not lead to logical chaos –, and their astonishing applications, going from inconsistent data base management to contradictory arithmetics capable of circumventing Gödel’s celebrated Incompleteness Theorem. The final part of the book discusses the philosophical motivations and difficulties of dialetheism, and shows how to extract from Aristotle’s ancient words a possible reply to the dialetheic challenge. How to Sell a Contradiction will appeal to anyone interested in non-classical logics, analytic metaphysics, and philosophy of mathematics, and especially to those who consider challenging our most entrenched beliefs the main duty of philosophical inquiry. (shrink)

C.S. Peirce's and Isaac Levi's accounts of the belief-doubt-belief model are discussed and evaluated. It is argued that the contemporary study of belief change has metamorphosed into a branch of philosophical logic where empirical considerations have become obsolete. A case is made for reformulations of belief change systems that do allow for empirical tests. Last, a belief change system is presented that (1) uses finite representations of information, (2) can adequately deal with (...) inconsistencies, (3) has finite operations of change, (4) can do without extra-logical elements, and (5) only licenses consistent beliefs. (shrink)

We further develop the formal foundations of Paraconsistent Belief Revision (PBR) by introducing Logics of Formal Inconsistency (_LFI_s) specifically designed to support the development of epistemic entrenchment-based models for belief change. The interpretation of formal consistency—and, more broadly, of paraconsistency—in terms of the epistemic attitudes adopted by rational agents and of these agents reasoning with potentially contradictory yet non-trivial epistemic states, respectively, is already well-established within the literature on PBR based on LFIs. However, previous approaches faced a (...) key limitation: the absence of replacement in most LFIs prevented the construction of entrenchment-based operations. We address this gap by first revisiting and systematizing core properties essential for such modeling, formalizing them within _Cbr_, a previously introduced logic whose foundational properties we now examine and develop in depth. Building on this, we introduce _RCbr_, a replacement-enriched, self-extensional extension of _Cbr_, which makes it possible—within an _LFI_-based framework—to formally define epistemic entrenchment and to construct entrenchment-based belief revision mechanisms. This development enables a fully constructive approach to Belief Revision in paraconsistent settings, further advancing the theoretical treatment of _LFI_s and paraconsistency within the broader landscape of epistemic states and belief dynamics. (shrink)

Through examples of embodied and learning-centered pedagogy, we discuss transformative learning of transgressive topics. We begin with a taxonomy of types of learning our students undergo as they resolve inconsistencies among their pre-existing beliefs and the material they confront in our course on feminist ethics and epistemology. We then discuss ways to help students maximize their learning while confronting internal inconsistencies. While we focus on feminist topics, our approach is broad enough to be relevant to anyone teaching a transgressive or (...) controversial topic. (shrink)

The main contribution of this dissertation is the development of a hyperintensional semantics for belief revision and a corresponding system of dynamic doxastic logic, with the intention of addressing various aspects of over-idealisation and the logical omniscience problem which repeatedly occurs in the literature on belief dynamics. The models introduced in Chapter 2 make up the core of this dissertation. The starting point in the development of these models is shifting the representational focus of doxastic models from (...) class='Hi'>belief sets to collections of information, and defining changes of beliefs as artifacts of changes of information. In this way, the current work is aimed at achieving a flexible and less idealised account of belief representation and belief change. This is done by accommodating object-linguistic belief change operators within a state-semantics for information dynamics, which results in suggesting a non-monotonic, hyperintensional and inconsistency tolerant belief dynamics. A number of important themes concerning belief dynamics result from these models, such as hyperintensionality, inconsistency-tolerance and deductive closure. In the rest of this dissertation, these themes are investigated in more detail, with the exception of Chapter 6. In particular, Chapter 3 aims for locating this work in the hyperintensionality literature, by presenting a comparative survey of various accounts of hyperintensional belief change, besides a brief history of the debate about hyperintensional meaning. Various comparison points arise from the analysis of these accounts, in particular between possible worlds and state-semantics representations of hyperintensional belief revision, which are discussed in detail in Section 3.3. The latter themes mentioned above, namely inconsistency-tolerance and deductive closure are first investigated under the umbrella of fragmentation of belief states. The debate on fragmented beliefs is focused on the requirements of deductive closure and consistency imposed on belief sets, and how these lead to the problem of logical omniscience. The review of the literature shows various modeling solutions to the problem, Chapter 4 is then aimed at locating the current work in this literature. The issue of inconsistency-tolerance reoccurs in Chapter 5, in relation to consistency-sensitive epistemic modalities. In this part of the dissertation, two new epistemic modalities are investigated. A consistency-sensitive evidence modality picks out the consistent parts of an otherwise inconsistent collection of information, by distinguishing trusted sources of information. A consistency-sensitive safe belief modality then determines a set of persistent beliefs based on evidence. While the models introduced here are heavily inspired by the presentation in Chapter 2, they exhibit various differences due to the choice of the underlying semantics. Finally, Chapter 6 steers the discussion towards another direction. Here, the models developed in Chapter 2 are reinterpreted and applied to represent a special form of conceptual change. The aim of this application is to suggest these models as a bridging component between theories of belief revision and of scientific change. In particular, it is proposed that a belief-revision-like system can be used to mirror radical types of conceptual change that might occur as part of scientific revolutions. It is not surprising that belief revision and scientific theory revision are strikingly similar, given that both can be understood as corpus of information and inferences (or hypothesis). The parallel between the two is manifested in this chapter, also by the translation of belief revision postulates into rationality postulates for conceptual change in Section 6.4. (shrink)

