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Modal Logic: Graph. Darst

New York: Cambridge University Press. Edited by Maarten de Rijke & Yde Venema (2001)

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  1. Are the Validities of Modal Logic Analytic? Or Analyticity Again, through Information, Proof, Modal Logic and Hintikka.Francesca Poggiolesi - 2015 - Philosophia Scientiae 19:221-243.
    Dans la philosophie de Hintikka la notion d'analyticité occupe une place particulière (e.g., [Hintikka 1973], [Hintikka 2007]) ; plus précisément, le philosophe finnois distingue deux notions d'analyticité : l'une qui est basée sur la notion d'information, l'autre sur la notion de preuve. Alors que ces deux notions ont été largement utilisées pour étudier la logique propositionnelle et la logique du premier ordre, aucun travail n'a été développé pour la logique modale. Cet article se propose de combler cette lacune et ainsi (...)
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  • Determining the environment: a modal logic for closed interaction.Jan Broersen, Rosja Mastop, John-Jules Meyer & Paolo Turrini - 2009 - Synthese 169 (2):351-369.
    The aim of the work is to provide a language to reason about Closed Interactions, i.e. all those situations in which the outcomes of an interaction can be determined by the agents themselves and in which the environment cannot interfere with they are able to determine. We will see that two different interpretations can be given of this restriction, both stemming from Pauly Representation Theorem. We will identify such restrictions and axiomatize their logic. We will apply the formal tools to (...)
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  • Von Wright’s “The Logic of Preference” revisited.Fenrong Liu - 2010 - Synthese 175 (1):69-88.
    Preference is a key area where analytic philosophy meets philosophical logic. I start with two related issues: reasons for preference, and changes in preference, first mentioned in von Wright’s book The Logic of Preference but not thoroughly explored there. I show how these two issues can be handled together in one dynamic logical framework, working with structured two-level models, and I investigate the resulting dynamics of reason-based preference in some detail. Next, I study the foundational issue of entanglement between preference (...)
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  • Public and private communication are different: results on relative expressivity.Bryan Renne - 2008 - Synthese 165 (2):225-245.
    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 (...)
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  • Semantics and truth relative to a world.Michael Glanzberg - 2009 - Synthese 166 (2):281-307.
    This paper argues that relativity of truth to a world plays no significant role in empirical semantic theory, even as it is done in the model-theoretic tradition relying on intensional type theory. Some philosophical views of content provide an important notion of truth at a world, but they do not constrain the empirical domain of semantic theory in a way that makes this notion empirically significant. As an application of this conclusion, this paper shows that a potential motivation for relativism (...)
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  • Arthur Prior and Hybrid Logic.Patrick Blackburn - 2006 - Synthese 150 (3):329-372.
    Contemporary hybrid logic is based on the idea of using formulas as terms, an idea invented and explored by Arthur Prior in the mid-1960s. But Prior’s own work on hybrid logic remains largely undiscussed. This is unfortunate, since hybridisation played a role that was both central to and problematic for his philosophical views on tense. In this paper I introduce hybrid logic from a contemporary perspective, and then examine the role it played in Prior’s work.
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  • Temporal Reference in Linear Tense Logic.M. J. Cresswell - 2010 - Journal of Philosophical Logic 39 (2):173-200.
    The paper introduces a first-order theory in the language of predicate tense logic which contains a single simple axiom. It is shewn that this theory enables times to be referred to and sentences involving ‘now’ and ‘then’ to be formalised. The paper then compares this way of increasing the expressive capacity of predicate tense logic with other mechanisms, and indicates how to generalise the results to other modal and tense systems.
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  • Expressive Power and Incompleteness of Propositional Logics.James W. Garson - 2010 - Journal of Philosophical Logic 39 (2):159-171.
    Natural deduction systems were motivated by the desire to define the meaning of each connective by specifying how it is introduced and eliminated from inference. In one sense, this attempt fails, for it is well known that propositional logic rules underdetermine the classical truth tables. Natural deduction rules are too weak to enforce the intended readings of the connectives; they allow non-standard models. Two reactions to this phenomenon appear in the literature. One is to try to restore the standard readings, (...)
