We investigate the expressive power of memory logics. These are modal logics extended with the possibility to store (or remove) the current node of evaluation in (or from) a memory, and to perform membership tests on the current memory. From this perspective, the hybrid logic (↓), for example, can be thought of as a particular case of a memory logic where the memory is an indexed list of elements of the domain.

The picture of information acquisition as the elimination of possibilities has proven fruitful in many domains, serving as a foundation for formal models in philosophy, linguistics, computer science, and economics. While the picture appears simple, its formalization in dynamic epistemic logic reveals subtleties: given a valid principle of information dynamics in the language of dynamic epistemic logic, substituting complex epistemic sentences for its atomic sentences may result in an invalid principle. In this article, we explore such failures of uniform substitution. (...) First, we give epistemic examples inspired by Moore, Fitch, and Williamson. Second, we answer affirmatively a question posed by van Benthem: can we effectively decide when every substitution instance of a given dynamic epistemic principle is valid? In technical terms, we prove the decidability of this schematic validity problem for public announcement logic (PAL and PAL-RC) over models for finitely many fully introspective agents, as well as models for infinitely many arbitrary agents. The proof of this result illuminates the reasons for the failure of uniform substitution. (shrink)

Larry Moss and Rohit Parikh used subset semantics to characterize a family of logics for reasoning about knowledge. An important feature of their framework is that subsets always decrease based on the assumption that knowledge always increases. We drop this assumption and modify the semantics to account for logics of knowledge that handle arbitrary changes, that is, changes that do not necessarily result in knowledge increase, such as the update of our knowledge due to an action. We present a system (...) which is complete for subset spaces and prove its decidability. (shrink)

The 1985 paper by Carlos Alchourrón (1931–1996), Peter Gärdenfors, and David Makinson (AGM), "On the Logic of Theory Change: Partial Meet Contraction and Revision Functions" was the starting-point of a large and rapidly growing literature that employs formal models in the investigation of changes in belief states and databases. In this review, the first twentyfive years of this development are summarized. The topics covered include equivalent characterizations of AGM operations, extended representations of the belief states, change operators not included in (...) the original framework, iterated change, applications of the model, its connections with other formal frameworks, computatibility of AGM operations, and criticism of the model. (shrink)

Paul Grice has given an account of conversational implicatures that hinges on the hypothesis that communication is a cooperative activity performed by rational agents which pursue a common goal. The attempt to derive Grice’s principles from game theory is a natural step, since its aim is to predict the behaviour of rational agents in situations where the outcome of one agent’s choice depends also on the choices of others. Generalised conversational implicatures, and in particular scalar ones, offer an ideal test (...) bed for this working hypothesis, since with this kind of implicatures the alternative choices available to the agents are less dependent on context, and they can be derived from the meanings of the sentences employed. Some rival game-theoretic accounts of the same phenomena will be criticised. The present paper shows that scalar implicatures can be explained using iterated admissibility, but that some of these need an additional assumption in order to be accounted for. (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)

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)

While dynamic epistemic logics with common knowledge have been extensively studied, dynamic epistemic logics with distributed knowledge have so far received far less attention. In this paper we study extensions of public announcement logic ( $\mathcal{PAL }$ ) with distributed knowledge, in particular their expressivity, axiomatisations and complexity. $\mathcal{PAL }$ extended only with distributed knowledge is not more expressive than standard epistemic logic with distributed knowledge. Our focus is therefore on $\mathcal{PACD }$ , the result of adding both common and (...) distributed knowledge to $\mathcal{PAL }$ , which is more expressive than each of its component logics. We introduce an axiomatisation of $\mathcal{PACD }$ , which is not surprising: it is the combination of well-known axioms. The completeness proof, however, is not trivial, and requires novel combinations and extensions of techniques for dealing with $S5$ knowledge, distributed knowledge, common knowledge and public announcements at the same time. We furthermore show that $\mathcal{PACD }$ is decidable, more precisely that it is $\textsc {exptime}$ -complete. This result also carries over to $\mathcal{S 5\mathcal CD }$ with common and distributed knowledge operators for all coalitions (and not only the grand coalition). Finally, we propose a notion of a trans-bisimulation to generalise certain results and give deeper insight into the proofs. (shrink)

We examine a special case of inquiry games and give an account of the informational import of asking questions. We focus on yes-or-no questions, which always carry information about the questioner's strategy, but never about the state of Nature, and show how strategic information reduces uncertainty through inferences about other players' goals and strategies. This uncertainty cannot always be captured by information structures of classical game theory. We conclude by discussing the connection with Gricean pragmatics and contextual constraints on interpretation.

