The paper develops an interface between syntax-based logical models of awareness and dynamic epistemic logic. The framework is shown to be able to accommodate a variety of notions of awareness and knowledge, as well as their dynamics. This, it is argued, offers a natural formal environment for the analysis of epistemic phenomena typical of multi-agent information exchange, such as how agents become aware of relevant details, how they perform inferences and how they share their information within a group. Technically, the (...) logics presented are all simple refinements of the logic of public announcements. (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 ...

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)

Paraconsistent approaches have received little attention in the literature on vagueness (at least compared to other proposals). The reason seems to be that many philosophers have found the idea that a contradiction might be true (or that a sentence and its negation might both be true) hard to swallow. Even advocates of paraconsistency on vagueness do not look very convinced when they consider this fact; since they seem to have spent more time arguing that paraconsistent theories are at least as (...) good as their paracomplete counterparts, than giving positive reasons to believe on a particular paraconsistent proposal. But it sometimes happens that the weakness of a theory turns out to be its mayor ally, and this is what (I claim) happens in a particular paraconsistent proposal known as subvaluationism. In order to make room for truth-value gluts subvaluationism needs to endorse a notion of logical consequence that is, in some sense, weaker than standard notions of consequence. But this weakness allows the subvaluationist theory to accommodate higher-order vagueness in a way that it is not available to other theories of vagueness (such as, for example, its paracomplete counterpart, supervaluationism). (shrink)

We continue the work initiated in Herzig and Lorini (J Logic Lang Inform, in press) whose aim is to provide a minimalistic logical framework combining the expressiveness of dynamic logic in which actions are first-class citizens in the object language, with the expressiveness of logics of agency such as STIT and logics of group capabilities such as CL and ATL. We present a logic called ( Deterministic Dynamic logic of Agency ) which supports reasoning about actions and joint actions of (...) agents and coalitions, and agentive and coalitional capabilities. In it is supposed that, once all agents have selected a joint action, the effect of this joint action is deterministic. In order to assess we prove that it embeds Coalition Logic. We then extend with modal operators for agents’ preferences, and show that the resulting logic is sufficiently expressive to capture the game-theoretic concepts of best response and Nash equilibrium. (shrink)

A variety of logical frameworks have been developed to study rational agents interacting over time. This paper takes a closer look at one particular interface, between two systems that both address the dynamics of knowledge and information flow. The first is Epistemic Temporal Logic (ETL) which uses linear or branching time models with added epistemic structure induced by agents’ different capabilities for observing events. The second framework is Dynamic Epistemic Logic (DEL) that describes interactive processes in terms of epistemic event (...) models which may occur inside modalities of the language. This paper systematically and rigorously relates the DEL framework with the ETL framework. The precise relationship between DEL and ETL is explored via a new representation theorem characterizing the largest class of ETL models corresponding to DEL protocols in terms of notions of Perfect Recall , No Miracles , and Bisimulation Invariance . We then focus on new issues of completeness . One contribution is an axiomatization for the dynamic logic of public announcements constrained by protocols, which has been an open problem for some years, as it does not fit the usual ‘reduction axiom’ format of DEL. Finally, we provide a number of examples that show how DEL suggests an interesting fine-structure inside ETL. (shrink)

In the tradition of quantified modal logic, it was assumed that significantly different linguistic systems underlie reference to individuals, to times and to 'possible worlds'. Various results from recent research in formal semantics suggest that this is not so, and that there is in fact a pervasive symmetry between the linguistic means with which we refer to these three domains. Reference to individuals, times and worlds is uniformly effected through generalized quantifiers, definite descriptions, and pronouns, and in each domain grammatical (...) features situate the reference of terms as near, far or 'further' from the actual or from a reported speech act. We outline various directions in which a program of ontological symmetry could be developed, and we offer in the Appendix a symmetric fragment developed in a logic that can be seen as a compromise between an extensional and an intensional system. (shrink)