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  • Restricted Arrow.C. M. Asmus - 2009 - Journal of Philosophical Logic 38 (4):405-431.
    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 (...)
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  • Awareness Dynamics.Brian Hill - 2010 - Journal of Philosophical Logic 39 (2):113-137.
    In recent years, much work has been dedicated by logicians, computer scientists and economists to understanding awareness, as its importance for human behaviour becomes evident. Although several logics of awareness have been proposed, little attention has been explicitly dedicated to change in awareness. However, one of the most crucial aspects of awareness is the changes it undergoes, which have countless important consequences for knowledge and action. The aim of this paper is to propose a formal model of awareness change, and (...)
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  • Inexact Knowledge with Introspection.Denis Bonnay & Paul Égré - 2009 - Journal of Philosophical Logic 38 (2):179-227.
    This paper supersedes an ealier version, entitled "A Non-Standard Semantics for Inexact Knowledge with Introspection", which appeared in the Proceedings of "Rationality and Knowledge". The definition of token semantics, in particular, has been modified, both for the single- and the multi-agent case.
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  • Inter-model connectives and substructural logics.Igor Sedlár - 2014 - In Roberto Ciuni, Heinrich Wansing & Caroline Willkommen (eds.), Recent Trends in Philosophical Logic (Proceedings of Trends in Logic XI). Cham, Switzerland: Springer. pp. 195-209.
    The paper provides an alternative interpretation of ‘pair points’, discussed in Beall et al., "On the ternary relation and conditionality", J. of Philosophical Logic 41(3), 595-612. Pair points are seen as points viewed from two different ‘perspectives’ and the latter are explicated in terms of two independent valuations. The interpretation is developed into a semantics using pairs of Kripke models (‘pair models’). It is demonstrated that, if certain conditions are fulfilled, pair models are validity-preserving copies of positive substructural models. This (...)
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  • A STIT Logic for Reasoning About Social Influence.Emiliano Lorini & Giovanni Sartor - 2016 - Studia Logica 104 (4):773-812.
    In this paper we propose a method for modeling social influence within the STIT approach to action. Our proposal consists in extending the STIT language with special operators that allow us to represent the consequences of an agent’s choices over the rational choices of another agent.
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  • Axiomatizing relativistic dynamics using formal thought experiments.Attila Molnár & Gergely Székely - 2015 - Synthese 192 (7):2183-2222.
    Thought experiments are widely used in the informal explanation of Relativity Theories; however, they are not present explicitly in formalized versions of Relativity Theory. In this paper, we present an axiom system of Special Relativity which is able to grasp thought experiments formally and explicitly. Moreover, using these thought experiments, we can provide an explicit definition of relativistic mass based only on kinematical concepts and we can geometrically prove the Mass Increase Formula in a natural way, without postulates of conservation (...)
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  • The interrogative model of inquiry meets dynamic epistemic logics.Yacin Hamami - 2015 - Synthese 192 (6):1609-1642.
    The Interrogative Model of Inquiry and Dynamic Epistemic Logics are two central paradigms in formal epistemology. This paper is motivated by the observation of a significant complementarity between them: on the one hand, the IMI provides a framework for investigating inquiry represented as an idealized game between an Inquirer and Nature, along with an account of the interaction between questions and inferences in information-seeking processes, but is lacking a formulation in the multi-agent case; on the other hand, DELs model various (...)
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  • Logics of temporal-epistemic actions.Bryan Renne, Joshua Sack & Audrey Yap - 2016 - Synthese 193 (3):813-849.
    We present Dynamic Epistemic Temporal Logic, a framework for reasoning about operations on multi-agent Kripke models that contain a designated temporal relation. These operations are natural extensions of the well-known “action models” from Dynamic Epistemic Logic. Our “temporal action models” may be used to define a number of informational actions that can modify the “objective” temporal structure of a model along with the agents’ basic and higher-order knowledge and beliefs about this structure, including their beliefs about the time. In essence, (...)
