Results for 'bisimulation'

156 found
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  1.  14
    Bisimulations and bisimulation games between Verbrugge models.Sebastijan Horvat, Tin Perkov & Mladen Vuković - 2023 - Mathematical Logic Quarterly 69 (2):231-243.
    Interpretability logic is a modal formalization of relative interpretability between first‐order arithmetical theories. Verbrugge semantics is a generalization of Veltman semantics, the basic semantics for interpretability logic. Bisimulation is the basic equivalence between models for modal logic. We study various notions of bisimulation between Verbrugge models and develop a new one, which we call w‐bisimulation. We show that the new notion, while keeping the basic property that bisimilarity implies modal equivalence, is weak enough to allow the converse (...)
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  2.  26
    Bisimulation and expressivity for conditional belief, degrees of belief, and safe belief.Martin Jensen, Hans Ditmarsch, Thomas Bolander & Mikkel Andersen - 2017 - Synthese 194 (7):2447-2487.
    Plausibility models are Kripke models that agents use to reason about knowledge and belief, both of themselves and of each other. Such models are used to interpret the notions of conditional belief, degrees of belief, and safe belief. The logic of conditional belief contains that modality and also the knowledge modality, and similarly for the logic of degrees of belief and the logic of safe belief. With respect to these logics, plausibility models may contain too much information. A proper notion (...)
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  3.  86
    Bisimulations and predicate logic.Tim Fernando - 1994 - Journal of Symbolic Logic 59 (3):924-944.
    are considered with a view toward analyzing operational semantics from the perspective of predicate logic. The notion of a bisimulation is employed in two distinct ways: (i) as an extensional notion of equivalence on programs (or processes) generalizing input/output equivalence (at a cost exceeding II' ,over certain transition predicates computable in log space). and (ii) as a tool for analyzing the dependence of transitions on data (which can be shown to be elementary or nonelementary. depending on the formulation of (...)
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  4.  31
    Bisimulations for Knowing How Logics.Raul Fervari, Fernando R. Velázquez-Quesada & Yanjing Wang - forthcoming - Review of Symbolic Logic:1-37.
    As a new type of epistemic logics, the logics of knowing how capture the high-level epistemic reasoning about the knowledge of various plans to achieve certain goals. Existing work on these logics focuses on axiomatizations; this paper makes the first study of their model theoretical properties. It does so by introducing suitable notions of bisimulation for a family of five knowing how logics based on different notions of plans. As an application, we study and compare the expressive power of (...)
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  5.  32
    Bisimulation for Conditional Modalities.A. Baltag & G. Cinà - 2018 - Studia Logica 106 (1):1-33.
    We give a definition of bisimulation for conditional modalities interpreted on selection functions and prove the correspondence between bisimilarity and modal equivalence, generalizing the Hennessy–Milner Theorem to a wide class of conditional operators. We further investigate the operators and semantics to which these results apply. First, we show how to derive a solid notion of bisimulation for conditional belief, behaving as desired both on plausibility models and on evidence models. These novel definitions of bisimulations are exploited in a (...)
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  6.  40
    Bisimulations and Boolean Vectors.Melvin Fitting - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 97-125.
    A modal accessibility relation is just a transition relation, and so can be represented by a {0, 1} valued transition matrix. Starting from this observation, I first show that the machinery of matrices, over Boolean algebras more general than the two-valued one, is appropriate for investigating multi-modal semantics. Then I show that bisimulations have a rather elegant theory, when expressed in terms of transformations on Boolean vector spaces. The resulting theory is a curious hybrid, fitting between conventional modal semantics and (...)
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  7.  39
    Inquisitive bisimulation.Ivano Ciardelli & Martin Otto - 2021 - Journal of Symbolic Logic 86 (1):77-109.
    Inquisitive modal logic, InqML, is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. Technically, InqML fits within the family of logics based on team semantics. From a model-theoretic perspective, it takes us a step in the direction of monadic second-order logic, as inquisitive modal operators involve quantification over sets of worlds. We introduce and investigate (...)
