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)

The First International Workshop brings together researchers from the theoretical ends of the logic programming and artificial intelligence communities to discuss their mutual interests. Logic programming deals with the use of models of mathematical logic as a way of programming computers, where theoretical AI deals with abstract issues in modeling and representing human knowledge and beliefs. One common ground is nonmonotonic reasoning, a family of logics that includes room for the kinds of variations that can be found (...) in human reasoning. Topics covered: Stable Semantics. Default Logic. AutoEpistemic Logic. Truth Maintenance Systems. Implementation Issues. Diagnosis. Applications. Inheritance Reasoning. Logics of Belief. Inconsistency and Non-Monotonicity. (shrink)

Ever since [4], systems of spheres have been considered to give an intuitive and elegant way to give a semantics for logics of theory- or belief- change. Several authors [5, 11] have considered giving up the rather strong assumption that systems of spheres be linearly ordered by inclusion. These more general structures are called hypertheories after [8]. It is shown that none of the proposed logics induced by these weaker structures are compact and thus cannot be given a strongly (...) complete axiomatization in a finitary logic. Complete infinitary axiomatizations are given for several intuitive logics based on hypertheories that are not linearly ordered by inclusion. (shrink)

Ever since [4], systems of spheres have been considered to give an intuitive and elegant way to give a semantics for logics of theory- or belief- change. Several authors [5, 11] have considered giving up the rather strong assumption that systems of spheres be linearly ordered by inclusion. These more general structures are called hypertheories after [8]. It is shown that none of the proposed logics induced by these weaker structures are compact and thus cannot be given a strongly (...) complete axiomatization in a finitary logic. Complete infinitary axiomatizations are given for several intuitive logics based on hypertheories that are not linearly ordered by inclusion. (shrink)

This paper adds evidence structure to standard models of belief, in the form of families of sets of worlds. We show how these more fine-grained models support natural actions of “evidence management”, ranging from update with external new information to internal rearrangement. We show how this perspective leads to new richer languages for existing neighborhood semantics for modal logic. Our main results are relative completeness theorems for the resulting dynamic logic of evidence.

The introduction of explicit notions of rejection, or disbelief, into logics for knowledge representation can be justified in a number of ways. Motivations range from the need for versions of negation weaker than classical negation, to the explicit recording of classic belief contraction operations in the area of belief change, and the additional levels of expressivity obtained from an extended version of belief change which includes disbelief contraction. In this paper we present four logics of disbelief which (...) address some or all of these intuitions. Soundness and completeness results are supplied and the logics are compared with respect to applicability and utility. (shrink)

When one thinks—knows, believes, imagines—that something is the case, one’s thought has a topic: it is about something, towards which one’s mind is directed. What is the logic of thought, so understood? This book begins to explore the idea that, to answer the question, we should take topics seriously. It proposes a hyperintensional account of the propositional contents of thought, arguing that these are individuated not only by the set of possible worlds at which they are true, but also (...) by their topic: what they are about. The book then builds epistemic, doxastic, probabilistic, and conditional logics based on this view. It applies them to issues ranging from dogmatism, scepticism, and epistemic fallibilism, to imagination and suppositional reasoning, belief revision, framing effects, and the acceptability of indicative conditionals. (shrink)

Patrick Grim has presented arguments supporting the intuition that any notion of a totality of truths is incoherent. We suggest a natural semantics for various logics of belief which reflect Grim’s intuition. The semantics is a topological semantics, and we suggest that the condition can be interpreted to reflect Grim’s intuition. Beyond this, we present a natural canonical topological model for K4 and KD4.