This chapter considers the notion of an inconsistent concept. Previous chapters have argued that—despite its name—conceptual engineering has no use for concepts. However, a number of conceptual engineers give a central role to the idea that certain concepts are inconsistent. One might think that because it has no role for concepts the author’s theory will be unable to speak to the concerns of such conceptual engineers. The aim in this chapter is to respond to this line of thought, (...) by explaining why such engineers (incorrectly) appeal to inconsistent concepts. In order to explain this notion, it appeals to three ideas: i) inconsistent beliefs or conceptions, ii) inconsistent introductory events, and iii) metasemantic messiness. It then compares this approach with that of philosophers who want to use conceptual engineering to solve paradoxes. (shrink)

Through examples of embodied and learning -centered pedagogy, we discuss transformative learning of transgressive topics. We begin with a taxonomy of types of learning our students undergo as they resolve inconsistencies among their pre-existing beliefs and the material they confront in our course on feminist ethics and epistemology. We then discuss ways to help students maximize their learning while confronting internal inconsistencies. While we focus on feminist topics, our approach is broad enough to be relevant to anyone teaching a transgressive (...) or controversial topic. (shrink)

I propose a novel hyperintensional semantics for belief revision and a corresponding system of dynamic doxastic logic. The main goal of the framework is to reduce some of the idealisations that are common in the belief revision literature and in dynamic epistemic logic. The models of the new framework are primarily based on potentially incomplete or inconsistent collections of information, represented by situations in a situation space. I propose that by shifting the representational focus of doxastic models (...) from belief sets to collections of information, and by defining changes of beliefs as artifacts of changes of information, we can achieve a more realistic account of belief representation and belief change. The proposed dynamic operation suggests a non-classical way of changing beliefs: belief revision occurs in non-explosive environments which allow for a non-monotonic and hyperintensional belief dynamics. A logic that is sound with respect to the semantics is also provided. (shrink)

The process of completing, correcting and prioritising specifications is an essential but very complex task for the maintenance and improvement of software systems. The preservation of functionalities and the ability to accommodate changes are main objectives of the software development cycle to guarantee system reliability. Logical theories able to fully model such processes are still insufficient. In this paper we propose a full formalisation of such operations on software systems inspired by the Alchourrón–Gärdenfors–Makinson paradigm for belief revision of human (...) epistemic states. We represent specifications as finite sets of formulas equipped with a priority relation that models functional entrenchment of properties. We propose to handle specification incompleteness through ordered expansion, inconsistency through ordered safe contraction and prioritisation through revision with reordering, and model all three in an algorithmic fashion. We show how the system satisfies basic properties of the AGM paradigm, including Levi’s and Harper’s identities. We offer a concrete example and complexity results for the inference and model checking problems on revision. We conclude by describing resilience and evolvability of software systems based on such revision operators. (shrink)