This paper presents the results of an experiment on mutual versus common knowledge of advice in a two-player weak-link game with random matching. Our experimental subjects play in pairs for thirteen rounds. After a brief learning phase common to all treatments, we vary the knowledge levels associated with external advice given in the form of a suggestion to pick the strategy supporting the payoff-dominant equilibrium. Our results are somewhat surprising and can be summarized as follows: in all our treatments both (...) the choice of the efficiency-inducing action and the percentage of efficient equilibrium play are higher with respect to the control treatment, revealing that even a condition as weak as mutual knowledge of level 1 is sufficient to significantly increase the salience of the efficient equilibrium with respect to the absence of advice. Furthermore, and contrary to our hypothesis, mutual knowledge of level 2 induces, under suitable conditions, successful coordination more frequently than common knowledge. (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)

This paper presents a new modal logic for ceteris paribus preferences understood in the sense of "all other things being equal". This reading goes back to the seminal work of Von Wright in the early 1960's and has returned in computer science in the 1990' s and in more abstract "dependency logics" today. We show how it differs from ceteris paribus as "all other things being normal", which is used in contexts with preference defeaters. We provide a semantic analysis and (...) several completeness theorems. We show how our system links up with Von Wright's work, and how it applies to game-theoretic solution concepts, to agenda setting in investigation, and to preference change. We finally consider its relation with infinitary modal logics. (shrink)

We study belief change in the branching-time structures introduced in Bonanno (Artif Intell 171:144–160, 2007 ). First, we identify a property of branching-time frames that is equivalent (when the set of states is finite) to AGM-consistency, which is defined as follows. A frame is AGM-consistent if the partial belief revision function associated with an arbitrary state-instant pair and an arbitrary model based on that frame can be extended to a full belief revision function that satisfies the AGM postulates. Second, we (...) provide a set of modal axioms that characterize the class of AGM-consistent frames within the modal logic introduced in Bonanno (Artif Intell 171:144–160, 2007 ). Third, we introduce a generalization of AGM belief revision functions that allows a clear statement of principles of iterated belief revision and discuss iterated revision both semantically and syntactically. (shrink)

Rational agents base their actions on information from observation, inference, introspection, or other sources. But this information comes in different kinds, and it is usually handled by different logical mechanisms. We discuss how to integrate external ‘updating information’ and internal ‘elucidating information’ into one system of dynamic epistemic logic, by distinguishing two basic informational actions: ‘bare seeing’ versus ‘conscious realization’.

Over the past decades, logicians interested in rational agency and intelligent interaction studied major components of these phenomena, such as knowledge, belief, and preference. In recent years, standard ‘static’ logics describing information states of agents have been generalized to dynamic logics describing actions and events that produce information, revise beliefs, or change preferences, as explicit parts of the logical system. Van Ditmarsch, van der Hoek & Kooi 2007, Baltag, van Ditmarsch & Moss 2008, van Benthem, to appear A, are up-to-date (...) accounts of this dynamic trend (the present paper follows Chapter 9 of the latter book). But in reality, concrete rational agency contains all these dynamic processes entangled. A concrete setting for this entanglement are games – and this paper is a survey of their interfaces with logic, both static and dynamic. Games are intriguing also since their analysis brings together two major streams, or tribal communities: ‘hard’ mathematical logics of computation, and ‘soft’ philosophical logics of propositional attitudes. Of course, this hard/soft distinction is spurious, and there is no natural border line between the two sources: it is their congenial mixture that makes current theories of agency so lively. (shrink)