We consider extending the modal logic KD45, commonly taken as the baseline system for belief, with propositional quantifiers that can be used to formalize natural language sentences such as “everything I believe is true” or “there is something that I neither believe nor disbelieve.” Our main results are axiomatizations of the logics with propositional quantifiers of natural classes of complete Boolean algebras with an operator validating KD45. Among them is the class of complete, atomic, and completely multiplicative BAOs (...) validating KD45. Hence, by duality, we also cover the usual method of adding propositional quantifiers to normal modal logics by considering their classes of Kripke frames. In addition, we obtain decidability for all the concrete logics we discuss. (shrink)

This paper adds evidence structure to standard models of belief, in the form of families of sets of worlds. We show how these more fine-grained models support natural actions of “evidence management”, ranging from update with external new information to internal rearrangement. We show how this perspective leads to new richer languages for existing neighborhood semantics for modal logic. Our main results are relative completeness theorems for the resulting dynamic logic of evidence.

In this paper I revisit R. M. Martin’s logic of belief. As with much of Martin’s work, his formal studies into belief and belief reports have gone largely unnoticed. However, in my article I suggest reasons for thinking that these studies warrant revisiting. One reason is that Martin adopted an account of the notion of belief which was more comprehensive than that employed by most rival theorists. Another reason is that Martin couched his theory in (...) a formal pragmatics which utilised a pragmatical meta-language. This method resulted in a rather novel approach which may turn out to be more enlightening than many popular alternative accounts. Martin was a constructivistic nominalist whose approach to philosophical analysis was characterised by a commitment to first-order extensional systems. Yet in the statement of his theory of belief he employed a platonistic syntax simply for the reason that this kind of syntax is a little easier to implement than one which is nominalistic. However Martin also supposed that a fully nominalised version of his theory could be developed. In my article I investigate whether it can. I do this by sketching an inscriptional pragmatics, where this pragmatical system presupposes an inscriptional semantics of the kind developed by Martin himself. While further work is required, I think that a nominalisation of Martin’s logic of belief may be developed. (shrink)

In recent work MacPherson argues that the standard method of modeling belief logically, as a necessity operator in a modal logic, is doomed to fail. The problem with normal modal logics as logics of belief is that they treat believers as "ideal" in unrealistic ways (i.e., as omnidoxastic); however, similar problems re-emerge for candidate non-normal logics. The authors argue that logics used to model belief in artificial intelligence (AI) are also flawed in this way. But for (...) AI systems, omnidoxasticity is impossible because of their finite nature, and this fact can be exploited to produce operational models of fallible belief. The relevance of this point to various philosophical views about belief is discussed. (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)

The examples with which Keith Graham has tried (in Inquiry, Vol. 17 [1974], No. 3) to undermine certain general features of the concept of belief fail to do so. Roughly speaking, he has not shown that the persons who make the puzzling assertions which he describes really mean what they say. His discussion has the merit of emphasizing the limits of philosophical analysis in adjudicating on the application of concepts in borderline cases.

John Locke proposed a straightforward relationship between qualitative and quantitative doxastic notions: belief corresponds to a sufficiently high degree of confidence. Richard Foley has further developed this Lockean thesis and applied it to an analysis of the preface and lottery paradoxes. Following Foley's lead, we exploit various versions of these paradoxes to chart a precise relationship between belief and probabilistic degrees of confidence. The resolutions of these paradoxes emphasize distinct but complementary features of coherent belief. These features (...) suggest principles that tie together qualitative and quantitative doxastic notions. We show how these principles may be employed to construct a quantitative model - in terms of degrees of confidence - of an agent's qualitative doxastic state. This analysis fleshes out the Lockean thesis and provides the foundation for a logic of belief that is responsive to the logic of degrees of confidence. (shrink)

In a penetrating investigation of the relationship between belief and quantitative degrees of confidence (or degrees of belief) Richard Foley (1992) suggests the following thesis: ... it is epistemically rational for us to believe a proposition just in case it is epistemically rational for us to have a sufficiently high degree of confidence in it, sufficiently high to make our attitude towards it one of belief. Foley goes on to suggest that rational belief may be just (...) rational degree of confidence above some threshold level that the agent deems sufficient for belief. He finds hints of this view in Locke’s discussion of probability and degrees of assent, so he calls it the Lockean Thesis.1 The Lockean Thesis has important implications for the logic of belief. Most prominently, it implies that even a logically ideal agent whose degrees of confidence satisfy the axioms of probability theory may quite rationally believe each of a large body of propositions that are jointly inconsistent. For example, an agent may legitimately believe that on each given occasion her well-maintained car will start, but nevertheless believe that she will eventually encounter a.. (shrink)

