Epistemic closure has been a central issue in epistemology over the last forty years. According to versions of the relevant alternatives and subjunctivist theories of knowledge, epistemic closure can fail: an agent who knows some propositions can fail to know a logical consequence of those propositions, even if the agent explicitly believes the consequence (having “competently deduced” it from the known propositions). In this sense, the claim that epistemic closure can fail must be distinguished from the fact (...) that agents do not always believe, let alone know, the consequences of what they know—a fact that raises the “problem of logical omniscience” that has been central in epistemic logic. This paper, part I of II, is a study of epistemic closure from the perspective of epistemic logic. First, I introduce models for epistemic logic, based on Lewis’s models for counterfactuals, that correspond closely to the pictures of the relevant alternatives and subjunctivist theories of knowledge in epistemology. Second, I give an exact characterization of the closure properties of knowledge according to these theories, as formalized. Finally, I consider the relation between closure and higher-order knowledge. The philosophical repercussions of these results and results from part II, which prompt a reassessment of the issue of closure in epistemology, are discussed further in companion papers. As a contribution to modal logic, this paper demonstrates an alternative approach to proving modal completeness theorems, without the standard canonical model construction. By “modal decomposition” I obtain completeness and other results for two non-normal modal logics with respect to new semantics. One of these logics, dubbed the logic of ranked relevant alternatives, appears not to have been previously identified in the modal logic literature. More broadly, the paper presents epistemology as a rich area for logical study. (shrink)

Information exchange can be seen as a dynamic process of raising and resolving issues. The goal of this paper is to provide a logical framework to model and reason about this process. We develop an inquisitive dynamic epistemic logic , which enriches the standard framework of dynamic epistemic logic , incorporating insights from recent work on inquisitive semantics. At a static level, IDEL does not only allow us to model the information available to a set of (...) agents, like standard epistemic logic, but also the issues that the agents entertain. At a dynamic level, IDEL does not only allow us to model the effects of communicative actions that provide new information, like standard DEL, but also the effects of actions that raise new issues. Thus, IDEL provides the fundamental tools needed to analyze information exchange as a dynamic process of raising and resolving issues. (shrink)

A well-known open problem in epistemic logic is to give a syntactic characterization of the successful formulas. Semantically, a formula is successful if and only if for any pointed model where it is true, it remains true after deleting all points where the formula was false. The classic example of a formula that is not successful in this sense is the “Moore sentence” p ∧ ¬BOXp, read as “p is true but you do not know p.” Not only (...) is the Moore sentence unsuccessful, it is self-refuting, for it never remains true as described. We show that in logics of knowledge and belief for a single agent (extended by S5), Moorean phenomena are the source of all self-refutation; moreover, in logics for an introspective agent (extending KD45), Moorean phenomena are the source of all unsuccessfulness as well. This is a distinctive feature of such logics, for with a non-introspective agent or multiple agents, non-Moorean unsuccessful formulas appear. We also consider how successful and self-refuting formulas relate to the Cartesian and learnable formulas, which have been discussed in connection with Fitch’s “paradox of knowability.” We show that the Cartesian formulas are exactly the formulas that are not eventually self-refuting and that not all learnable formulas are successful. In an appendix, we give syntactic characterizations of the successful and the self-refuting formulas. (shrink)

A dynamic epistemic logic is presented in which the single agent can reason about his knowledge stages before and after announcements. The logic is generated by reinterpreting multi agent private announcements in a single agent environment. It is shown that a knowability principle is valid for such logic: any initially true ϕ can be known after a certain number of announcements.

Epistemic logic with its possible worlds semantic model is a powerful framework that allows us to represent an agent’s information not only about propositional facts, but also about her own information. Nevertheless, agents represented in this framework are logically omniscient: their information is closed under logical consequence. This property, useful in some applications, is an unrealistic idealisation in some others. Many proposals to solve this problem focus on weakening the properties of the agent’s information, but some authors have (...) argued that solutions of this kind are not completely adequate because they do not look at the heart of the matter: the actions that allow the agent to reach such omniscient state. Recent works have explored how acts of observation, inference, consideration and forgetting affect an agent’s implicit and explicit knowledge; the present work focuses on acts that affect an agent’s implicit and explicit beliefs. It starts by proposing a framework in which these two notions can be represented, and then it looks into their dynamics, first by reviewing the existing notion of belief revision, and then by introducing a rich framework for representing diverse forms of inference that involve both knowledge and beliefs. (shrink)

The five commentators on my paper ‘Gettier Cases in Epistemic Logic’ (GCEL) demonstrate how fruitful the topic can be. Especially in Brian Weatherson's contribution, and to some extent in those of Jennifer Nagel and Jeremy Goodman, much of the material constitutes valuable development and refinement of ideas in GCEL, rather than criticism. In response, I draw some threads together, and answer objections, mainly those in the papers by Stewart Cohen and Juan Comesaña and by Goodman.