Epistemology is the study of knowledge and justified belief. Belief is thus central to epistemology. It comes in a qualitative form, as when Sophia believes that Vienna is the capital of Austria, and a quantitative form, as when Sophia's degree of belief that Vienna is the capital of Austria is at least twice her degree of belief that tomorrow it will be sunny in Vienna. Formal epistemology, as opposed to mainstream epistemology (Hendricks 2006), is epistemology done in a formal way, (...) that is, by employing tools from logic and mathematics. The goal of this entry is to give the reader an overview of the formal tools available to epistemologists for the representation of belief. A particular focus will be the relation between formal representations of qualitative belief and formal representations of quantitative degrees of belief. (shrink)

We establish a correspondence between the rationalizability of choice studied in the revealed preference literature and the notion of minimal belief revision captured by the AGM postulates. A choice frame consists of a set of alternatives , a collection E of subsets of (representing possible choice sets) and a function f : E ! 2 (representing choices made). A choice frame is rationalizable if there exists a total pre-order R on..

Epistemic logic is the logic of knowledge and belief. It provides insight into the properties of individual knowers, has provided a means to model complicated scenarios involving groups of knowers and has improved our understanding of the dynamics of inquiry.

_Framing effects_ concern the having of different attitudes towards logically or necessarily equivalent contents. Framing is of crucial importance for cognitive science, behavioral economics, decision theory, and the social sciences at large. We model a typical kind of framing, grounded in (i) the structural distinction between beliefs activated in working memory and beliefs left inactive in long term memory, and (ii) the topic- or subject matter-sensitivity of belief: a feature of propositional attitudes which is attracting growing research attention. We introduce (...) a class of models featuring (i) and (ii) to represent, and reason about, agents whose belief states can be subject to framing effects. We axiomatize a logic which we prove to be sound and complete with respect to the class. (shrink)

In this paper, we propose a dynamic epistemic framework to capture the knowledge evolution in multi-agent systems where agents are not able to observe. We formalize multi-agent conformant planning with group knowledge, and reduce planning problems to model checking problems. We prove that multi-agent conformant planning with group knowledge is Pspace -complete on the size of dynamic epistemic models. We also consider the alternative Kripke semantics, and show that for each Kripke model with perfect recall and no miracles, there is (...) an equivalent dynamic epistemic model and vice versa. (shrink)

Dynamic epistemic logic (DEL) is a multi-modal logic for reasoning about the change of knowledge in multi-agent systems. It extends epistemic logic by a modal operator for actions which announce logical formulas to other agents. In Hilbert-style proof calculi for DEL, modal action formulas are reduced to epistemic logic, whereas current sequent calculi for DEL are labelled systems which internalize the semantic accessibility relation of the modal operators, as well as the accessibility relation underlying the semantics of the actions. We (...) present a novel cut-free ordinary sequent calculus, called |$ \textbf{G4}_{P,A}[] $|⁠, for propositional DEL. In contrast to the known sequent calculi, our calculus does not internalize the accessibility relations, but—similar to Hilbert style proof calculi—action formulas are reduced to epistemic formulas. Since no ordinary sequent calculus for full S5 modal logic is known, the proof rules for the knowledge operator and the Boolean operators are those of an underlying S4 modal calculus. We show the soundness and completeness of |$ \textbf{G4}_{P,A}[] $| and prove also the admissibility of the cut-rule and of several other rules for introducing the action modality. (shrink)

In this paper we present an extension of (bunched) separation logic, Boolean BI, with epistemic and dynamic epistemic modalities. This logic, called action model separation logic ( \(\mathrm {AMSL}\) ), can be seen as a generalization of public announcement separation logic in which we replace public announcements with action models. Then we not only model public information change (public announcements) but also non-public forms of information change, such as private announcements. In this context the semantics for the connectives \(*\) and (...) \(\mathrel {-*}\) from separation logic are epistemic versions of their usual semantics. This is because formulas are interpreted in states, not in resources, and agents may be uncertain between different states representing the same resource. We present the logic \(\mathrm {AMSL}\) and its semantics, with a detailed case study that highlights its interest for modeling. We also prove the elimination of the dynamics modalities and discuss some alternative epistemic semantics for the separation connectives. (shrink)

