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 volume is a collation of original contributions from the key actors of a new trend in the contemporary theory of knowledge and belief, that we call “dynamic epistemology”. It brings the works of these researchers under a single umbrella by highlighting the coherence of their current themes, and by establishing connections between topics that, up until now, have been investigated independently. It also illustrates how the new analytical toolbox unveils questions about the theory of knowledge, belief, preference, action, and (...) rationality, in a number of central axes in dynamic epistemology: temporal, social, probabilistic and even deontic dynamics. (shrink)

Since its modern inception in the early 1970s, informal logic has placed a special emphasis on the analysis of fallacies and argumentative dialogue schemes. Concurrent developments in speech communication circles exhibit a like concentration on the dialectical character of argument.

This is a case-study in knowledge representation and dynamic epistemic protocol verification. We analyze the ‘one hundred prisoners and a lightbulb’ puzzle. In this puzzle it is relevant what the agents know, how their knowledge changes due to observations, and how they affect the state of the world by changing facts, i.e., by their actions. These actions depend on the history of previous actions and observations. Part of its interest is that all actions are local, i.e. not publicly observable, and (...) part of the problem is therefore how to disseminate local results to other agents, and make them global. The various solutions to the puzzle are presented as protocols. The paper consists of three parts. First, we present different versions of the puzzle, and their solutions. This includes a probabilistic version, and a version assuming synchronicity. The latter is very informative for the prisoners, and allows different protocols. Then, we model the puzzle in an epistemic logic incorporating dynamic operators for the effects of information changing events. Such events include both informative actions, where agents become more informed about the non-changing state of the world, and factual changes, wherein the world and the facts describing it change themselves as well. Finally, we verify the basic protocol to solve the problem. Novel contributions in this paper are: Firstly, Protocol 2 and Protocol 4. Secondly, the modelling in dynamic epistemic logic in its entirety — we do not know of a case study that combines factual and informational dynamics in a setting of non-public events, or of a similar proposal to handle asynchronous behaviour in a dynamic epistemic logic. Thirdly, our method to verify dynamic epistemic protocols by reasoning over possibly infinite execution sequences of these protocols. A precursor of the present paper, entitled ‘One hundred prisoners and a lightbulb – logic and computation’, was presented at KR 2010, Toronto. The differences with the present contribution are as follows: the former contains a section with computational results, whereas the focus of the present paper is the verification of one of the presented protocols in the former. (shrink)

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

We study the extension of public announcement logic PAL by public assignments, which we call PALA. Just as in the case of PAL, the standard procedure for deciding PALA validity, i.e. the use of so-called reduction axioms to translate PALA formulae into formulae in epistemic logic EL, may lead to exponential growth. In this paper, we show that such a price is not mandatory, for we provide a polynomial translation of PALA into EL. This is based on abbreviations of subformulae (...) by new propositional letters. Such optimal translation also enables us to show the computational complexity of the problem of deciding PALA validity, which turns out to be coNP-complete in the single-agent case and PSPACE-complete in the multiagent case. (shrink)

We propose a dynamic logic of lying, wherein a ‘lie that $\varphi $ ’ (where $\varphi $ is a formula in the logic) is an action in the sense of dynamic modal logic, that is interpreted as a state transformer relative to the formula $\varphi $ . The states that are being transformed are pointed Kripke models encoding the uncertainty of agents about their beliefs. Lies can be about factual propositions but also about modal formulas, such as the beliefs of (...) other agents or the belief consequences of the lies of other agents. We distinguish two speaker perspectives: (Obs) an outside observer who is lying to an agent that is modelled in the system, and (Ag) an agent who is lying to another agent, and where both are modelled in the system. We distinguish three addressee perspectives: (Cred) the credulous agent who believes everything that it is told (even at the price of inconsistency), (Skep) the skeptical agent who only believes what it is told if that is consistent with its current beliefs, and (Rev) the belief revising agent who believes everything that it is told by consistently revising its current, possibly conflicting, beliefs. The logics have complete axiomatizations, which can most elegantly be shown by way of their embedding in what is known as action model logic or in the extension of that logic to belief revision. (shrink)

We show how belief revision can be treated systematically in the format of dynamicepistemic logic, when operators of conditional belief are added. The core engine consists of definable update rules for changing plausibility relations between worlds, which have been proposed independently in the dynamic-epistemic literature on preference change. Our analysis yields two new types of modal result. First, we obtain complete logics for concrete mechanisms of belief revision, based on compositional reduction axioms. Next, we show how various abstract postulates for (...) belief revision can be analyzed by standard modal frame correspondences for model-changing operations. (shrink)