The logical omniscience problem, whereby standard models of epistemic logic treat an agent as believing all consequences of its beliefs and knowing whatever follows from what else it knows, has received plenty of attention in the literature. But many attempted solutions focus on a fairly narrow specification of the problem: avoiding the closure of belief or knowledge, rather than showing how the proposed logic is of philosophical interest or of use in computer science or artificial intelligence. Sentential (...) epistemic logics, as opposed to traditional possible worlds approaches, do not suffer from the problems of logical omniscience but are often thought to lack interesting epistemic properties. In this paper, I focus on the case of rule-based agents, which play a key role in contemporary AI research but have been neglected in the logical literature. I develop a framework for modelling monotonic, nonmonotonic and introspective rule-based reasoners which have limited cognitive resources and prove that the resulting models have a number of interesting properties. An axiomatization of the resulting logic is given, together with completeness, decidability and complexity results. (shrink)

This paper introduces Agreement Theorems to dynamic-epistemic logic. We show first that common belief of posteriors is sufficient for agreement in epistemic-plausibility models, under common and well-founded priors. We do not restrict ourselves to the finite case, showing that in countable structures the results hold if and only if the underlying plausibility ordering is well-founded. We then show that neither well-foundedness nor common priors are expressible in the language commonly used to describe and reason about epistemic-plausibility (...) models. The static agreement result is, however, finitely derivable in an extended modal logic. We provide the full derivation. We finally consider dynamic agreement results. We show they have a counterpart in epistemic-plausibility models, and provide a new form of agreements via public announcements. (shrink)

In this paper I combine the dynamic epistemic logic ofGerbrandy (1999) with the probabilistic logic of Fagin and Halpern (1994). The resultis a new probabilistic dynamic epistemic logic, a logic for reasoning aboutprobability, information, and information change that takes higher orderinformation into account. Probabilistic epistemic models are defined, and away to build them for applications is given. Semantics and a proof systemis presented and a number of examples are discussed, including the MontyHall Dilemma.

The present work is motivated by two questions. (1) What should an intuitionistic epistemic logic look like? (2) How should one interpret the knowledge operator in a Kripke-model for it? In what follows we outline an answer to (2) and give a model-theoretic definition of the operator K. This will shed some light also on (1), since it turns out that K, defined as we do, fulfills the properties of a necessity operator for a normal modal logic. (...) The interest of our construction also lies in a better insight into the intuitionistic solution to Fitch's paradox, which is discussed in the third section. In particular we examine, in the light of our definition, De Vidi and Solomon's proposal of formulating the verification thesis as Φ → ¬¬KΦ. We show, as our main result, that this definition excapes the paradox, though it is validated only under restrictive conditions on the models. (shrink)

The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent with convergence in Stone topology. Presented is a flexible, parametrized family of metrics inducing the latter, used as an analytical aid. We show (...) maps induced by action model transformations continuous with respect to the Stone topology and present results on the recurrent behavior of said maps. (shrink)

We develop a conceptually clear, intuitive, and feasible decision procedure for testing satisfiability in the full multi\-agent epistemic logic \CMAELCD\ with operators for common and distributed knowledge for all coalitions of agents mentioned in the language. To that end, we introduce Hintikka structures for \CMAELCD\ and prove that satisfiability in such structures is equivalent to satisfiability in standard models. Using that result, we design an incremental tableau-building procedure that eventually constructs a satisfying Hintikka structure for every satisfiable input (...) set of formulae of \CMAELCD\ and closes for every unsatisfiable input set of formulae. (shrink)

Compositional verification aims at managing the complexity of theverification process by exploiting compositionality of the systemarchitecture. In this paper we explore the use of a temporal epistemiclogic to formalize the process of verification of compositionalmulti-agent systems. The specification of a system, its properties andtheir proofs are of a compositional nature, and are formalized within acompositional temporal logic: Temporal Multi-Epistemic Logic. It isshown that compositional proofs are valid under certain conditions.Moreover, the possibility of incorporating default persistence ofinformation in (...) a system, is explored. A completion operation on aspecific type of temporal theories, temporal completion, is introducedto be able to use classical proof techniques in verification withrespect to non-classical semantics covering default persistence. (shrink)