This volume seeks to further the use of formal methods in clarifying one of the central problems of philosophy: that of our free human agency and its place in our indeterministic world. It celebrates the important contributions made in this area by Nuel Belnap, American logician and philosopher. Philosophically, indeterminism and free action can seem far apart, but in Belnap’s work, they are intimately linked. This book explores their philosophical interconnectedness through a selection of original research papers that build forth (...) on Belnap’s logical and philosophical work. Some contributions take the form of critical discussions of Belnap's published work, some develop points made in his publications in new directions, and others provide additional insights on the topics of indeterminism and free action. In Nuel Belnap’s work on indeterminism and free action, three formal frameworks figure prominently: the simple branching histories framework known as "branching time;" its relativistic spatio-temporal extension, branching space-times; and the “seeing to it that” logic of agency. As those frameworks provide the formal background for the contributed papers, the volume introduction gives an overview of the current state of their development. It also introduces case-intensional first order logic, a general intensional logic offering resources for a first-order extension of the mentioned frameworks and a recent research focus of Belnap’s. The volume also contains an extended biographical interview with Nuel Belnap. (shrink)

Orthodox semantics for natural language modals give rise to two puzzles for their interactions with disjunction: Ross’s puzzle and the puzzle of free choice permission. It is widely assumed that each puzzle can be explained in terms of the licensing of ‘Diversity’ inferences: from the truth of a possibility or necessity modal with an embedded disjunction, hearers infer that each disjunct is compatible with the relevant set of worlds. I argue that Diversity inferences are too weak to explain the full (...) range of data. Instead, I argue, modals with embedded disjunctions license ‘Independence’ inferences: from the truth of a modal with an embedded disjunction, hearers infer that each disjunct is an independent alternative among the relevant set of worlds. I then develop a bilateral inquisitive semantics for modals that predicts the validity of these Independence inferences. My account vindicates common intuitions about both Ross’s puzzle and the puzzle of free choice permission, and explains the full range of data. (shrink)

The negative particles lā/ ’al in Ugaritic change from positive to negative in modal contexts, conditional, questions, disjunctions, etc. They have usually been studied from a Semitic and linguistic points of view. On the basis of their occurrence in Ugaritic texts, we pretend to explain their uncommon behaviour from a philosophical and logico-semantic perspective. Is it possible to translate this linguistic structure in our Modern languages? Starting from a general view of their use in Ugaritic language, we claim that this (...) phenomenon can be more clearly understood in relation to modality. We interpret these negation as a negative evidential paradigm and we explain how they change in different contexts. Methodologically, we make use of formal tools of Dynamic Epistemic Logic in order to provide a more fine-grained understanding of these negations, and their dynamics. (shrink)

In recent decades, the logical study of rational belief dynamics has played an increasingly important role in philosophy. However, the dynamics of concepts such as conceptual learning received comparatively little attention within this debate. This is problematic insofar as the occurrence of conceptual change (especially in the sciences) has been an influential argument against a merely logical analysis of beliefs. Especially Kuhn’s ideas about the incommensurability, i.e., untranslatability, of succeeding theories seem to stand in the way of logical reconstruction. This (...) paper investigates conceptual change as model-changing operations similar to belief revision and relates it to the notion of incommensurability. I consider several versions of conceptual change and discuss their influences on the expressive power, translatability and the potential arising of incommensurability. The paper concludes with a discussion of animal taxonomy in Aristotle’s and Linnaeus’s work. (shrink)

In this paper, we aim to explore connections between a Carnapian semantics of theoretical terms and an eliminative structuralist approach in the philosophy of mathematics. Specifically, we will interpret the language of Peano arithmetic by applying the modal semantics of theoretical terms introduced in Andreas (Synthese 174(3):367–383, 2010). We will thereby show that the application to Peano arithmetic yields a formal semantics of universal structuralism, i.e., the view that ordinary mathematical statements in arithmetic express general claims about all admissible interpretations (...) of the Peano axioms. Moreover, we compare this application with the modal structuralism by Hellman (Mathematics without numbers: towards a modal-structural interpretation. Oxford University Press: Oxford, 1989), arguing that it provides us with an easier epistemology of statements in arithmetic. (shrink)

This is an essay on the understanding of disposition concepts, which exploits the Ramsey test semantics of conditionals for a refined conditional analysis of dispositions. I will show that this semantics allows for a more accurate account of disposition concepts than the standard semantics of conditionals by David Lewis. This includes dealing with the counterexamples to the conditional analysis, which are known as finks, antidotes, and mimics.