This paper introduces a multi-agent dynamic epistemic logic for abstract argumentation. Its main motivation is to build a general framework for modelling the dynamics of a debate, which entails reasoning about goals, beliefs, as well as policies of communication and information update by the participants. After locating our proposal and introducing the relevant tools from abstract argumentation, we proceed to build a three-tiered logical approach. At the first level, we use the language of propositional logic to encode states of a (...) multi-agent debate. This language allows to specify which arguments any agent is aware of, as well as their subjective justification status. We then extend our language and semantics to that of epistemic logic, in order to model individuals’ beliefs about the state of the debate, which includes uncertainty about the information available to others. As a third step, we introduce a framework of dynamic epistemic logic and its semantics, which is essentially based on so-called event models with factual change. We provide completeness results for a number of systems and show how existing formalisms for argumentation dynamics and unquantified uncertainty can be reduced to their semantics. The resulting framework allows reasoning about subtle epistemic and argumentative updates—such as the effects of different levels of trust in a source—and more in general about the epistemic dimensions of strategic communication. (shrink)

We propose a general framework for dynamic epistemic logics. It consists of a generic language for DELs and a class of structures, called model transition systems, that describe model transformations in a static way. An MTS can be viewed as a two-layered Kripke model and consequently inherits standard concepts such as bisimulation and bounded morphism from the ordinary Kripke models. In the second half of this article we add the global operator to the language, which enables us to define the (...) notions of a canonical MTS and canonicity of a DEL formula for a property of MTSs. Using these notions, we clarify correspondences between axioms of DELs and properties of MTSs. (shrink)

A commonly used dynamic epistemic logic is one obtained by adding commonknowledge and public announcements to a basic epistemic logic. It is known from Kooi (2007) that adding public substitutions to such a logic adds expressivity over the class K of models. Here I show that substitutions also add expressivity over the classes KD45, S4 and S5 of models. Since the combination of common knowledge, public announcements and substitutions, was shown in Kooi (2007) to be equally expressive to relativized common (...) knowledge these results also show that relativized common knowledge is more expressive than common knowledge and public announcements over KD45, S4 and S5. These results therefore extend the result from van Benthem et al. (2006) that shows that relativized common knowledge is more expressive than common knowledge and public announcements over K. (shrink)

In this paper we investigate a logic for modelling individual and collective acceptances that is called acceptance logic. The logic has formulae of the form $A_{Gx} \phi $ reading 'if the agents in the set of agents G identify themselves with institution x then they together accept that φ'. We extend acceptance logic by two kinds of dynamic modal operators. The first kind are public announcements of the form x!ψ, meaning that the agents learn that ψ is the case in (...) context x. Formulae of the form [x!ψ]φ mean that φ is the case after every possible occurrence of the event x!ψ. Semantically, public announcements diminish the space of possible worlds accepted by agents and sets of agents. The announcement of ψ in context x makes all ¬ψ-Worlds inaccessible to the agents in such context. In this logic, if the set of accessible worlds of G in context x is empty, then the agents in G are not functioning as members of x, they do not identify themselves with x. In such a situation the agents in G may have the possibility to join x. To model this we introduce here a second kind of dynamic modal operator of acceptance shifting of the form G:x↑ψ. The latter means that the agents in G shift (change) their acceptances in order to accept ψ in context x. Semantically, they make ψ-worlds accessible to G in the context x, which means that, after such operation, G is functioning as member of x (unless there are no ψ-worlds). We show that the resulting logic has a complete axiomatization in terms of reduction axioms for both dynamic operators. In the paper we also show how the logic of acceptance and its dynamic extension can be used to model some interesting aspects of judgement aggregation. In particular, we apply our logic of acceptance to a classical scenario in judgment aggregation, the so-called 'doctrinal paradox' or 'discursive dilemma' (Pettit, Philosophical Issues 11: 268-299, 2001; Kornhauser and Sager, Yale Law Journal 96: 82-117, 1986). (shrink)