"Paraconsistent Belief Revision Based on a Formal Consistency Operator" delves into Belief Revision—a significant area of research in Formal Philosophy that uses logic to model the ways in which human and artificial agents modify their beliefs in response to new information and examines how these changes can be considered rational. -/- Originally authored as a PhD thesis (previously published in Portuguese), this work provides a novel epistemic interpretation of Paraconsistency through Paraconsistent Belief Revision systems. It explores the (...) concept of paraconsistency from the standpoint of epistemic attitudes of acceptance and rejection. -/- This work challenges the traditional notion that accepting a new belief requires retracting its negation from the current epistemic state. The author contends that such reflexive retraction goes against the principle of informational economy, which is a crucial aspect of rationality in the context of belief change. Consequently, the phenomenon of paraconsistency is further examined from this fresh perspective of belief change, shedding light on the complexities of the Logics of Formal Inconsistency (LFIs). These LFIs provide the foundational logic, offering a comprehensive framework for understanding and implementing paraconsistent principles within belief revision systems. -/- This thesis was supervised by Marcelo Esteban Coniglio and co-supervised by Márcio Moretto Ribeiro, as part of Rafael Rodrigues Testa's doctoral studies at the University of Campinas (Unicamp), Brazil. (shrink)

Agents need to be able to change their beliefs; in particular, they should be able to contract or remove a certain belief in order to restore consistency to their set of beliefs, and revise their beliefs by incorporating a new belief which may be inconsistent with their previous beliefs. An influential theory of belief change proposed by Alchourron, G¨ardenfors and Makinson (AGM) [1] describes postulates which a rational belief revision and contraction operations should (...) satisfy. The AGM postulates have been perceived as characterising idealised rational reasoners, and the corresponding belief change operations are considered unsuitable for implementable agents due to their high computational cost [3]. The main result of this paper is showing that an efficient (linear time) belief contraction operation nevertheless satisfies all but one of the AGM postulates for contraction. This contraction operation is defined for a realistic rule-based agent which can be seen as a reasoner in a very weak logic; although the agent’s beliefs are deductively closed with respect to this logic, checking consistency and tracing dependencies between beliefs is not computationally expensive. Finally, we give a non-standard definition of belief revision in terms of contraction for our agent. (shrink)

The AGM (Alchourrón-Gärdenfors-Makinson) model of belief change is extended to cover changes on sets of beliefs that are not closed under logical consequence (belief bases). Three major types of change operations, namely contraction, internal revision, and external revision are axiomatically characterized, and their interrelations are studied. In external revision, the Levi identity is reversed in the sense that one first adds the new belief to the belief base, and afterwards contracts its negation. It is (...) argued that external revision represents an intuitively plausible way of revising one's beliefs. Since it typically involves the temporary acceptance of an inconsistent set of beliefs, it can only be used in belief representations that distinguish between different inconsistent sets of belief. (shrink)

In our approach credibility of information plays an importantrole in modeling of both belief state and belief change [4]. It turns out thatthe credibility-based consequence operators used to define the notion of beliefstate tolerate inconsistency under some conditions.

What is the role of equality in the evaluation of populations of different sizes in respect to their goodness? The field of population ethics has been riddled with paradoxes which purport to show that our considered beliefs are inconsistent in cases where the number of people and their welfare varies. Parfit's well-known Mere Addition Paradox is a case in point. These paradoxes challenge at a fundamental level the existence of a satisfactory theory of our duties to future generations and (...) intergenerational justice. This chapter discusses whether egalitarian concerns can help us solve these paradoxes. It is claimed that whereas egalitarian considerations are applicable in different number cases and can help us solve the Mere Addition Paradox, such considerations are not of much help in another paradox. The implications of the Priority View in different number cases are also examined. (shrink)

On Hume’s account of motivation, beliefs and desires are very different kinds of propositional attitudes. Beliefs are cognitive attitudes, desires emotive ones. An agent’s belief in a proposition captures the weight he or she assigns to this proposition in his or her cognitive representation of the world. An agent’s desire for a proposition captures the degree to which he or she prefers its truth, motivating him or her to act accordingly. Although beliefs and desires are sometimes entangled, they play (...) very different roles in rational agency. In two classic papers (Lewis 1988, 1996), David Lewis discusses several challenges to this Humean picture, but ultimately rejects them. We think that his discussion of a central anti-Humean alternative – the desire-as-belief thesis – is in need of refinnement. On this thesis, the desire for proposition p is given by the belief that p is desirable. Lewis claims that ‘[e]xcept in trivial cases, [this thesis] collapses into contradiction’(Lewis 1996, p. 308). The problem, he argues, is that the thesis is inconsistent with the purportedly plausible requirement that one’s desire for a proposition should not change upon learning that the proposition is true; call this the invariance requirement. In this paper, we revisit Lewis’s argument. We show that, if one carefully distinguishes between non-evaluative and evaluative propositions, the desire-asbelief thesis can be rendered consistent with the invariance requirement. Lewis’s conclusion holds only under certain conditions: the desire-as-belief thesis conflicts with the invariance requirement if and only if there are certain correlations between non-evaluative and evaluative propositions. But when there are such correlations, we suggest, the invariance requirement loses its plausibility. Thus Lewis’s argument against the desire-as-belief thesis appears to be valid only in cases in which it is unsound. (shrink)