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  • Syntactic awareness in logical dynamics.Davide Grossi & Fernando R. Velázquez-Quesada - 2015 - Synthese 192 (12):4071-4105.
    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 (...)
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  • Separation logics and modalities: a survey.Stéphane Demri & Morgan Deters - 2015 - Journal of Applied Non-Classical Logics 25 (1):50-99.
    Like modal logic, temporal logic, and description logic, separation logic has become a popular class of logical formalisms in computer science, conceived as assertion languages for Hoare-style proof systems with the goal to perform automatic program analysis. In a broad sense, separation logic is often understood as a programming language, an assertion language and a family of rules involving Hoare triples. In this survey, we present similarities between separation logic as an assertion language and modal and temporal logics. Moreover, we (...)
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  • Intelligent Alarm Correlation and Abductive Reasoning.Stefania Bandini, Alessandro Mosca & Matteo Palmonari - 2006 - Logic Journal of the IGPL 14 (2):347-362.
    The main aim of this paper is to present a way to improve the e.ciency of an intelligent alarm correlation module by means of an abductive reasoner. The alarm correlation module is integrated in a more complex system that performs monitoring and control tasks over a tract of a highway. On the basis of a specific theory on the domain, explanations of anomalous traffic patterns can be provided taking into account those situations not directly detected by data acquisition technology. The (...)
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  • Agency and fictional truth: a formal study on fiction-making.Giuseppe Spolaore - 2015 - Synthese 192 (5):1235-1265.
    Fictional truth, or truth in fiction/pretense, has been the object of extended scrutiny among philosophers and logicians in recent decades. Comparatively little attention, however, has been paid to its inferential relationships with time and with certain deliberate and contingent human activities, namely, the creation of fictional works. The aim of the paper is to contribute to filling the gap. Toward this goal, a formal framework is outlined that is consistent with a variety of conceptions of fictional truth and based upon (...)
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  • Variants of multi-relational semantics for propositional non-normal modal logics.Erica Calardo & Antonino Rotolo - 2014 - Journal of Applied Non-Classical Logics 24 (4):293-320.
    A number of significant contributions in the last four decades show that non-normal modal logics can be fruitfully employed in several applied fields. Well-known domains are epistemic logic, deontic logic, and systems capturing different aspects of action and agency such as the modal logic of agency, concurrent propositional dynamic logic, game logic, and coalition logic. Semantics for such logics are traditionally based on neighbourhood models. However, other model-theoretic semantics can be used for this purpose. Here, we systematically study multi-relational structures, (...)
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  • Duality for the Logic of Quantum Actions.Jort M. Bergfeld, Kohei Kishida, Joshua Sack & Shengyang Zhong - 2015 - Studia Logica 103 (4):781-805.
    In this paper we show a duality between two approaches to represent quantum structures abstractly and to model the logic and dynamics therein. One approach puts forward a “quantum dynamic frame” :2267–2282, 2005), a labelled transition system whose transition relations are intended to represent projections and unitaries on a Hilbert space. The other approach considers a “Piron lattice”, which characterizes the algebra of closed linear subspaces of a Hilbert space. We define categories of these two sorts of structures and show (...)
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  • A Generalization of the Routley-Meyer Semantic Framework.Morgan Thomas - 2015 - Journal of Philosophical Logic 44 (4):411-427.
    We develop an axiomatic theory of “generalized Routley-Meyer logics.” These are first-order logics which are can be characterized by model theories in a certain generalization of Routley-Meyer semantics. We show that all GRM logics are subclassical, have recursively enumerable consequence relations, satisfy the compactness theorem, and satisfy the standard structural rules and conjunction and disjunction introduction/elimination rules. We also show that the GRM logics include classical logic, intuitionistic logic, LP/K3/FDE, and the relevant logics.
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  • A New Algebraic Version of Monteiro’s Four-Valued Propositional Calculus.Aldo Victorio Figallo, Estela Bianco & Alicia Ziliani - 2014 - Open Journal of Philosophy 4 (3):319-331.