Abstract. The aim of this paper is to show that the topological interpretation of knowledge as an interior kernel operator K of a topological space (X, OX) comes along with a partially ordered family of belief modalities B that fit K in the sense that the pairs (K, B) satisfy all axioms of Stalnaker’s KB logic of knowledge and belief with the exception of the contentious axiom of negative introspection (NI). The new belief modalities B introduced in this paper are (...) defined with the help of the (dense) nuclei of the Heyting algebra OX of open subsets on the topological space (X, OX). In this way, the natural context for the belief operators B related to topological knowledge operator K is shown to be the Heyting algebra NUC(OX) of the nuclei of the Heyting algebra OX.1 More precisely, the dense nuclei of NUC(OX) can be used to define a variety of bimodal logics of knowledge operators K and belief operators B. The operators K and B are compatible with each other in the sense that the pairs (K, B) satisfy all axioms of Stalnaker’s KB system with the exception of the axiom (NI). Therefore, for (X, OX), one obtains a bounded, partially ordered family of belief operators B defined by the elements of NUC(OX). (shrink)

Recent ideas about epistemic modals and indicative conditionals in formal semantics have significant overlap with ideas in modal logic and dynamic epistemic logic. The purpose of this paper is to show how greater interaction between formal semantics and dynamic epistemic logic in this area can be of mutual benefit. In one direction, we show how concepts and tools from modal logic and dynamic epistemic logic can be used to give a simple, complete axiomatization of Yalcin's [16] semantic consequence relation for (...) a language with epistemic modals and indicative conditionals. In the other direction, the formal semantics for indicative conditionals due to Kolodny and MacFarlane [9] gives rise to a new dynamic operator that is very natural from the point of view of dynamic epistemic logic, allowing succinct expression of dependence (as in dependence logic) or supervenience statements. We prove decidability for the logic with epistemic modals and Kolodny and MacFarlane's indicative conditional via a full and faithful computable translation from their logic to the modal logic K45. (shrink)

In the tradition of quantified modal logic, it was assumed that significantly different linguistic systems underlie reference to individuals, to times and to ‘possible worlds’. Various results from recent research in formal semantics suggest that this is not so, and that there is in fact apervasive symmetrybetween the linguistic means with which we refer to these three domains. Reference to individuals, times and worlds is uniformly effected through generalized quantifiers, definite descriptions, and pronouns, and in each domain grammatical features situate (...) the reference of terms as near, far or ‘further’ from the actual or from a reported speech act. We outline various directions in which a program ofontological symmetrycould be developed, and we offer in theAppendixa symmetric fragment developed in a logic that can be seen as a compromise between an extensional and an intensional system. (shrink)

In this paper, a pragmatic approach to the phenomenon of free choice permission is proposed. Free choice permission is explained as due to taking the speaker (i) to obey certain Gricean maxims of conversation and (ii) to be competent on the deontic options, i.e. to know the valid obligations and permissions. The approach differs from other pragmatic approaches to free choice permission in giving a formally precise description of the class of inferences that can be derived based on these two (...) assumptions. This formalization builds on work of Halpern and Moses (1984) on the concept of ‘only knowing’, generalized by Hoek et al., (1999, 2000), and Zimmermann’s (2000) approach to competence. (shrink)

In this paper I present a range of substructural logics for a conditional connective ↦. This connective was original introduced semantically via restriction on the ternary accessibility relation R for a relevant conditional. I give sound and complete proof systems for a number of variations of this semantic definition. The completeness result in this paper proceeds by step-by-step improvements of models, rather than by the one-step canonical model method. This gradual technique allows for the additional control, lacking in the canonical (...) model method, that is required. (shrink)

Notions of k-asimulation and asimulation are introduced as asymmetric counterparts to k-bisimulation and bisimulation, respectively. It is proved that a first-order formula is equivalent to a standard translation of an intuitionistic propositional formula iff it is invariant with respect to k-asimulations for some k, and then that a first-order formula is equivalent to a standard translation of an intuitionistic propositional formula iff it is invariant with respect to asimulations. Finally, it is proved that a first-order formula is equivalent to a (...) standard translation of an intuitionistic propositional formula over the class of intuitionistic Kripke models iff it is invariant with respect to asimulations between intuitionistic models. (shrink)

The paper sketches an analysis of the notion of a self-fulfilling belief in terms of doxastic modal logic. We point out a connection between self-fulfilling beliefs and Moore’s paradox. Then we look at self-fulfilling beliefs in the context of neighborhood semantics. We argue that the analysis of several interesting self-fulfilling beliefs has to make essential use of propositional quantification.