In this paper we investigate a logic for modelling individual and collective acceptances that is called acceptance logic. The logic has formulae of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm A}_{G:x} \varphi$$\end{document} reading ‘if the agents in the set of agents G identify themselves with institution x then they together accept that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varphi}$$\end{document} ’. We extend acceptance logic by two kinds of dynamic modal operators. The first (...) kind are public announcements of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x!\psi}$$\end{document}, meaning that the agents learn that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\psi}$$\end{document} is the case in context x. Formulae of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${[x!\psi]\varphi}$$\end{document} mean that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varphi}$$\end{document} is the case after every possible occurrence of the event x!ψ. Semantically, public announcements diminish the space of possible worlds accepted by agents and sets of agents. The announcement of ψ in context x makes all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\lnot\psi}$$\end{document} -worlds inaccessible to the agents in such context. In this logic, if the set of accessible worlds of G in context x is empty, then the agents in G are not functioning as members of x, they do not identify themselves with x. In such a situation the agents in G may have the possibility to join x. To model this we introduce here a second kind of dynamic modal operator of acceptance shifting of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${G:x\uparrow\psi}$$\end{document}. The latter means that the agents in G shift (change) their acceptances in order to accept ψ in context x. Semantically, they make ψ-worlds accessible to G in the context x, which means that, after such operation, G is functioning as member of x (unless there are no ψ-worlds). We show that the resulting logic has a complete axiomatization in terms of reduction axioms for both dynamic operators. In the paper we also show how the logic of acceptance and its dynamic extension can be used to model some interesting aspects of judgement aggregation. In particular, we apply our logic of acceptance to a classical scenario in judgment aggregation, the so-called ‘doctrinal paradox’ or ‘discursive dilemma’ (Pettit, Philosophical Issues 11:268–299, 2001; Kornhauser and Sager, Yale Law Journal 96:82–117, 1986). (shrink)

Dynamic epistemic logics provide an account of the evolution of agents’ belief and knowledge when they learn the occurrence of an event. These logics started to become popular about 20 years ago and by now there exists a huge number of publications about them. The present paper briefly summarises the existing body of literature, discusses some problems and shortcomings, and proposes some avenues for future research.

Obligations can be affected by knowledge. Several approaches exist to formalize knowledge-based obligations, but no formalism has been developed yet to capture the dynamic interaction between knowledge and obligations. We introduce the dynamic extension of an existing logic for knowledge-based obligations here. We motivate the logic by analyzing several scenarios and by showing how it can capture in an original manner several fundamental deontic notions such as absolute, prima facie and all-things-considered obligations. Finally, in the dynamic epistemic logic tradition, we (...) provide reduction axioms for the dynamic operator of the new logic. (shrink)

A true lie is a lie that becomes true when announced. In a logic of announcements, where the announcing agent is not modelled, a true lie is a formula that becomes true when announced. We investigate true lies and other types of interaction between announced formulas, their preconditions and their postconditions, in the setting of Gerbrandy’s logic of believed announcements, wherein agents may have or obtain incorrect beliefs. Our results are on the satisfiability and validity of instantiations of these semantically (...) defined categories, on iterated announcements, including arbitrarily often iterated announcements, and on syntactic characterization. We close with results for iterated announcements in the logic of knowledge, and for lying as private announcements to different agents. Detailed examples illustrate our lying concepts. (shrink)

It has been an open question whether or not we can define a belief revision operation that is distinct from simple belief expansion using paraconsistent logic. In this paper, we investigate the possibility of meeting the challenge of defining a belief revision operation using the resources made available by the study of dynamic epistemic logic in the presence of paraconsistent logic. We will show that it is possible to define dynamic operations of belief revision in a paraconsistent setting.

In public announcement logic it is assumed that all agents pay attention to the announcement. Weaker observational conditions can be modelled in action model logic. In this work, we propose a version of public announcement logic wherein it is encoded in the states of the epistemic model which agents pay attention to the announcement. This logic is called attention-based announcement logic. We give an axiomatization of the logic and prove that complexity of satisfiability is the same as that of public (...) announcement logic, and therefore lower than that of action model logic. An attention-based announcement can also be described as an action model. We extend our logic by integrating attention change. Finally, we add the notion of common belief to the language, we exploit this to formalize the concept of joint attention, that has been widely discussed in the philosophical and cognitive science literature, and we provide a corresponding axiomatization. This axiomatization also employs the auxiliary notion of attention-based relativized common belief. (shrink)

Dynamic Epistemic Logic (DEL) deals with the representation and the study in a multi-agent setting of knowledge and belief change. It can express in a uniform way epistemic statements about: 1. what is true about an initial situation 2. what is true about an event occurring in this situation 3. what is true about the resulting situation after the event has occurred. We axiomatize within the DEL framework what we can infer about (iii) given (i) and (ii). Given three formulas (...) φ,φ' and φ" describing respectively (i), (ii) and (iii), we also show how to build a formula φ ? φ' which captures all the information which can be inferred about (iii) from φ and φ'. We show how our results extend to other modal logics than K. In our proofs and definitions, we resort to a large extent to the normal form formulas for modal logic originally introduced by Kit Fine. In a companion paper (Aucher, 2012), we axiomatize what we can infer about (ii) given (i) and (iii), and what we can infer about (i) given (ii) and (iii), and show how to build two formulas φ ? φ" and φ' ? φ" which capture respectively all the information which can be inferred about (ii) from φ and φ", and all the information which can be inferred about (i) from φ' and φ". (shrink)

Belief revision from the point of view of doxastic logic. Logic Journal of the IGPL, 3(4), 535–553. Segerberg, K. (1995). Conditional action. In G. Crocco, L. Fariñas, & A. Herzig (Eds.), Conditionals: From philosophy to computer science, Studies ...