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  • Paradoxes of Interaction?Johannes Stern & Martin Fischer - 2015 - Journal of Philosophical Logic 44 (3):287-308.
    Since Montague’s work it is well known that treating a single modality as a predicate may lead to paradox. In their paper “No Future”, Horsten and Leitgeb show that if the two temporal modalities are treated as predicates paradox might arise as well. In our paper we investigate whether paradoxes of multiple modalities, such as the No Future paradox, are genuinely new paradoxes or whether they “reduce” to the paradoxes of single modalities. In order to address this question we develop (...)
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  • Modality and axiomatic theories of truth I: Friedman-Sheard.Johannes Stern - 2014 - Review of Symbolic Logic 7 (2):273-298.
    In this investigation we explore a general strategy for constructing modal theories where the modal notion is conceived as a predicate. The idea of this strategy is to develop modal theories over axiomatic theories of truth. In this first paper of our two part investigation we develop the general strategy and then apply it to the axiomatic theory of truth Friedman-Sheard. We thereby obtain the theory Modal Friedman-Sheard. The theory Modal Friedman-Sheard is then discussed from three different perspectives. First, we (...)
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  • Dynamic Epistemic Logic for Implicit and Explicit Beliefs.Fernando R. Velázquez-Quesada - 2014 - Journal of Logic, Language and Information 23 (2):107-140.
    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 (...)
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  • In the Beginning was Game Semantics?Giorgi Japaridze - 2009 - In Ondrej Majer, Ahti-Veikko Pietarinen & Tero Tulenheimo (eds.), Games: Unifying Logic, Language, and Philosophy. Dordrecht, Netherland: Springer Verlag. pp. 249--350.
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  • Truth-values as labels: a general recipe for labelled deduction.Cristina Sernadas, Luca Viganò, João Rasga & Amílcar Sernadas - 2003 - Journal of Applied Non-Classical Logics 13 (3):277-315.
    We introduce a general recipe for presenting non-classical logics in a modular and uniform way as labelled deduction systems. Our recipe is based on a labelling mechanism where labels are general entities that are present, in one way or another, in all logics, namely truth-values. More specifically, the main idea underlying our approach is the use of algebras of truth-values, whose operators reflect the semantics we have in mind, as the labelling algebras of our labelled deduction systems. The “truth-values as (...)
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  • A Catalog ofWeak Many-Valued Modal Axioms and their Corresponding Frame Classes.Costas D. Koutras - 2003 - Journal of Applied Non-Classical Logics 13 (1):47-71.
    In this paper we provide frame definability results for weak versions of classical modal axioms that can be expressed in Fitting's many-valued modal languages. These languages were introduced by M. Fitting in the early '90s and are built on Heyting algebras which serve as the space of truth values. The possible-worlds frames interpreting these languages are directed graphs whose edges are labelled with an element of the underlying Heyting algebra, providing us a form of many-valued accessibility relation. Weak axioms of (...)
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  • BDD-based decision procedures for the modal logic K ★.Guoqiang Pan, Ulrike Sattler & Moshe Y. Vardi - 2006 - Journal of Applied Non-Classical Logics 16 (1-2):169-207.
    We describe BDD-based decision procedures for the modal logic K. Our approach is inspired by the automata-theoretic approach, but we avoid explicit automata construction. Instead, we compute certain fixpoints of a set of types — which can be viewed as an on-the-fly emptiness of the automaton. We use BDDs to represent and manipulate such type sets, and investigate different kinds of representations as well as a “level-based” representation scheme. The latter turns out to speed up construction and reduce memory consumption (...)
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  • Modal and guarded characterisation theorems over finite transition systems.Martin Otto - 2004 - Annals of Pure and Applied Logic 130 (1-3):173-205.
    We explore the finite model theory of the characterisation theorems for modal and guarded fragments of first-order logic over transition systems and relational structures of width two. A new construction of locally acyclic bisimilar covers provides a useful analogue of the well known tree-like unravellings that can be used for the purposes of finite model theory. Together with various other finitary bisimulation respecting model transformations, and Ehrenfeucht–Fraïssé game arguments, these covers allow us to upgrade finite approximations for full bisimulation equivalence (...)