I propose a modal logic that enables to reason about self-regarding and otherregarding motivations in strategic games. This logic integrates the concepts of joint action, belief, individual and group payoff. The first part of the article is focused on self-regarding agents. A self-regarding agent decides to perform a certain action only if he believes that this action maximizes his own personal benefit. The second part of the article explores different kinds of other-regarding motivations such as fairness and reciprocity. Differently from (...) self-regarding agents, other-regarding agents also consider the benefits of their choices for the group. Moreover, their decisions can be affected by their beliefs about other agents' willingness to act for the well-being of the group. The analysis also considers team-directed reasoning, i.e. the mode of reasoning that people use when they take themselves to be acting as members of a group or a team. (shrink)

The aim of this paper is to initiate a systematic exploration of the model theory of epistemic plausibility models (EPMs). There are two subtly different definitions in the literature: one by van Benthem and one by Baltag and Smets. Because van Benthem's notion is the most general, most of the paper is dedicated to this notion. We focus on the notion of bisimulation, and show that the most natural generalization of bisimulation to van Benthem-type EPMs fails. We then introduce parametrized (...) bisimulations, and prove various bisimulationimplies- equivalence theorems, a Hennessy-Milner theorem, and several (un)definability results. We discuss the problems arising from the fact that these bisimulations are syntax-dependent (and thus not fully structural), and we present and compare two different ways of coping with this issue: adding a modality to the language, and putting extra constraints on the models. We argue that the most successful solution involves restricting to uniform and locally connected (van Benthem-type) EPMs: for this subclass the intuitively most natural notion of bisimulation and the technically sound notion coincide. Such EPMs turn out to correspond exactly with Baltag/Smets-type EPMs, which can be interpreted as constituting a methodological argument, favoring Baltag and Smets's definition of EPM over that of van Benthem. (shrink)

Logic is breaking out of the confines of the single-agent static paradigm that has been implicit in all formal systems until recent times. We sketch some recent developments that take logic as an account of information-driven interaction. These two features, the dynamic and the social, throw fresh light on many issues within logic and its connections with other areas, such as epistemology and game theory.

Dynamic epistemic logic, broadly conceived, is the study of logics of information change. This is the first paper in a two-part series introducing this research area. In this paper, I introduce the basic logical systems for reasoning about the knowledge and beliefs of a group of agents.

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)

We investigate the process of truth-seeking by iterated belief revision with higher-level doxastic information . We elaborate further on the main results in Baltag and Smets (Proceedings of TARK, 2009a , Proceedings of WOLLIC’09 LNAI 5514, 2009b ), applying them to the issue of convergence to truth . We study the conditions under which the belief revision induced by a series of truthful iterated upgrades eventually stabilizes on true beliefs. We give two different conditions ensuring that beliefs converge to “full” (...) (complete) truth , as well as a condition ensuring only that they converge to true (but not necessarily complete) beliefs. (shrink)

We formalize what it means to have permission to say something. We adapt the dynamic logic of permission by van der Meyden (J Log Comput 6(3):465–479, 1996 ) to the case where atomic actions are public truthful announcements. We also add a notion of obligation. Our logic is an extension of the logic of public announcements introduced by Plaza ( 1989 ) with dynamic modal operators for permission and for obligation. We axiomatize the logic and show that it is decidable.

We describe a logic of preference in which modal connectives reflect reasons to desire that a sentence be true. Various conditions on models are introduced and analyzed.