When reasoning about complex domains, where information available is usually only partial, nonmonotonic reasoning can be an important tool. One of the formalisms introduced in this area is Reiter's Default Logic (1980). A characteristic of this formalism is that the applicability of default (inference) rules can only be verified in the future of the reasoning process. We describe an interpretation of default logic in temporal epistemic logic which makes this characteristic explicit. It is shown that this (...) interpretation yields a semantics for default logic based on temporal epistemic models. A comparison between the various semantics for default logic will show the differences and similarities of these approaches and ours. (shrink)

It is known that a theory in S5-epistemic logic with several agents may have numerous models. This is because each such model specifies also what an agent knows about infinite intersections of events, while the expressive power of the logic is limited to finite conjunctions of formulas. We show that this asymmetry between syntax and semantics persists also when infinite conjunctions are permitted in the language. We develop a strengthened S5-axiomatic system for such infinitary logics, and prove (...) a strong completeness theorem for them. Then we show that in every such logic there is always a theory with more than one model. (shrink)

A combination of epistemic logic and dynamic logic of programs is presented. Although rich enough to formalize some simple game-theoretic scenarios, its axiomatization is problematic as it leads to the paradoxical conclusion that agents are omniscient. A cut-free labelled Gentzen-style proof system is then introduced where knowledge and action, as well as their combinations, are formulated as rules of inference, rather than axioms. This provides a logical framework for reasoning about games in a modular and systematic way, (...) and to give a step-by-step reconstruction of agents omniscience. In particular, its semantic assumptions are made explicit and a possible solution can be found in weakening the properties of the knowledge operator. (shrink)

Epistemic logics based on the possible worlds semantics suffer from the problem of logical omniscience, whereby agents are described as knowing all logical consequences of what they know, including all tautologies. This problem is doubly challenging: on the one hand, agents should be treated as logically non-omniscient, and on the other hand, as moderately logically competent. Many responses to logical omniscience fail to meet this double challenge because the concepts of knowledge and reasoning are not properly separated. In this (...) paper, I present a dynamic logic of knowledge that models an agent’s epistemic state as it evolves over the course of reasoning. I show that the logic does not sacrifice logical competence on the altar of logical non- omniscience. (shrink)

The paper explains how Gettier’s conclusion can be reached on general theoretical grounds within the framework of epistemic logic, without reliance on thought experiments. It extends the argument to permissive conceptions of justification that invalidate principles of multi-premise closure and require neighbourhood semantics rather than semantics of a more standard type. The paper concludes by recommending a robust methodology that aims at convergence in results between thought experimentation and more formal methods. It also warns against conjunctive definitions as (...) sharing several of the drawbacks of disjunctive definitions. (shrink)

This paper is concerned with representations of belief by means of nonadditive probabilities of the Dempster-Shafer (DS) type. After surveying some foundational issues and results in the D.S. theory, including Suppes's related contributions, the paper proceeds to analyze the connection of the D.S. theory with some of the work currently pursued in epistemic logic. A preliminary investigation of the modal logic of belief functions à la Shafer is made. There it is shown that the Alchourrron-Gärdenfors-Makinson (A.G.M.) (...) class='Hi'>logic of belief change is closely related to the D.S. theory. The final section compares the critique of Bayesianism which underlies the present paper with some important objections raised by Suppes against this doctrine. -/- . (shrink)

van Bentham et al. (Merging frameworks for interaction: DEL and ETL, 2007) provides a framework for generating the models of Epistemic Temporal Logic ( ETL : Fagin et al., Reasoning about knowledge, 1995; Parikh and Ramanujam, Journal of Logic, Language, and Information, 2003) from the models of Dynamic Epistemic Logic ( DEL : Baltag et al., in: Gilboa (ed.) Tark 1998, 1998; Gerbrandy, Bisimulations on Planet Kripke, 1999). We consider the logic TDEL on the (...) merged semantic framework, and its extension with the labeled past-operator “ P ϵ ” (“The event ϵ has happened before which. . .”). To axiomatize the extension, we introduce a method for transforming a given model into a normal form in a suitable sense. These logics suggest further applications of DEL in the theory of agency, the theory of learning, etc. (shrink)

This chapter provides a brief introduction to propositional epistemic logic and its applications to epistemology. No previous exposure to epistemic logic is assumed. Epistemic-logical topics discussed include the language and semantics of basic epistemic logic, multi-agent epistemic logic, combined epistemic-doxastic logic, and a glimpse of dynamic epistemic logic. Epistemological topics discussed include Moore-paradoxical phenomena, the surprise exam paradox, logical omniscience and epistemic closure, formalized theories of knowledge, (...) debates about higher-order knowledge, and issues of knowability raised by Fitch’s paradox. The references and recommended readings provide gateways for further exploration. (shrink)