In recent work, Stalnaker proposes a logical framework in which belief is realized as a weakened form of knowledge. Building on Stalnaker’s core insights, we employ topological tools to refine and, we argue, improve on this analysis. The structure of topological subset spaces allows for a natural distinction between what is known and what is knowable; we argue that the foundational axioms of Stalnaker’s system rely intuitively on both of these notions. More precisely, we argue that the plausibility of the (...) principles Stalnaker proposes relating knowledge and belief relies on a subtle equivocation between an “evidence-in-hand” conception of knowledge and a weaker “evidence-out-there” notion of what could come to be known. Our analysis leads to a trimodal logic of knowledge, knowability, and belief interpreted in topological subset spaces in which belief is definable in terms of knowledge and knowability. We provide a sound and complete axiomatization for this logic as well as its uni-modal belief fragment. We then consider weaker logics that preserve suitable translations of Stalnaker’s postulates, yet do not allow for any reduction of belief. We propose novel topological semantics for these irreducible notions of belief, generalizing our previous semantics, and provide sound and complete axiomatizations for the corresponding logics. (shrink)

Orthodox Bayesianism is a highly idealized theory of how we ought to live our epistemic lives. One of the most widely discussed idealizations is that of logical omniscience: the assumption that an agent’s degrees of belief must be probabilistically coherent to be rational. It is widely agreed that this assumption is problematic if we want to reason about bounded rationality, logical learning, or other aspects of non-ideal epistemic agency. Yet, we still lack a satisfying way to avoid logical omniscience within (...) a Bayesian framework. Some proposals merely replace logical omniscience with a different logical idealization; others sacrifice all traits of logical competence on the altar of logical non-omniscience. We think a better strategy is available: by enriching the Bayesian framework with tools that allow us to capture what agents can and cannot infer given their limited cognitive resources, we can avoid logical omniscience while retaining the idea that rational degrees of belief are in an important way constrained by the laws of probability. In this paper, we offer a formal implementation of this strategy, show how the resulting framework solves the problem of logical omniscience, and compare it to orthodox Bayesianism as we know it. (shrink)

En este ensayo exploramos una perspectiva epistemológica en la que el elemento social y colectivo del conocimiento juega un papel fundamental en la explicación de su producción y transmisión. Primero presentamos y criticamos una posición individualista que ha sido dominante en la epistemología contemporánea y cuyas raíces pueden trazarse, al menos, hasta Descartes. Posteriormente introducimos y defendemos nuestra propia mirada, una en la que el conocimiento es un proceso constituido por un conjunto de actividades y prácticas que tiene un carácter (...) material. (shrink)

Dynamic Epistemic Logic (DEL) is the study of how to reason about knowledge, belief, and communication. This paper studies the relative expressivity of certain fragments of the DEL language for public and private communication. It is shown that the language of public communication with common knowledge and the language of private communication with common knowledge are expressively incomparable for the class of all pointed Kripke models, which provides a formal proof that public and private communication are fundamentally different in the (...) presence of common knowledge. It is also shown that single-recipient private communication does not add expressive power to the language of modal logic with common knowledge for any class of transitive pointed Kripke models. The latter result provides a sense in which positive introspection—believing our own beliefs—induces a kind of self-dialog. (shrink)