People use commonsense science knowledge to flexibly explain, predict, and manipulate the world around them, yet we lack computational models of how this commonsense science knowledge is represented, acquired, utilized, and revised. This is an important challenge for cognitive science: Building higher order computational models in this area will help characterize one of the hallmarks of human reasoning, and it will allow us to build more robust reasoning systems. This paper presents a novel assembled coherence theory of human conceptual (...) class='Hi'>change, whereby people revise beliefs and mental models by constructing and evaluating explanations using fragmentary, globally inconsistent knowledge. We implement AC theory with Timber, a computational model of conceptual change that revises its beliefs and generates human-like explanations in commonsense science. Timber represents domain knowledge using predicate calculus and qualitative model fragments, and uses an abductive model formulation algorithm to construct competing explanations for phenomena. Timber then scores competing explanations with respect to previously accepted beliefs, using a cost function based on simplicity and credibility, identifies a low-cost, preferred explanation and accepts its constituent beliefs, and then greedily alters previous explanation preferences to reduce global cost and thereby revise beliefs. Consistency is a soft constraint in Timber; it is biased to select explanations that share consistent beliefs, assumptions, and causal structure with its other, preferred explanations. In this paper, we use Timber to simulate the belief changes of students during clinical interviews about how the seasons change. We show that Timber produces and revises a sequence of explanations similar to those of the students, which supports the psychological plausibility of AC theory. (shrink)

The principle of belief persistence, or conservativity principle, states that ’\Nhen changing beliefs in response to new evidence, you should continue to believe as many of the old beliefs as possible' (Harman, 1986, p. 46). In particular, this means that if an individual gets new information, she has to accommodate it in her new belief set (the set of propositions she believes), and, if the new information is not inconsistent with the old belief set, then (1) (...) the individual has to maintain all the beliefs she previously had and (2) the change should be minimal in the sense that every proposition in the new belief set must be deducible from the union of the old belief set and the new information (see, e.g., Gardenfors, 1988; Stalnaker, 1984). We focus on this minimal notion of belief persistence and characterize it both semantically and syntactically. A ’possible world' semantic formalization of the principle easily comes to mind. The set of all the propositions that the individual believes corresponds to the set of states of the world that she considers possible and is a subset of the set of states that are not ruled out by the individual's information (or knowledge). It is required that, if the individual considers a state possible and her new information does not exclude this state, then she continue to consider it possible. Furthermore, if the individual regards a particular state as impossible, then she should continue to regard it as impossible unless her new information excludes all the states that she previously regarded as possible. This is closely related to the.. (shrink)

Hansson's kernel contraction is a fundamental operation for contracting information from belief bases, which adheres to the Success postulate, ensuring that all non-tautological beliefs are retractable. In this article, we propose a non-prioritised, weakened variant of kernel contraction. To formalise this operation, we introduce the degree of firmness of arbitrary sentences within a belief base (a measure of epistemic entrenchment), drawing from well-established measures of inconsistency. Instead of necessarily withdrawing beliefs, non-prioritised kernel contraction allows for adjusting their degree (...) of firmness, thereby violating the (controversial) Success postulate, while offering greater flexibility in belief change. As we demonstrate, non-prioritised kernel contraction is also perfectly suitable for mitigating inconsistency within belief bases. This new contraction method is constructed using a special type of incision function that determines which sentences are subject to retraction, and is axiomatically characterised by a relaxation of Hansson's original postulates. Finally, we introduce a refined form of classical kernel contraction designed to mitigate inconsistencies within belief bases. (shrink)