The aim of this paper, is to provide a logical framework for reasoning about actions, agency, and powers of agents and coalitions in game-like multi-agent systems. First we define our basic Dynamic Logic of Agency ( ). Differently from other logics of individual and coalitional capability such as Alternating-time Temporal Logic (ATL) and Coalition Logic, in cooperation modalities for expressing powers of agents and coalitions are not primitive, but are defined from more basic dynamic logic operators of action and (historic) (...) necessity. We show that STIT logic can be reconstructed in . We then extend with epistemic operators, which allows us to distinguish capability and power. We finally characterize the conditions under which agents are aware of their capabilities and powers. (shrink)

In this paper I present a dynamic-epistemic hybrid logic for reasoning about information and intention changes in situations of strategic interaction. I provide a complete axiomatization for this logic, and then use it to study intentions-based transformations of decision problems.

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

It is well known that the non-orthogonality relation between the (pure) states of a quantum system is reflexive and symmetric, and the modal logic $$\mathbf {KTB}$$ is sound and complete with respect to the class of sets each equipped with a reflexive and symmetric binary relation. In this paper, we consider two properties of the non-orthogonality relation: Separation and Superposition. We find sound and complete modal axiomatizations for the classes of sets each equipped with a reflexive and symmetric relation that (...) satisfies each one of these two properties and both, respectively. We also show that the modal logics involved are decidable. (shrink)

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)

Since it was first proposed by Moses, Shoham, and Tennenholtz, the social laws paradigm has proved to be one of the most compelling approaches to the offline coordination of multiagent systems. In this paper, we make four key contributions to the theory and practice of social laws in multiagent systems. First, we show that the Alternating-time Temporal Logic (atl) of Alur, Henzinger, and Kupferman provides an elegant and powerful framework within which to express and understand social laws for multiagent systems. (...) Second, we show that the effectiveness, feasibility, and synthesis problems for social laws may naturally be framed as atl model checking problems, and that as a consequence, existing atl model checkers may be applied to these problems. Third, we show that the complexity of the feasibility problem in our framework is no more complex in the general case than that of the corresponding problem in the Shoham–Tennenholtz framework (it is np-complete). Finally, we show how our basic framework can easily be extended to permit social laws in which constraints on the legality or otherwise of some action may be explicitly required. We illustrate the concepts and techniques developed by means of a running example. (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)

• We study a new composition operation on (epistemic) multiagent models and update actions that takes vocabulary extensions into account.

The hybrid logic and the independence friendly modal logic IFML are compared for their expressive powers. We introduce a logic IFML c having a non-standard syntax and a compositional semantics; in terms of this logic a syntactic fragment of IFML is singled out, denoted IFML c . (In the Appendix it is shown that the game-theoretic semantics of IFML c coincides with the compositional semantics of IFML c .) The hybrid logic is proven to be strictly more expressive than IFML (...) c . By contrast, and the full IFML are shown to be incomparable for their expressive powers. Building on earlier research (Tulenheimo and Sevenster 2006), a PSPACE -decidable fragment of the undecidable logic is disclosed. This fragment is not translatable into the hybrid logic and has not been studied previously in connection with hybrid logics. In the Appendix IFML c is shown to lack the property of ‘quasi-positionality’ but proven to enjoy the weaker property of ‘ bounded quasi-positionality’. The latter fact provides from the IFML internal perspective an account of what makes the compositional semantics of IFML c possible. (shrink)

In the paper we present a technique for eliminating quantifiers of arbitrary order, in particular of first-order. Such a uniform treatment of the elimination problem has been problematic up to now, since techniques for eliminating first-order quantifiers do not scale up to higher-order contexts and those for eliminating higher-order quantifiers are usually based on a form of monotonicity w.r.t implication (set inclusion) and are not applicable to the first-order case. We make a shift to arbitrary relations “ordering” the underlying universe. (...) This allows us to incorporate background theories into higher-order quantifier elimination methods which, up to now, has not been achieved. The technique we propose subsumes many other results, including the Ackermann's lemma and various forms of fixpoint approaches when the “ordering” relations are interpreted as implication and reveals the common principle behind these approaches. (shrink)