The well known AGM framework for belief revision has recently been extended to include a model of the research agenda of the agent, i.e. a set of questions to which the agent wishes to find answers (Olsson & Westlund in Erkenntnis , 65 , 165–183, 2006 ). The resulting model has later come to be called interrogative belief revision . While belief revision has been studied extensively from the point of view of modal logic, so far interrogative belief revision has (...) only been dealt with in the metalanguage approach in which AGM was originally presented. In this paper, I show how to model interrogative belief revision in a modal object language using a class of operators for questions. In particular, the solution I propose will be shown to capture the notion of K-truncation , a method for agenda update in the case of expansion constructed by Olsson & Westlund. Two case studies are conducted: first, an interrogative extension of Krister Segerberg’s system DDL, and then a similar extension of Giacomo Bonanno’s modal logic for belief revision. Sound and complete axioms will be provided for both of the resulting logics. (shrink)

The paper relates evidence and justification logics, both philosophically and technically. On the philosophical side, it is suggested that the difference between the approaches to evidence in the two families of logics can be explained as a result of their focusing on two different notions of support provided by evidence. On the technical side, a justification logic with operators pertaining to both kinds of support is shown to be sound and complete with respect to a special class of awareness models. (...) In addition, a realization theorem with respect to K is shown to hold for the logic. (shrink)

We explore the possibilities that dynamic epistemic logic offers to model abductive reasoning. We show that many of the problems with formal approaches to abduction based on classical logic can be solved when considering an epistemic agent that reasons and acts.Exploramos las posibilidades que ofrece la lógica epistémica dinámica para modelar el razonamiento abductivo. Mostramos que muchos de los problemas que encuentran los tratamientos formales de la abducción basados en lógica clásica pueden ser resueltos al considerar un agente epistémico que (...) razona y actúa. (shrink)

Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or objective Bayesianism (...) or non-deductive logic), and some detailed examples of its use in mathematics surveyed. Examples of inductive reasoning in experimental mathematics are given and it is argued that the problem of induction is best appreciated in the mathematical case. (shrink)

Logical theories for representing knowledge are often plagued by the so-called Logical Omniscience Problem. The problem stems from the clash between the desire to model rational agents, which should be capable of simple logical inferences, and the fact that any logical inference, however complex, almost inevitably consists of inference steps that are simple enough. This contradiction points to the fruitlessness of trying to solve the Logical Omniscience Problem qualitatively if the rationality of agents is to be maintained. We provide a (...) quantitative solution to the problem compatible with the two important facets of the reasoning agent: rationality and resource boundedness. More precisely, we provide a test for the logical omniscience problem in a given formal theory of knowledge. The quantitative measures we use are inspired by the complexity theory. We illustrate our framework with a number of examples ranging from the traditional implicit representation of knowledge in modal logic to the language of justification logic, which is capable of spelling out the internal inference process. We use these examples to divide representations of knowledge into logically omniscient and not logically omniscient, thus trying to determine how much information about the reasoning process needs to be present in a theory to avoid logical omniscience. (shrink)

We study a logic for reasoning about agents that pass messages according to a protocol. Protocols are specified extensionally, as sets of sequences of ?legal? actions assigned to each state in a Kripke model. Message-passing events that are licensed by the protocol are modeled as updates in the style of dynamic epistemic logic. We also consider changes to the protocol by introducing message-encoding modalities, corresponding to communications actions that lead to protocol extensions. While in our general framework, messages are arbitrary (...) objects, we also consider the case that the messages that are passed are sentences of the object language itself. We present complete calculi for our logics and clarify the relationship of our proposal to earlier work on public announcement logic. (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)

Computer software is written in languages like C, Java or Haskell. In many cases social software is expressed in natural language. The paper explores connections between the areas of natural language analysis and analysis of social protocols, and proposes an extended program for natural language semantics, where the goals of natural language communication are derived from the demands of specific social protocols.

Current dynamic-epistemic logics model different types of information change in multi-agent scenarios. We generalize these logics to a probabilistic setting, obtaining a calculus for multi-agent update with three natural slots: prior probability on states, occurrence probabilities in the relevant process taking place, and observation probabilities of events. To match this update mechanism, we present a complete dynamic logic of information change with a probabilistic character. The completeness proof follows a compositional methodology that applies to a much larger class of dynamic-probabilistic (...) logics as well. Finally, we discuss how our basic update rule can be parameterized for different update policies, or learning methods. (shrink)