The book generalises earlier theories of belief change to cover all kinds of changes of sets by sets. The principal focus is still on changes of belief sets in response to new evidence, but the formal theory extends to all domains with a closure operation and a preference structure including, for example, systems of action. Contraction is the key notion; all other changes can be defined. Various new applications of the theory are outlined. A sentential version of (...) contraction, subtraction, is proposed as a formal counterpart to 'except'-locutions in natural language. Connections are emphasised with other areas at the interface between philosophical logic and artificial intelligence such as reasoning from default assumptions or from inconsistent premises. A relation of merge inference is proposed as a means of retrieving maximal but nontrivial information from inconsistent premises. Merge inference respects certain anti-Boolean intuitions while avoiding a revision of classical logic. (shrink)

The purpose of these studies was to test the hypothesis that changing perspectives from one's own to another's promotes the engagement of analytic processing and, in turn, reduces the impact of beliefs. In two experiments participants evaluated research vignettes containing belief-consistent and belief-inconsistent conclusions, and indicated whether the data supported a correlation between two variables. Consistent with our hypothesis, the tendency to endorse correlations consistent with prior belief was reduced when participants evaluated the data from the (...) researcher's perspective relative to their own. We also administered the Actively Open Minded Thinking (AOT) scale (Stanovich & West, 2007, 2008), which did not predict belief effects on our task. We did however observe that the AOT was reliably associated with different response strategies: high AOT scorers were more inclined to choose ambiguous response options, such as “no conclusion is warranted”, whereas low scorers evinced a preference for more determinate options (e.g., there is no relationship between the two variables). We interpret our findings in the context of dual process theories of reasoning and from a Bayesian perspective. (shrink)

Learning by doing, a change in beliefs due to experience, is crucial to the adaptive behaviours of organizations as well as the individuals that inhabit them. In this review paper, we summarise different pathologies of learning noted in past literature using a common underlying mechanism based on self-confirming biased beliefs. These are inaccurate beliefs about the environment that are self-confirming because acting upon these beliefs prevents their falsification. We provide a formal definition for self-confirming biased beliefs as an attractor (...) that can lock learning by doing systems into suboptimal actions and provide illustrations based on simulations. We then compare and distinguish self-confirming biased beliefs from other related theoretical constructs, including confirmation bias, self-fulfilling prophecies, and sticking points, and underscore that self-confirming biased beliefs underlie inefficient self-confirming equilibria and hot-stove effects. Lastly, we highlight two fundamental ways to escape self-confirming biased beliefs: taking actions inconsistent with beliefs and getting information on unchosen actions. (shrink)

In this study, we examine the problem of belief revision, defined as deciding whic h of several initially-accepted sentences to disbelieve, when new information presents a l ogical inconsistency with the initial set. In the first three experiments, the initial sentence set included a conditional sentence, a non-conditional sentence, and an inferred conclusi on drawn from the first two. The new information contradicted the inferred conclusion. Results indicated that the conditional sentences were more readily abandoned than non-c onditional sentences, (...) even when either choice would lead to a consistent belief state, and that this preference was more pronounced when problems used natural language cover sto ries rather than symbols. The pattern of belief revision choices differed depending on whe ther the contradicted conclusion from the initial belief set had been a modus ponens or m odus tollens inference. Two additional experiments examined alternative model-theoretic definitions of minimal change to a belief state, using problems that contained multiple mo dels of the initial belief state and of the new information that provided the contradiction. The results indicated that people did not follow any of four formal definitions of minimal change on these problems. The new information and the contradiction it offered was not, for example, used to select a particular model of the initial belief state as a way of reconci ling the contradiction. The preferred revision was to retain only those initial sentences th at had the same, unambiguous truth value within and across both the initial and new info rmation sets. The study and results are presented in the context of certain logic-based for malizations of belief revision, syntactic and model-theoretic representations of belief stat es, and performance models of human deduction. Principles by which some types of sent ences might be more "entrenched" than others in the face of contradiction are also discuss ed from the perspective of induction and theory revision. (shrink)

Since it is desirable to be able to talk about rational agents forming attitudes toward their concrete agency, we suggest an introduction of doxastic, volitional, and intentional modalities into the multi-agent logic of deliberatively seeing to it that, dstit logic. These modalities are borrowed from the well-known BDI (belief-desire-intention) logic. We change the semantics of the belief and desire operators from a relational one to a monotonic neighbourhood semantic in order to handle ascriptions of conflicting but not (...) inconsistent beliefs and desires as being satisfiable. The proposed bdi-stit logic is defined with respect to branching time frames, and it is shown that this logic is a generalization of a bdi logic based on branching time possible worlds frames (but without temporal operators) and dstit logic. The new bdi-stit logic generalizes bdi and dstit logic in the sense that for any model of bdi or dstit logic, there is an equivalent bdi-stit model. (shrink)