John Locke proposed a straightforward relationship between qualitative and quantitative doxastic notions: belief corresponds to a sufficiently high degree of confidence. Richard Foley has further developed this Lockean thesis and applied it to an analysis of the preface and lottery paradoxes. Following Foley's lead, we exploit various versions of these paradoxes to chart a precise relationship between belief and probabilistic degrees of confidence. The resolutions of these paradoxes emphasize distinct but complementary features of coherent belief. These features (...) suggest principles that tie together qualitative and quantitative doxastic notions. We show how these principles may be employed to construct a quantitative model - in terms of degrees of confidence - of an agent's qualitative doxastic state. This analysis fleshes out the Lockean thesis and provides the foundation for a logic of belief that is responsive to the logic of degrees of confidence. (shrink)

The logic of indicative conditionals remains the topic of deep and intractable philosophical disagreement. I show that two influential epistemic norms—the Lockean theory of belief and the Ramsey test for conditional belief—are jointly sufficient to ground a powerful new argument for a particular conception of the logic of indicative conditionals. Specifically, the argument demonstrates, contrary to the received historical narrative, that there is a real sense in which Stalnaker’s semantics for the indicative did succeed in capturing (...) the logic of the Ramseyan indicative conditional. (shrink)

The problems that surround iterated contractions and expansions of beliefs are approached by studying hypertheories, a generalisation of Adam Grove's notion of systems of spheres. By using a language with dynamic and doxastic operators different ideas about the basic nature of belief change are axiomatised. It is shown that by imposing quite natural constraints on how hypertheories may change, the basic logics for belief change can be strengthened considerably to bring one closer to a theory of iterated (...) class='Hi'>belief change. It is then argued that the logic of expansion, in particular, cannot without loss of generality be strengthened any further to allow for a full logic of iterated belief change. To remedy this situation a notion of directed expansion is introduced that allows for a full logic of iterated belief change. The new operation is given an axiomatisation that is complete for linear hypertheories. (shrink)

This paper shows how propositional dynamic logic can be interpreted as a logic for multi-agent belief revision. For that we revise and extend the logic of communication and change of [9]. Like LCC, our logic uses PDL as a base epistemic language. Unlike LCC, we start out from agent plausibilities, add their converses, and build knowledge and belief operators from these with the PDL constructs. We extend the update mechanism of LCC to an update (...) mechanism that handles belief change as relation substitution, and we show that the update part of this logic is more expressive than either that of LCC or that of doxastic/epistemic PDL with a belief change modality. It is shown that the properties of knowledge and belief are preserved under any update, and that the logic is complete. © 2008 Springer-Verlag Berlin Heidelberg. (shrink)

Probability logics have been an active topic of investigation of beliefs in type spaces in game theoretical economics. Beliefs are expressed as subjective probability measures. Savage’s postulates in decision theory imply that subjective probability measures are not necessarily countably additive but finitely additive. In this paper, we formulate a probability logic Σ + that is strongly complete with respect to this class of type spaces with finitely additive probability measures, i.e. a set of formulas is consistent in Σ + (...) iff it is satisfied in a finitely additive type space. Although we can characterize Σ + -theories satisfiable in the class as maximally consistent sets of formulas, we prove that any canonical model of maximally consistent sets is not universal in the class of type spaces with finitely additive measures, and, moreover, it is not a type space. At the end of this paper, we show that even a minimal use of probability indices causes the failure of compactness in probability logics. (shrink)