In this paper, we extend the canonicity methodology in Ghilardi & Meloni (1997) to arbitrary lattice expansions, and syntactically describe canonical inequalities for lattice expansions consisting of -meet preserving operations, -multiplicative operations, adjoint pairs, and constants. This approach gives us a uniform account of canonicity for substructural and lattice-based logics. Our method not only covers existing results, but also systematically accounts for many canonical inequalities containing nonsmooth additive and multiplicative uniform operations. Furthermore, we compare our technique with the approach in (...) Dunn et al. (2005) and Gehrke et al. (2005). (shrink)

This paper is concerned with removing the identity schema from the axiomatic basis of deontic conditionals. This is in order to allow a stipulated ideal to be contrary or opposite in nature to the fact it is predicated upon. It is desirable, or so it is argued, to retain the order-theoretic orientation of preferential semantics towards the analysis of deontic conditionals, more specifically of maximality semantics in the tradition from Bengt Hansson. So understood, the problem involves abstracting away the settledness (...) assumption that is built in to maximality semantics. This is the assumption that what is optimal given ϕ is that which all the best ϕ-states have in common, notably ϕ itself. We propose a solution based on a strict and finite preference relation over which deontic conditionals are evaluated by letting ϕ-states evolve freely, as fate or fortune would have it, into different possibly ensuing optima that may but need not be ϕ-states themselves. The result is a deontic conditional that does not have identity. This new conditional is shown to be a proper generalization of the Hansson conditional. Hansson’s conditional can be recovered in the new idiom as a special case. Indeed, the new semantics is general enough to cover several apparently very different conceptions of deontic conditionality. For instance, the input/output logic known as basic output is a sublogic of the new system. This is somewhat surprising and suggests that there may yet be unity to be had in the field of deontic logic. (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)

In this paper we investigate Kripke models, used to model knowledge or belief in a static situation, and action models, used to model communicative actions that change this knowledge or belief. The appropriate notion for structural equivalence between modal structures such as Kripke models is bisimulation: Kripke models that are bisimilar are modally equivalent. We would like to find a structural relation that can play the same role for the action models that play a prominent role in information updating. Two (...) action models are equivalent if they yield the same results when updating Kripke models. More precisely, two action models are equivalent if it holds for all Kripke models that the result of updating with one action model is bisimilar to the result of updating with the other action model. We propose a new notion of action emulation that characterizes the structural equivalence of the important class of canonical action models. Since every action model has an equivalent canonical action model, this gives a method to decide the equivalence of any pair of action models. We also give a partial result that holds for the class of all action models. Our results extend the work in van Eijck et al. (Synthese 185(1):131–151, 2012). (shrink)

In this paper, we explore the relation between an agent’s doxastic attitude and her arguments in support of a given claim. Our main contribution is the design of a logical setting that allows us reason about binary arguments which are either in favour or against a certain claim. This is a setting in which arguments and propositions are the basic building blocks so that the concept of argument-based belief emerges in a straightforward way. We work against the background of Dung’s (...) abstract argumentation framework, extending it to a new setting in which we can study the formal properties of binary arguments as well as the larger structures they establish. This paper introduces a formal ‘two-dimensional’ language to talk about propositions and arguments, for which a sound and complete axiom system is provided. (shrink)

In this paper we consider an independence-friendly modal logic, IFML. It follows from results in the literature that qua expressive power, IFML is a fragment of second-order existential logic, , that cannot be translated into first-order logic. It is also known that IFML lacks the tree structure property. We show that IFML has the , a weaker version of the tree structure property, and that its satisfiability problem is solvable in 2NEXP. This implies that this paper reveals a new decidable (...) fragment of . We also show that IFML becomes undecidable if we add the identity symbol to its vocabulary by means of a reduction from the tiling problem. (shrink)

We consider a simple modal logic whose nonmodal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of axioms corresponding to the characteristic axioms of _T_, _S4_, and _S5_, such logics are useful, as shown in previous work by Baltag, Coecke, and the first author, for encoding and reasoning about information and misinformation in multiagent systems. For the propositional-only fragment of such (...) a dynamic epistemic logic, we present an algebraic semantics, using lattices with agent-indexed families of adjoint pairs of operators, and a cut-free sequent calculus. The calculus exploits operators on sequents, in the style of “nested” or “tree-sequent” calculi; cut-admissibility is shown by constructive syntactic methods. The applicability of the logic is illustrated by reasoning about the muddy children puzzle, for which the calculus is augmented with extra rules to express the facts of the muddy children scenario. (shrink)