In standard Bayesian probability revision, the adoption of full beliefs (propositions with probability 1) is irreversible. Once an agent has full belief in a proposition, no subsequent revision can remove that belief. This is an unrealistic feature, and it also makes probability revision incompatible with belief change theory, which focuses on how the set of full beliefs is modified through both additions and retractions. This problem in probability theory can be solved in a model that (i) (...) lets the codomain of the probability function be a hyperreal-valued rather than the real-valued closed interval [0, 1], and (ii) identifies the full beliefs as the propositions whose probability is either 1 or infinitesimally smaller than 1. In this model, changes in the probability function will result in changes in the set of full beliefs (belief set), which constitutes a submodel that can be conceived as the “tip of the iceberg” within the larger model that also contains beliefs on lower levels of probability. The patterns of change in the set of full beliefs in this modified Bayesian model coincides with the corresponding pattern in a slightly modified version of AGM revision, which is commonly conceived as the gold standard of (dichotomous) belief change. The modification only concerns the marginal case of revision by an inconsistent input sentence. These results show that probability revision and dichotomous belief change can be unified in one and the same framework, or – if we so wish – that belief change theory can be subsumed under a modified version of probability revision that allows for iterated change and for the removal of full beliefs. (shrink)

ABSTRACT Semi-revision is a mode of belief change that differs from revision in that the input sentence is not always accepted. A constructive approach to semi-revision is proposed. It requires an efficient treatment of local inconsistencies, which is more easily obtainable in belief base models than in belief set models. Axiomatic characterizations of two semi-revision operators are reported.

One of the main applications of the logic of theory change is to the epistemic analysis of conditionals via the so-called Ramsey test. In the first part of the present note this test is studied in the “limiting case” where the theory being revised is inconsistent, and it is shown that this case manifests an intrinsic incompatibility between the Ramsey test and the AGM postulate of “success”. The paper then analyses the use of the postulate of success, and (...) a weakening of it, generating axioms of conditional logic via the test, and it is shown that for certain purposes both success and weak success are quite superfluous. This suggests the proposal of abandoning both success and weak success entirely, thus permitting retention of the postulate of “preservation” discarded by Gärdenfors. (shrink)

Some concepts generate paradoxes by licensing inconsistent beliefs. We can try to revise some of those beliefs by doing some “conceptual engineering,” but this leads to a puzzle. However exactly the details of conceptual engineering get filled in, it seems that what happens is we revise our beliefs without gaining any evidence against our old views or in support of our new views. But epistemically rational belief change always requires new evidence—or so it seems.I respond to the (...) puzzle by proposing a view of epistemic rationality on which we are required to hold a belief only if two conditions hold: Our evidence supports the belief, and our attention is directed at the evidence and the supported belief's content. Thus, we can rationally withdraw a belief by withdrawing our attention to its content, even without having any new evidence. Its ability to solve this puzzle for conceptual engineering, in addition to some other important puzzles that I briefly show it also solves, gives us a strong case for this proposed connection between rationality and attention. (shrink)

This study investigated whether perspective-taking reduces belief bias independently of argument strength. Belief bias occurs when individuals evaluate belief-consistent arguments more favourably than belief-inconsistent arguments. Undergraduates read arguments that varied with respect to belief-consistency and strength about the topic of climate change. After participants read each argument, those in the perspective-taking condition rated the argument's strength from a perspective of a climate scientist and then from their own perspectives, whereas those in the no (...) perspective-taking condition only rated the arguments from their own perspectives. Perspective-taking eliminated belief bias for weak arguments, but not for strong arguments. Theoretical and practical implications of the results are discussed, and directions for future research are provided. (shrink)

In the area known as model-based diagnosis, a system is described by-means of a set of formulas together with assumptions that all the components are functioning correctly. When we observe a behavior of the system which is inconsistent with the system description, we must relax some of the assumptions. In previous work, we have presented operations of belief change which only affect the relevant part of a belief base. In this paper, we propose the application of (...) the same strategy to the problem of model-based diagnosis. We Erst isolate the subset of the system description which is relevant for a given observation. By doing this, we reduce the size of the problem and then solve the diagnosis problem for the relevant subset. (shrink)