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  • A Hilbert-Style Axiomatisation for Equational Hybrid Logic.Luís S. Barbosa, Manuel A. Martins & Marta Carreteiro - 2014 - Journal of Logic, Language and Information 23 (1):31-52.
    This paper introduces an axiomatisation for equational hybrid logic based on previous axiomatizations and natural deduction systems for propositional and first-order hybrid logic. Its soundness and completeness is discussed. This work is part of a broader research project on the development a general proof calculus for hybrid logics.
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  • A logical characterisation of qualitative coalitional games.Paul E. Dunne, Wiebe van der Hoek & Michael Wooldridge - 2007 - Journal of Applied Non-Classical Logics 17 (4):477-509.
    Qualitative coalitional games (QCGs) were introduced as abstract formal models of goal-oriented cooperative systems. A QCG is a game in which each agent is assumed to have some goal to achieve, and in which agents must typically cooperate with others in order to satisfy their goals. In this paper, we show how it is possible to reason about QCGs using Coalition Logic (CL), a formalism intended to facilitate reasoning about coalitional powers in game-like multiagent systems. We introduce a correspondence relation (...)
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  • Dynamic logics of the region-based theory of discrete spaces.Philippe Balbiani, Tinko Tinchev & Dimiter Vakarelov - 2007 - Journal of Applied Non-Classical Logics 17 (1):39-61.
    The aim of this paper is to give new kinds of modal logics suitable for reasoning about regions in discrete spaces. We call them dynamic logics of the region-based theory of discrete spaces. These modal logics are linguistic restrictions of propositional dynamic logic with the global diamond E. Their formulas are equivalent to Boolean combinations of modal formulas like E(A ∧ ⟨α⟩ B) where A and B are Boolean terms and α is a relational term. Examining what we can say (...)
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  • Towards incorporating background theories into quantifier elimination.Andrzej Szalas - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):325-340.
    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. (...)
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  • Hyper arrow logic with indiscernibility and complementarity.Philippe Balbiani - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):137-152.
    In this paper, we study indiscernibility relations and complementarity relations in hyper arrow structures. A first-order characterization of indiscernibility and complementarity is obtained through a duality result between hyper arrow structures and certain structures of relational type characterized by first-order conditions. A modal analysis of indiscernibility and complementarity is performed through a modal logic which modalities correspond to indiscernibility relations and complementarity relations in hyper arrow structures.
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  • An extension of Kracht's theorem to generalized Sahlqvist formulas.Stanislav Kikot - 2009 - Journal of Applied Non-Classical Logics 19 (2):227-251.
    Sahlqvist formulas are a syntactically specified class of modal formulas proposed by Hendrik Sahlqvist in 1975. They are important because of their first-order definability and canonicity, and hence axiomatize complete modal logics. The first-order properties definable by Sahlqvist formulas were syntactically characterized by Marcus Kracht in 1993. The present paper extends Kracht's theorem to the class of ‘generalized Sahlqvist formulas' introduced by Goranko and Vakarelov and describes an appropriate generalization of Kracht formulas.
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  • The expressive power of memory logics.Carlos Areces, Diego Figueira, Santiago Figueira & Sergio Mera - 2011 - Review of Symbolic Logic 4 (2):290-318.
    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.
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  • Model-theoretic characterization of intuitionistic propositional formulas.Grigory K. Olkhovikov - 2013 - Review of Symbolic Logic 6 (2):348-365.
    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 (...)
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  • Jedan sustav obilježene prirodne dedukcije za Kangerovu teoriju prava.Berislav Žarnić - 2006 - Filozofska Istrazivanja 26 (3):731-755.
    Basin-Matthews-Viganò approach to construction of labelled deduction systems for normal modal logics is adapted to „Fitch proof-format“, and it is applied to the language of deontic-praxeological logic. Segerberg's suggestion on how to asses the adequacy of a logic for Kanger's theory of rights is being formally explicated and it is proved that herewith proposed system of labelled deduction satisfies Segerberg's criteria of adequacy. For the purpose of building the proof a semantics is given, which connects „the simplest semantics of action“ (...)