Inspired by an interesting quotation from the literature, we propose four modalities, called ‘sane belief’, ‘insane belief’, ‘reliable belief’ and ‘unreliable belief’, and introduce logics with each operator as the modal primitive. We show that the four modalities constitute a square of opposition, which indicates some interesting relationships among them. We compare the relative expressivity of these logics and other related logics, including a logic of false beliefs from the literature. The four main logics are (...) all less expressive than the standard modal logic over various model classes, and the logics of sane and insane beliefs are, respectively, equally expressive as the logics of unreliable and reliable beliefs on any class of models. The logics of reliable and unreliable beliefs are then combined into a bimodal logic, which turns out to be equally expressive as the standard modal logic. Despite this, we cannot obtain a complete axiomatization of the minimal bimodal logic, by simply translating the axioms and rules of the minimal modal logic $\textbf{K}$ into the bimodal language. We then introduce a schematic modality which unifies reliable and unreliable beliefs and axiomatize it over the class of all frames and also the class of serial frames. This line of research is finally extended to unify sane and insane beliefs and some axiomatizations are given. (shrink)

We present a complete, decidable logic for reasoning about a notion of completely trustworthy evidence and its relations to justifiable belief and knowledge, as well as to their explicit justifications. This logic makes use of a number of evidence-related notions such as availability, admissibility, and “goodness” of a piece of evidence, and is based on an innovative modification of the Fitting semantics for Artemovʼs Justification Logic designed to preempt Gettier-type counterexamples. We combine this with ideas from (...) belief revision and awareness logics to provide an account for explicitly justified knowledge based on conclusive evidence that addresses the problem of omniscience. (shrink)

If the logic of belief changes is extended to cover belief states which contain both factual and normative beliefs, it is easily shown that a change of a factual belief (an 'Is') in a mixed belief state can imply a change of a normative belief (an 'Ought') in the same state. With regard to Hume's so-called 'Is-Ought problem', this means that one has to distinguish its statics from its dynamics. When this is done, it (...) becomes clear that changes of factual beliefs can, for rational reasons, have far-reaching normative consequences. Similarly, a change of a factual belief can imply a change of a value belief. (shrink)

Nothing seems to follow strictly from 'X believes that p'. But if we reinterpret it to mean: 'X can consistently be described as consistently believing p'--which roughly renders, I think, Hintikka's notion of "defensibility"--we can get on with the subject, freed from the inhibitions of descriptive adequacy. But defensibility is neither necessary nor sufficient for truth: it tells us little, therefore, about the concept of belief on which it is based. It cannot, in particular, specify necessary conditions for the (...) consistent ascription of belief--as opposed to rational belief. If there are no such conditions, all belief ascriptions must be treated as atomic: which is implausible. If there are some, they must be settled on before an account of consistency can be complete. The reason is simple: it is that we have beliefs about our own beliefs. A set of first order beliefs is consistent if they can all be true together; but it is a lesson of Moore's paradox that consistency of second-order beliefs requires additional constraints. If someone both believes that p and that he does not believe that p, the propositions he believes might all be true together, yet he is inconsistent. And the characterization of second order consistency will remain incomplete, so long as nothing is said about the consistency of first order belief ascriptions. Suppose someone says and believes: "I am inconsistent: I believe both p and ~p." This is "indefensible": but is it insight, or nonsense? Breast-beating of this sort is guaranteed success: something he believes is bound to be false. But that remains diagnostically frustrating: is he inconsistent because what he said is true, or on the contrary because it is inconsistent? (shrink)