We establish a direct connection between time preference and risk about an attribute of the instantaneous utility function. In doing so, we derive a risk-induced discount function that corresponds to a normalized expectation of that attribute. We provide several results characterizing this risk-induced discount function depending on the stochastic properties of the risk, which we model as a discrete Markov process. When it is well-defined, which we refer to as full approximation, the risk-induced discount function coincides with exponential discounting if (...) the Markov process is stationary. However, a slight perturbation of the beliefs can trigger time-inconsistent discounting. When considering non-stationary Markov processes, time-inconsistency also emerges in situations where individuals’ beliefs change in a non-anticipated fashion over time, as exemplified by quasi-hyperbolic discounting. Results are illustrated via several applications. (shrink)

How do opinion diversity and belief polarisation affect epistemic group decision-making, particularly if decisions must be made without delay and on the basis of permissive evidence? In an agent-based model, we track the consistency of group opinions aggregated through sentence-wise majority voting. Simulations on the model reveal that high opinion diversity, but not polarisation, incurs a significant inconsistency risk. These results indicate that epistemic group decisions based on permissive evidence can be particularly difficult for diverse groups. The results also (...) improve our understanding of what can reasonably be expected of expert groups, and where expert advice might have limits. (shrink)

In this paper it is argued that, in order to solve the problem of iterated belief change, both the belief state and its input should be represented as epistemic entrenchment (EE) relations. A belief revision operation is constructed that updates a given EE relation to a new one in light of an evidential EE relation. It is shown that the operation in question satisfies generalized versions of the Gärdenfors revision postulates. The account offered is motivated by (...) Spohn's ordinal conditionalization functions, and can be seen as the Jeffrization of a proposal considered by Rott. (shrink)

A sentence A is epistemically less entrenched in a belief state K than a sentence B if and only if a person in belief state K who is forced to give up either A or B will give up A and hold on to B. This is the fundamental idea of epistemic entrenchment as introduced by Gärdenfors (1988) and elaborated by Gärdenfors and Makinson (1988). Another distinguishing feature of relations of epistemic entrenchment is that they permit particularly simple (...) and elegant construction recipes for minimal changes of belief states. These relations, however, are required to satisfy rather demanding conditions. In the present paper we liberalize the concept of epistemic entrenchment by removing connectivity, minimality and maximality conditions. Correspondingly, we achieve a liberalization of the concept of rational belief change that does no longer presuppose the postulates of success and rational monotony. We show that the central results of Gärdenfors and Makinson are preserved in our more flexible setting. Moreover, the generalized concept of epistemic entrenchment turns out to be applicable also to relational and iterated belief changes. (shrink)

This paper uses Popper's treatment of probability and an epistemic constraint on probability assignments to conditionals to extend the Bayesian representation of rational belief so that revision of previously accepted evidence is allowed for. Results of this extension include an epistemic semantics for Lewis' theory of counterfactual conditionals and a representation for one kind of conceptual change.

The axiom of recovery, while capturing a central intuition regarding belief change, has been the source of much controversy. We argue briefly against putative counterexamples to the axiom—while agreeing that some of their insight deserves to be preserved—and present additional recovery-like axioms in a framework that uses epistemic states, which encode preferences, as the object of revisions. This makes iterated revision possible and renders explicit the connection between iterated belief change and the axiom of recovery. We (...) provide a representation theorem that connects the semantic conditions we impose on iterated revision and our additional syntactical properties. We show interesting similarities between our framework and that of Darwiche–Pearl (Artificial Intelligence 89:1–29 1997). In particular, we show that intuitions underlying the controversial (C2) postulate are captured by the recovery axiom and our recovery-like postulates (the latter can be seen as weakenings of (C2)). We present postulates for contraction, in the same spirit as the Darwiche–Pearl postulates for revision, and provide a theorem that connects our syntactic postulates with a set of semantic conditions. Lastly, we show a connection between the contraction postulates and a generalisation of the recovery axiom. (shrink)

This book explains how the logic of theory change employs formal models in the investigation of changes in belief states and databases. The topics covered include equivalent characterizations of AGM operations, extended representations of the belief states, change operators not included in the original framework, iterated change, applications of the model, its connections with other formal frameworks, and criticism of the model.