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  • Coalgebraic logic for stochastic right coalgebras.Ernst-Erich Doberkat & Christoph Schubert - 2009 - Annals of Pure and Applied Logic 159 (3):268-284.
    We generalize stochastic Kripke models and Markov transition systems to stochastic right coalgebras. These are coalgebras for a functor with as an endofunctor on the category of analytic spaces, and is the subprobability functor. The modal operators are generalized through predicate liftings which are set-valued natural transformations involving the functor. Two states are equivalent iff they cannot be separated by a formula. This equivalence relation is used to construct a cospan for logical equivalent coalgebras under a separation condition for the (...)
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  • Information dynamics and uniform substitution.Wesley H. Holliday, Tomohiro Hoshi & Thomas F. Icard Iii - 2013 - Synthese 190 (1):31-55.
    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. (...)
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  • An efficient approach to nominal equalities in hybrid logic tableaux.Serenella Cerrito & Marta Cialdea Mayer - 2010 - Journal of Applied Non-Classical Logics 20 (1-2):39-61.
    Basic hybrid logic extends modal logic with the possibility of naming worlds by means of a distinguished class of atoms (called nominals) and the so-called satisfaction operator, that allows one to state that a given formula holds at the world named a, for some nominal a. Hence, in particular, hybrid formulae include “equality” assertions, stating that two nominals are distinct names for the same world. The treatment of such nominal equalities in proof systems for hybrid logics may induce many redundancies. (...)
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  • Label-free natural deduction systems for intuitionistic and classical modal logics.Didier Galmiche & Yakoub Salhi - 2010 - Journal of Applied Non-Classical Logics 20 (4):373-421.
    In this paper we study natural deduction for the intuitionistic and classical (normal) modal logics obtained from the combinations of the axioms T, B, 4 and 5. In this context we introduce a new multi-contextual structure, called T-sequent, that allows to design simple labelfree natural deduction systems for these logics. After proving that they are sound and complete we show that they satisfy the normalization property and consequently the subformula property in the intuitionistic case.
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  • V čom sa nemôžete mýliť?Igor Sedlár - 2011 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 18 (3):351-362.
    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.
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  • Axiomatization and completeness of lexicographic products of modal logics.Philippe Balbiani - 2011 - Journal of Applied Non-Classical Logics 21 (2):141-176.
    This paper sets out a new way of combining Kripke-complete modal logics: lexicographic product. It discusses some basic properties of the lexicographic product construction and proves axiomatization/completeness results.
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  • Canonicity results of substructural and lattice-based logics.Tomoyuki Suzuki - 2011 - Review of Symbolic Logic 4 (1):1-42.
    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 (...)
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  • Multi-Modal CTL: Completeness, Complexity, and an Application. [REVIEW]Thomas Ågotnes, Wiebe Van der Hoek, Juan A. Rodríguez-Aguilar, Carles Sierra & Michael Wooldridge - 2009 - Studia Logica 92 (1):1-26.
    We define a multi-modal version of Computation Tree Logic (ctl) by extending the language with path quantifiers E δ and A δ where δ denotes one of finitely many dimensions, interpreted over Kripke structures with one total relation for each dimension. As expected, the logic is axiomatised by taking a copy of a ctl axiomatisation for each dimension. Completeness is proved by employing the completeness result for ctl to obtain a model along each dimension in turn. We also show that (...)
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  • Reasoning with protocols under imperfect information.Eric Pacuit & Sunil Simon - 2011 - Review of Symbolic Logic 4 (3):412-444.
    We introduce and study a PDL-style logic for reasoning about protocols, or plans, under imperfect information. Our paper touches on a number of issues surrounding the relationship between an agent’s abilities, available choices, and information in an interactive situation. The main question we address is under what circumstances can the agent commit to a protocol or plan, and what can she achieve by doing so?
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