This paper studies the Lockean thesis from the perspective of contemporary epistemic logic. The Lockean thesis states that belief can be defined as ‘sufficiently high degree of belief’. Its main problem is that it gives rise to a notion of belief which is not closed under conjunction. This problem is typical for classical epistemic logic: it is single-agent and static. I argue that from the perspective of contemporary epistemic logic, the Lockean thesis fares much (...) better. I briefly mention that it can successfully be extended from single-agent to multi-agent settings. More importantly, I show that accepting the Lockean thesis (and a more sophisticated version for conditional beliefs) leads to a significant and unexpected unification in the dynamic behavior of (conditional) belief and high (conditional) probability with respect to public announcements. This constitutes a methodological argument in favor of the Lockean thesis. Furthermore, if one accepts Baltag’s Erlangen program for epistemology, this technical observation has even stronger philosophical implications: because belief and high probability display the same dynamic behavior, it is plausible that they are indeed one and the same epistemic notion. (shrink)

Many criticisms of epistemic logic have centered around its use of devices such as idealized knowers with logical omniscience and perfect self-knowledge. One possible response to such criticisms is to say that these idealizations are normative devices, and that epistemic logic tells us how agents ought to behave. This paper will take a different approach, treating epistemic logic as descriptive, and drawing the analogy between its formal models and idealized scientific models on that basis. (...) Treating it as descriptive matches the way in which some philosophers, including one of its founders, Jaako Hintikka, have thought about epistemic logic early in its history. Further, the analogy between the two fields will give us a way to defuse criticisms that see epistemic logic as unrealistic. For example, criticizing models of epistemic logic in which agents know all propositional tautologies as being unrealistic would be like criticizing frictionless planes in physics for being unrealistic. Each one would certainly be an unsuitable model for studying some kinds of phenomena, but is entirely appropriate for others. After outlining the analogy between epistemic and scientific models, we will discuss some ways in which idealizations are used by different research programs in epistemic logic. (shrink)

This paper studies Aumann’s agreeing to disagree theorem from the perspective of dynamic epistemic logic. This was first done by Dégremont and Roy (J Phil Log 41:735–764, 2012) in the qualitative framework of plausibility models. The current paper uses a probabilistic framework, and thus stays closer to Aumann’s original formulation. The paper first introduces enriched probabilistic Kripke frames and models, and various ways of updating them. This framework is then used to prove several agreement theorems, which are natural (...) formalizations of Aumann’s original result. Furthermore, a sound and complete axiomatization of a dynamic agreement logic is provided, in which one of these agreement theorems can be derived syntactically. These technical results are used to show the importance of explicitly representing the dynamics behind the agreement theorem, and lead to a clarification of some conceptual issues surrounding the agreement theorem, in particular concerning the role of common knowledge. The formalization of the agreement theorem thus constitutes a concrete example of the so-called dynamic turn in logic. (shrink)

This paper discusses the possibility of modelling inductive inference (Gold 1967) in dynamic epistemic logic (see e.g. van Ditmarsch et al. 2007). The general purpose is to propose a semantic basis for designing a modal logic for learning in the limit. First, we analyze a variety of epistemological notions involved in identification in the limit and match it with traditional epistemic and doxastic logic approaches. Then, we provide a comparison of learning by erasing (Lange et (...) al. 1996) and iterated epistemic update (Baltag and Moss 2004) as analyzed in dynamic epistemic logic. We show that finite identification can be modelled in dynamic epistemic logic, and that the elimination process of learning by erasing can be seen as iterated belief-revision modelled in dynamic doxastic logic. Finally, we propose viewing hypothesis spaces as temporal frames and discuss possible advantages of that perspective. (shrink)

All standard epistemic logics legitimate something akin to the principle of closure, according to which knowledge is closed under competent deductive inference. And yet the principle of closure, particularly in its multiple premise guise, has a somewhat ambivalent status within epistemology. One might think that serious concerns about closure point us away from epistemic logic altogether—away from the very idea that the knowledge relation could be fruitfully treated as a kind of modal operator. This, however, need not (...) be so. The abandonment of closure may yet leave in place plenty of formal structure amenable to systematic logical treatment. In this paper we describe a family of weak epistemic logics in which closure fails, and describe two alternative semantic frameworks in which these logics can be modelled. One of these—which we term plurality semantics—is relatively unfamiliar. We explore under what conditions plurality frames validate certain much-discussed principles of epistemic logic. It turns out that plurality frames can be interpreted in a very natural way in light of one motivation for rejecting closure, adding to the significance of our technical work. The second framework that we employ—neighbourhood semantics—is much better known. But we show that it too can be interpreted in a way that comports with a certain motivation for rejecting closure. (shrink)