“Probably Peirce’s best-known works are the first two articles in a series of six that originally were collectively entitled Illustrations of the Logic of Science and published in Popular Science Monthly from November 1877 through August 1878. The first is entitled ‘The Fixation of Belief’ and the second is entitled ‘How to Make Our Ideas Clear.’ In the first of these papers Peirce defended, in a manner consistent with not accepting naive realism, the superiority of the scientific method (...) over other methods of overcoming doubt and ‘fixing belief.’” — Robert Burch, “Charles Sanders Peirce,” entry in the Stanford Encyclopedia of Philosophy (2021 revision) -/- “Pragmatist epistemologies often explore how we can carry out inquiries in a self-controlled and fruitful way. (Where much analytic epistemology centres around the concept of knowledge, considered as an idealised end-point of human thought, pragmatist epistemology centres around the concept of inquiry, considered as the process of knowledge-seeking and how we can improve it.) So pragmatists often provide rich accounts of the capacities or virtues that we must possess in order to inquire well, and the rules or guiding principles that we should adopt. A canonical account is Peirce’s classic early paper ‘The Fixation of Belief‘. Here Peirce states that inquiry is a struggle to replace doubt with “settled belief“, and that the only method of inquiry that can make sense of the fact that at least some of us are disturbed by inconsistent beliefs, and will subsequently reflect upon which methods of fixing belief are correct is the Method of Science, which draws on the Pragmatic Maxim described above. This contrasts with three other methods of fixing belief: i) refusing to consider evidence contrary to one’s favored beliefs (the Method of Tenacity), ii) accepting an institution’s dictates (the Method of Authority), iii) developing the most rationally coherent or elegant-seeming belief-set (the A Priori Method).“ — Catherine Legg, “Pragmatism,” entry in the Stanford Encyclopedia of Philosophy (2021 revision). (shrink)

Moore’s Paradox is a test case for any formal theory of belief. In Knowledge and Belief, Hintikka developed a multimodal logic for statements that express sentences containing the epistemic notions of knowledge and belief. His account purports to offer an explanation of the paradox. In this paper I argue that Hintikka’s interpretation of one of the doxastic operators is philosophically problematic and leads to an unnecessarily strong logical system. I offer a weaker alternative that captures in (...) a more accurate way our logical intuitions about the notion of belief without sacrificing the possibility of providing an explanation for problematic cases such as Moore’s Paradox. (shrink)

CHAPTER ONE IDEOLOGY AND CONFUSION Among political concepts none is more muddled or more fraught than ideology. This is not for the want of theories to ...

Intentions are an important concept in Artificial Intelligence and Cognitive Science. We present a formal theory of intentions and beliefs based on Discourse Representation Theory that captures many of their important logical properties. Unlike possible worlds approaches, this theory does not assume that agents are perfect reasoners, and gives a realistic view of their internal architecture; unlike most representational approaches, it has an objective semantics, and does not rely on an ad hoc labeling of the internal states of agents. We (...) describe a minimal logic for intentions and beliefs that is sound and complete relative to our semantics. We discuss several additional axioms, and the constraints on the models that validate them. (shrink)

Scientists collect evidence in order to confirm or falsify scientific theories. Unfortunately, scientific evidence may sometimes be false or deceiving and as a consequence lead individuals to believe in a false theory. By interaction between scientists, such false beliefs may spread through the entire community. There is currently a debate about the effect of various network configurations on the epistemic reliability of scientific communities. To contribute to this debate from a logical perspective, this paper introduces an epistemic logical framework of (...) observation, interaction and belief revision in scientific communities. The presented sound and complete system provides the formal tools for qualitative analysis of the social dynamics of scientific inquiry. Furthermore, this paper includes detailed suggestions for future applications of the framework. (shrink)

For Derrida, the ‘‘as if’’, as a regulative principle directly appropriated and modified from its Kantian context, becomes the central lynchpin for understanding, not only Derrida's philosophical system as a whole, but also his numerous seemingly enigmatic references to his ‘‘jewishness’’. Through an analysis of the function of the ‘‘as if’’ within the history of thought, from Greek tragedy to the poetry of Wallace Stevens, I hope to show how Derrida can only appropriate his Judaic roots as an act of (...) mourning that seeks to render the lost object as present, ‘‘as if’’ it were incorporated by the subject for whom this act nevertheless remains an impossibility. As Derrida discerns within the poetry of Paul Celan, bringing a sense of presence/presentness to our experiences, and as a confirmation of the subject which the human being struggles to assert, is the poetic task par excellence. It is seemingly also, if Derrida is to be understood on this point, the only option left to a humanity wherein poetry comes to express what religious formulations can no longer justify. (shrink)