We analyse the computational complexity of comparing informational structures. Intuitively, we study the complexity of deciding queries such as the following: Is Alice’s epistemic information strictly coarser than Bob’s? Do Alice and Bob have the same knowledge about each other’s knowledge? Is it possible to manipulate Alice in a way that she will have the same beliefs as Bob? The results show that these problems lie on both sides of the border between tractability (P) and intractability (NP-hard). In particular, we (...) investigate the impact of assuming information structures to be partition-based (rather than arbitrary relational structures) on the complexity of various problems. We focus on the tractability of concrete epistemic tasks and not on epistemic logics describing them. (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)

In this paper I use the distinction between hard and soft information from the dynamic epistemic logic tradition to extend prior work on informational conceptions of logic to include non-monotonic consequence-relations. In particular, I defend the claim that at least some non-monotonic logics can be understood on the basis of soft or “belief-like” logical information, and thereby question the orthodox view that all logical information is hard, “knowledge-like”, information.

Biological modalities (e.g., biological possibility, necessity and counterfactuality) play an important explanatory role in biological practice. However, biological modalities lack truth conditions and the inferential relationship between biological and other modalities is unclear. This thesis addresses these problems, first, by improving upon Daniel Dennett's Library of Mendel. Second, a family of modal logics is introduced. In the simplest model, states are interpreted as codons, the binary relation is interpreted as single substitution mutation and the valuation induces a partition of blocks (...) of codons that code for some amino acid. In addition, the proposed framework allows for a grading of biological possibility and captures various competing notions of biological possibility. Applications include a model checker and a lawless Lewis-style semantics for biological counterfactuals. In short, this thesis lays the groundwork for a theory of biological modalities. (shrink)

This paper discusses a new aporia, the aporia of future directed beliefs. This aporia contains three propositions: (1) It is possible that there is someone who is infallible that believes something about the future that is not historically settled, (2) it is necessary that someone is infallible if and only if it is necessary that everything she believes is true, and (3) it is necessary that all our beliefs are historically settled. Every claim in this set is intuitively plausible, and (...) there are interesting arguments for or against each of them. Nevertheless, {(1), (2), (3)} entails a contradiction. Consequently, at least one of the sentences in this set must be false. I consider some possible solutions to the problem and discuss some arguments for and against these solutions. Five solutions, in particular, stand out. Three solutions reject (1), one solution rejects (2), and one solution rejects (3). No solution is without problems, and it is not obvious which one we should choose. Yet, we have to give up at least one sentence in {(1), (2), (3)}. This is the nature of an aporia. (shrink)

In this paper, I will develop a set of boulesic-doxastic tableau systems and prove that they are sound and complete. Boulesic-doxastic logic consists of two main parts: a boulesic part and a doxastic part. By ‘boulesic logic’ I mean ‘the logic of the will’, and by ‘doxastic logic’ I mean ‘the logic of belief’. The first part deals with ‘boulesic’ concepts, expressions, sentences, arguments and theorems. I will concentrate on two types of boulesic expression: ‘individual x wants it to be (...) the case that’ and ‘individual x accepts that it is the case that’. The second part deals with ‘doxastic’ concepts, expressions, sentences, arguments and theorems. I will concentrate on two types of doxastic expression: ‘individual x believes that’ and ‘it is imaginable to individual x that’. Boulesic-doxastic logic investigates how these concepts are related to each other. Boulesic logic is a new kind of logic. Doxastic logic has been around for a while, but the approach to this branch of logic in this paper is new. Each system is combined with modal logic with two kinds of modal operators for historical and absolute necessity and predicate logic with necessary identity and ‘possibilist’ quantifiers. I use a kind of possible world semantics to describe the systems semantically. I also sketch out how our basic language can be extended with propositional quantifiers. All the systems developed in this paper are new. (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)