This paper contributes to an increasing literature strengthening the connection between epistemic logic and epistemology (Van Benthem, Hendricks). I give a survey of the most important applications of epistemic logic in epistemology. I show how it is used in the history of philosophy (Steiner's reconstruction of Descartes' sceptical argument), in solutions to Moore's paradox (Hintikka), in discussions about the relation between knowledge and belief (Lenzen) and in an alleged refutation of verificationism (Fitch) and I examine an (...) early argument about the (im)possibility of epistemic logic (Hocutt). Subsequently, I deal with interpretive questions about epistemic logic that, although implicitly, already appeared in the first section. I contend that a conception of epistemic logic as a theory of knowledge assertions is incoherent, and I argue that it does not make sense to adopt a normative interpretation of epistemic logic. Finally, I show ways to extend epistemic logic with other branches of philosophical logic so as to make it useful for some epistemological questions. Conditional logics and logics of public announcement are used to understand causal theories of knowledge and versions of reliabilism. Temporal logic helps understand some dynamic aspects of knowledge as well as the verificationist thesis. (shrink)

Various conceptual approaches to the notion of information can currently be traced in the literature in logic and formal epistemology. A main issue of disagreement is the attribution of truthfulness to informational data, the so called Veridicality Thesis (Floridi 2005). The notion of Epistemic Constructive Information (Primiero 2007) is one of those rejecting VT. The present paper develops a formal framework for ECI. It extends on the basic approach of Artemov’s logic of proofs (Artemov 1994), representing an (...) epistemic logic based on dependent justifications, where the definition of information relies on a strict distinction from factual truth. The definition obtained by comparison with a Normal Modal Logic translates a constructive logic for “becoming informed”: its distinction from the logic of “being informed”—which internalizes truthfulness—is essential to a general evaluation of information with respect to truth. The formal disentanglement of these two logics, and the description of the modal version of the former as a weaker embedding into the latter, allows for a proper understanding of the Veridicality Thesis with respect to epistemic states defined in terms of information. (shrink)

This paper aims to extend in two directions the probabilistic dynamic epistemic logic provided in Kooi’s paper (J Logic Lang Inform 12(4):381–408, 2003) and to relate these extensions to ones made in van Benthem et al. (Proceedings of LOFT’06. Liverpool, 2006). Kooi’s probabilistic dynamic epistemic logic adds to probabilistic epistemic logic sentences that express consequences of public announcements. The paper (van Benthem et al., Proceedings of LOFT’06. Liverpool, 2006) extends (Kooi, J Logic (...) Lang Inform 12(4):381–408, 2003) to using action models, but in both papers, the probabilities are discrete, and are defined on trivial σ -algebras over finite sample spaces. The first extension offered in this paper is to add a previous-time operator to a probabilistic dynamic epistemic logic similar to Kooi’s in (J Logic Lang Inform 12(4):381–408, 2003). The other is to involve non-trivial σ -algebras and continuous probabilities in probabilistic dynamic epistemic logic. (shrink)

According to the Relevant Alternatives (RA) Theory of knowledge, knowing that something is the case involves ruling out (only) the relevant alternatives. The conception of knowledge in epistemic logic also involves the elimination of possibilities, but without an explicit distinction, among the possibilities consistent with an agent’s information, between those relevant possibilities that an agent must rule out in order to know and those remote, far-fetched or otherwise irrelevant possibilities. In this article, I propose formalizations of two versions (...) of the RA theory. Doing so clarifies a famous debate in epistemology, pitting Fred Dretske against David Lewis, about whether the RA theorist should accept the principle that knowledge is closed under known implication, familiar as the K axiom in epistemic logic. Dretske’s case against closure under known implication leads to a study of other closure principles, while Lewis’s defense of closure by appeal to the claimed context sensitivity of knowledge attributions leads to a study of the dynamics of context. Having followed the first lead at length in other work, here I focus more on the second, especially on logical issues associated with developing a dynamic epistemic logic of context change over models for the RA theory. (shrink)

The following analysis shows how developments in epistemic logic can play a nontrivial role in cognitive neuroscience. We argue that the striking correspondence between two modes of identification, as distinguished in the epistemic context, and two cognitive systems distinguished by neuroscientific investigation of the visual system (the "where" and "what" systems) is not coincidental, and that it can play a clarificatory role at the most fundamental levels of neuroscientific theory.