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)

This is indeed a very nice draft that I have read with great pleasure, and that has helped me to better understand the completeness proof for LCC. Modal fixed point logic allows for an illuminating new version (and a further extension) of that proof. But still. My main comment is that I think the perspective on substitutions in the draft paper is flawed. The general drift of the paper is that relativization, (predicate) substitution and product update are general operations on (...) models, and that it is important to check whether given logical languages are closed under these operations. FO logic is closed under relativization, predicate substitution and product constructions (such as those involved in relative interpretation). The minimal modal logic is closed under relativization, which explains the reduction of epistemic logic (withhout common knowledge) + public announcement to epistemic logic simpliciter (as observed in Van Benthem, [2]). The reduction breaks down as soon as one adds common knowledge. The minimal modal logic is also closed under substitution, which explains the reduction of epistemic logic plus (publicly observable) factual change to epistemic logic simpliciter, via the following reduction axioms (I use !p := φ for the operation of publicly changing the truth value of p to φ): [!p := φ]p ↔ φ [!p := φ]q ↔ q (p and q syntactically different ) [!p := φ]¬ψ ↔ ¬[!p := φ]ψ [!p := φ](ψ1 ∧ ψ2) ↔ [!p := φ]ψ1 ∧ [!p := φ]ψ2 [!p := φ][i]ψ ↔ [i][!p := φ]ψ Unlike the case of relativisation, this can be extended to the case of epistemic logic with common knowledge, by means of: [!p := φ]CGψ ↔ CG[!p := φ]ψ We get the following.. (shrink)

Collective intentionality is one of the most fundamental notions in social ontology. However, it is often thought to refer to a capacity which does not presuppose the existence of any other social facts. This chapter critically examines this view from the perspective of one specific theory of collective intentionality, the theory of Margaret Gilbert. On the basis of Gilbert’s arguments, the chapter claims that collective intentionality is a highly contingent achievement of complex social practices and, thus, not a basic social (...) phenomenon. The argument proceeds in three steps. First, Gilbert’s thesis that certain kinds of collective intentionality presuppose joint normative commitments is introduced. Second, it is argued that, on this view, individual commitments can only constitute the relevant kinds of collective intentional states if there are socially shared “principles of membership” that connect the force of individual commitments to a shared content. Third, it is shown that strong collective intentionality depends on the practical acceptance of shared norms and on the establishment of authority relations through mutual recognition. (shrink)

Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitution. A distinction therefore arises between the logic and its substitution core, the set of formulas all of whose substitution instances are valid. The classic example of a non-uniform dynamic epistemic logic is Public Announcement Logic (PAL), and a well-known open problem is to axiomatize the substitution core of PAL. In this paper we solve this problem for PAL over the class of all relational models with infinitely (...) many agents, PAL-K_omega, as well as standard extensions thereof, e.g., PAL-T_omega, PAL-S4_omega, and PAL-S5_omega. We introduce a new Uniform Public Announcement Logic (UPAL), prove completeness of a deductive system with respect to UPAL semantics, and show that this system axiomatizes the substitution core of PAL. (shrink)

We look at lying as an act of communication, where (i) the proposition that is communicated is not true, (ii) the utterer of the lie knows that what she communicates is not true, and (iii) the utterer of the lie intends the lie to be taken as truth. Rather than dwell on the moral issues, we provide a sketch of what goes on logically when a lie is communicated. We present a complete logic of manipulative updating, to analyse the effects (...) of lying in public discourse. Next, we turn to the study of lying in games. First, a game-theoretical analysis is used to explain how the possibility of lying makes such games interesting, and how lying is put to use in optimal strategies for playing the game. Finally, we give a matching logical analysis. Our running example of lying in games in liar’s dice. (shrink)

Three key ways of updating one’s knowledge are (i) perception of states of affairs, e.g., seeing with one’s own eyes that something is the case, (ii) reception of messages, e.g., being told that something is the case, and (iii) drawing new conclusions from known facts. If one represents knowledge by means of Kripke models, the implicit assumption is that drawing conclusions is immediate. This assumption of logical omniscience is a useful abstraction. It leaves the distinction between (i) and (ii) to (...) be accounted for. In current versions of Update Logic (Dynamic Epistemic Logic, Logic of Communication and Change) perception and message reception are not distinguished. This paper proposes an extension of Update Logic that makes this distinction explicit. The logic deals with three kinds of updates: announcements, changes of the world, and observations about the world in the presence of witnesses. The resulting logic is shown to be complete by means of a reduction to epistemic propositional dynamic logic by a well known method. (shrink)