Epistemic logic in the tradition of Hintikka provides, as one of its many applications, a toolkit for the precise analysis of certain epistemological problems. In recent years, dynamic epistemic logic has expanded this toolkit. Dynamic epistemic logic has been used in analyses of well-known epistemic “paradoxes”, such as the Paradox of the Surprise Examination and Fitch’s Paradox of Knowability, and related epistemic phenomena, such as what Hintikka called the “anti-performatory effect” of Moorean (...) announcements. In this paper, we explore a variation on basic dynamic epistemic logic—what we call sequential epistemic logic—and argue that it allows more faithful and fine-grained analyses of those epistemological topics. (shrink)

This collection of papers in epistemic logic is oriented towards applications to game theory and individual decision theory. Most of these papers were presented at the inaugural conference of the LOFT (Logic for the Theory and Games and Decisions) conference series, which took place in 1994 in Marseille. Among the notions dealt with are those of common knowledge and common belief, infinite hierarchies of beliefs and belief spaces, logical omniscience, positive and negative introspection, backward induction and rationalizable (...) equilibria in game theory. (shrink)

Epistemic logic in the tradition of Hintikka provides, as one of its many applications, a toolkit for the precise analysis of certain epistemological problems. In recent years, dynamic epistemic logic has expanded this toolkit. Dynamic epistemic logic has been used in analyses of well-known epistemic “paradoxes”, such as the Paradox of the Surprise Examination and Fitch’s Paradox of Knowability, and related epistemic phenomena, such as what Hintikka called the “anti-performatory effect” of Moorean (...) announcements. In this paper, we explore a variation on basic dynamic epistemic logic—what we call sequential epistemic logic—and argue that it allows more faithful and fine-grained analyses of those epistemological topics. (shrink)

This article describes the historical development of epistemic logic, focusing on the dynamic turn that has taken place in the last few decades. Although this dynamic turn was mainly motivated by technical considerations in computer science and game theory, it is argued that it can also be relevant from a more philosophical perspective: the application of dynamic epistemic logics to analyze prima facie static notions, theorems, etc. fits perfectly in a Wittgensteinian approach to philosophy as conceptual elucidation. (...) Furthermore, it turns out that these conceptual elucidations often lead to a number of other advantages, such as a higher degree of empirical adequacy. In order to illustrate this line of argumentation, the system of public announcement logic is presented, and it is shown how this system can be used to analyze the psychological phenomenon of surprise in a conceptually and empirically fruitful way. (shrink)

In the literature there are at least two main formal structures to deal with situations of interactive epistemology: Kripke models and type spaces. As shown in many papers :149–225, 1999; Battigalli and Siniscalchi in J Econ Theory 106:356–391, 2002; Klein and Pacuit in Stud Log 102:297–319, 2014; Lorini in J Philos Log 42:863–904, 2013), both these frameworks can be used to express epistemic conditions for solution concepts in game theory. The main result of this paper is a formal comparison (...) between the two and a statement of semantic equivalence with respect to two different logical systems: a doxastic logic for belief and an epistemic–doxastic logic for belief and knowledge. Moreover, a sound and complete axiomatization of these logics with respect to the two equivalent Kripke semantics and type spaces semantics is provided. Finally, a probabilistic extension of the result is also presented. A further result of the paper is a study of the relationship between the epistemic–doxastic logic for belief and knowledge and the logic STIT by Belnap and colleagues. (shrink)

Recent years witnessed a growing interest in non-standard epistemic logics of knowing whether, knowing how, knowing what, knowing why and so on. The new epistemic modalities introduced in those logics all share, in their semantics, the general schema of ∃x◻φ, e.g., knowing how to achieve φ roughly means that there exists a way such that you know that it is a way to ensure that φ. Moreover, the resulting logics are decidable. Inspired by those particular logics, in this (...) work, we propose a very general and powerful framework based on quantifier-free predicate language extended by a new modality, which packs exactly ∃x◻ together. We show that the resulting language, though much more expressive, shares many good properties of the basic propositional modal logic over arbitrary models, such as finite-tree-model property and van Benthem-like characterization w.r.t.\ first-order modal logic. We axiomatize the logic over S5 frames with intuitive axioms to capture the interaction between the new modality and know-that operator in an epistemic setting. (shrink)

The possibility of justified true belief without knowledge is normally motivated by informally classified examples. This paper shows that it can also be motivated more formally, by a natural class of epistemic models in which both knowledge and justified belief (in the relevant sense) are represented. The models involve a distinction between appearance and reality. Gettier cases arise because the agent's ignorance increases as the gap between appearance and reality widens. The models also exhibit an epistemic asymmetry between (...) good and bad cases that sceptics seem to ignore or deny. (shrink)

A recent no-go theorem (Frauchiger and Renner in Nat Commun 9(1):3711, 2018) establishes a contradiction from a specific application of quantum theory to a multi- agent setting. The proof of this theorem relies heavily on notions such as ‘knows’ or ‘is certain that’. This has stimulated an analysis of the theorem by Nurgalieva and del Rio (in: Selinger P, Chiribella G (eds) Proceedings of the 15th international conference on quantum physics and logic (QPL 2018). EPTCS 287, Open Publishing Association, (...) Waterloo, 2018), in which they claim that it shows the “[i]nadequacy of modal logic in quantum settings” (ibid.). In this paper, we will offer a significantly extended and refined reconstruction of the theorem in multi-agent modal logic. We will then show that a thorough reconstruction of the proof as given by Frauchiger and Renner requires the reflexivity of access relations (system T). However, a stronger theorem is possible that already follows in serial frames, and hence also holds in systems of doxastic logic (such as KD45). After proving this, we will discuss the general implications for different interpretations of quantum probabilities as well as several options for dealing with the result. (shrink)

Syntactic logics do not suffer from the problems of logical omniscience but are often thought to lack interesting properties relating to epistemic notions. By focusing on the case of rule-based agents, I develop a framework for modelling resource-bounded agents and show that the resulting models have a number of interesting properties.

We present epistemic multilateral logic, a general logical framework for reasoning involving epistemic modality. Standard bilateral systems use propositional formulae marked with signs for assertion and rejection. Epistemic multilateral logic extends standard bilateral systems with a sign for the speech act of weak assertion (Incurvati and Schlöder 2019) and an operator for epistemic modality. We prove that epistemic multilateral logic is sound and complete with respect to the modal logic S5 modulo (...) an appropriate translation. The logical framework developed provides the basis for a novel, proof-theoretic approach to the study of epistemic modality. To demonstrate the fruitfulness of the approach, we show how the framework allows us to reconcile classical logic with the contradictoriness of so-called Yalcin sentences and to distinguish between various inference patterns on the basis of the epistemic properties they preserve. (shrink)

An introduction to the special issue on epistemic logic and the foundations of game theory edited by Michael Bacharach and Philippe Mongin. Contributors are Michael Bacharach, Robert Stalnaker, Salvatore Modica and Aldo Rustichini, Luc Lismont and Philippe Mongin, and Hyun-Song Shin and Timothy Williamson.

1) We will begin by offering a short introduction to Epistemic Logic and presenting Fitch’s paradox in an epistemic‑modal logic. (2) Then, we will proceed to presenting three Epistemic Temporal logical frameworks creat‑ ed by Hoshi (2009) : TPAL (Temporal Public Announcement Logic), TAPAL (Temporal Arbitrary Public Announcement Logic) and TPAL+P ! (Temporal Public Announcement Logic with Labeled Past Operators). We will show how Hoshi stated the Verificationist Thesis in the language of (...) TAPAL and analyze his argument on why this version of it is immune from paradox. (3) Edgington (1985) offered an interpretation of the Verificationist Thesis that blocks Fitch’s paradox and we will propose a way to formulate it in a TAPAL‑based lan‑ guage. The language we will use is a combination of TAPAL and TPAL+P ! with an Indefinite (Unlabeled) Past Operator (TAPAL+P !+P). Using indexed satisfi‑ ability relations (as introduced in (Wang 2010 ; 2011)) we will offer a prospec ‑ tive semantics for this language. We will investigate whether the tentative re‑ formulation of Edgington’s Verificationist Thesis in TAPAL+P !+P is free from paradox and adequate to Edgington’s ideas on how „all truths are knowable“ should be interpreted. (shrink)

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

This paper proposes a logical framework for representing static and dynamic properties of different kinds of individual and collective attitudes. A complete axiomatization as well as a decidability result for the logic are given. The logic is applied to game theory by providing a formal analysis of the epistemic conditions of iterated deletion of weakly dominated strategies (IDWDS), or iterated weak dominance for short. The main difference between the analysis of the epistemic conditions of iterated weak (...) dominance given in this paper and other analysis is that we use a semi-qualitative approach to uncertainty based on the notion of plausibility first introduced by Spohn, whereas other analysis are based on a quantitative representation of uncertainty in terms of probabilities. (shrink)

We suggest that developing automata theoretic foundations is relevant for knowledge theory, so that we study not only what is known by agents, but also the mechanisms by which such knowledge is arrived at. We define a class of epistemic automata, in which agents’ local states are annotated with abstract knowledge assertions about others. These are finite state agents who communicate synchronously with each other and information exchange is ‘perfect’. We show that the class of recognizable languages has good (...) closure properties, leading to a Kleene-type theorem using what we call regular knowledge expressions. These automata model distributed causal knowledge in the following way: each agent in the system has a partial knowledge of the temporal evolution of the system, and every time agents synchronize, they update each other’s knowledge, resulting in a more up-to-date view of the system state. Hence we show that these automata can be used to solve the satisfiability problem for a natural epistemic temporal logic for local properties. Finally, we characterize the class of languages recognized by epistemic automata as the regular consistent languages studied in concurrency theory. (shrink)

Dynamic Epistemic Logic This article tells the story of the rise of dynamic epistemic logic, which began with epistemic logic, the logic of knowledge, in the 1960s. Then, in the late 1980s, came dynamic epistemic logic, the logic of change of knowledge. Much of it was motivated by puzzles and paradoxes. The number … Continue reading Dynamic Epistemic Logic →.

Epistemology and epistemic logic At first sight, the modern agenda of epistemology has little to do with logic. Topics include different definitions of knowledge, its basic formal properties, debates between externalist and internalist positions, and above all: perennial encounters with sceptics lurking behind every street corner, especially in the US. The entry 'Epistemology' in the Routledge Encyclopedia of Philosophy (Klein 1993) and the anthology (Kim and Sosa 2000) give an up-to-date impression of the field. Now, epistemic (...) logic started as a contribution to epistemology, or at least a tool in its modus operandi, with the seminal book Knowledge and Belief (Hintikka's 1962, 2005). Formulas like Ki for "the agent i knows that " Bi for "the agent i believes that " provided logical forms for stating and analyzing philosophical propositions and arguments. And more than that, their model-theoretic semantics in terms of ranges of alternatives provided an appealing extensional way of thinking about what agents know or believe in a given situation. In particular, on Hintikka's view, an agent knows those propositions which are true in all situations compatible with what she knows about the actual world; i.e., her current range of uncertainty. (shrink)

Branching-time temporal logics have proved to be an extraordinarily successful tool in the formal specification and verification of distributed systems. Much of their success stems from the tractability of the model checking problem for the branching time logic CTL, which has made it possible to implement tools that allow designers to automatically verify that systems satisfy requirements expressed in CTL. Recently, CTL was generalised by Alur, Henzinger, and Kupferman in a logic known as Alternating-time Temporal Logic (ATL). (...) The key insight in ATL is that the path quantifiers of CTL could be replaced by cooperation modalities, of the form , where is a set of agents. The intended interpretation of an ATL formula is that the agents can cooperate to ensure that holds (equivalently, that have a winning strategy for ). In this paper, we extend ATL with knowledge modalities, of the kind made popular in the work of Fagin, Halpern, Moses, Vardi and colleagues. Combining these knowledge modalities with ATL, it becomes possible to express such properties as group can cooperate to bring about iff it is common knowledge in that . The resulting logic — Alternating-time Temporal Epistemic Logic (ATEL) — shares the tractability of model checking with its ATL parent, and is a succinct and expressive language for reasoning about game-like multiagent systems. (shrink)

Epistemic logic begins with the recognition that our everyday talk about knowing and believing has some systematic features that we can track and re‡ect upon. Epistemic logicians have studied and extended these glints of systematic structure in fascinating and important ways since the early 1960s. However, for one reason or another, mainstream epistemologists have shown little interest. It is striking to contrast the marginal role of epistemic logic in contemporary epistemology with the centrality of modal (...) logic for metaphysicians. This article is intended to help in correcting this oversight by presenting some important developments in epistemic logic and suggesting ways to understand their applicability to traditional epistemological problems. Obviously, by itself, tweaking the formal apparatus of epistemic logic does not solve traditional epistemological problems. Epistemic logic can help us to navigate through problems in a systematic fashion by unpacking the logic of the problematic concepts, it can also lead us to recognize problems that we had not anticipated. This is basically analogous to the role that modal logic has played in contemporary metaphysics. (shrink)