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  8. Bisimulation and expressivity for conditional belief, degrees of belief, and safe belief.Mikkel Birkegaard Andersen, Thomas Bolander, Hans van Ditmarsch & Martin Holm Jensen - 2017 - Synthese 194 (7):2447-2487.
    Plausibility models are Kripke models that agents use to reason about knowledge and belief, both of themselves and of each other. Such models are used to interpret the notions of conditional belief, degrees of belief, and safe belief. The logic of conditional belief contains that modality and also the knowledge modality, and similarly for the logic of degrees of belief and the logic of safe belief. With respect to these logics, plausibility models may contain too much information. A proper notion (...)
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  9.  60
    A bisimulation characterization theorem for hybrid logic with the current-state Binder.Ian Hodkinson & Hicham Tahiri - 2010 - Review of Symbolic Logic 3 (2):247-261.
    We prove that every first-order formula that is invariant under quasi-injective bisimulations is equivalent to a formula of the hybrid logic . Our proof uses a variation of the usual unravelling technique. We also briefly survey related results, and show in a standard way that it is undecidable whether a first-order formula is invariant under quasi-injective bisimulations.
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  10.  50
    Bisimulations for temporal logic.Natasha Kurtonina & Maarten de Rijke - 1997 - Journal of Logic, Language and Information 6 (4):403-425.
    We define bisimulations for temporal logic with Since and Until. This new notion is compared to existing notions of bisimulations, and then used to develop the basic model theory of temporal logic with Since and Until. Our results concern both invariance and definability. We conclude with a brief discussion of the wider applicability of our ideas.
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  11.  33
    Μ-programs, uniform interpolation and bisimulation quantifiers for modal logics ★.Giovanna D'Agostino, Giacomo Lenzi & Tim French - 2006 - Journal of Applied Non-Classical Logics 16 (3-4):297-309.
    We consider the relation between the uniform interpolation property and the elimination of non-standard quantifiers (the bisimulation quantifiers) in the context of the ?-calculus. In particular, we isolate classes of frames where the correspondence between these two properties is nicely smooth.
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  12.  8
    A bisimulation characterization for interpretability logic.T. Perkov & M. Vukovi - 2014 - Logic Journal of the IGPL 22 (6):872-879.
  13.  22
    Bisimulations and p-morphisms.Szymon Frankowski - 2009 - Bulletin of the Section of Logic 38 (3/4):229-235.
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  14.  24
    Bisimulations between generalized Veltman models and Veltman models.Mladen Vuković - 2008 - Mathematical Logic Quarterly 54 (4):368-373.
    Interpretability logic is an extension of provability logic. Veltman models and generalized Veltman models are two semantics for interpretability logic. We consider a connection between Veltman semantics and generalized Veltman semantics. We prove that for a complete image-finite generalized Veltman modelW there is a Veltman model W ′ that is bisimular to W.
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  15.  33
    Modality, bisimulation and interpolation in infinitary logic.Johan van Benthem - 1999 - Annals of Pure and Applied Logic 96 (1-3):29-41.
  16.  24
    Bisimulation and Coverings for Graphs and Hypergraphs.Martin Otto - 2013 - In Kamal Lodaya (ed.), Logic and Its Applications. Springer. pp. 5--16.
  17.  34
    Games and Bisimulations for Intuitionistic First-Order Kripke Models.Małgorzata Kruszelnicka - 2021 - Studia Logica 109 (5):903-916.
    The aim of this paper is to introduce the notion of a game for intuitionistic first-order Kripke models. We also establish links between notions presented here and the notions of logical equivalence and bounded bisimulation for intuitionistic first-order Kripke models, and the Ehrenfeucht–Fraïssé game for classical first-order structures.
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  18.  8
    Bisimulation Quantified Modal Logics: Decidability.Tim French - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 147-166.
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  19.  37
    A Note on Bisimulation and Modal Equivalence in Provability Logic and Interpretability Logic.Vedran Čačić & Domagoj Vrgoč - 2013 - Studia Logica 101 (1):31-44.
    Provability logic is a modal logic for studying properties of provability predicates, and Interpretability logic for studying interpretability between logical theories. Their natural models are GL-models and Veltman models, for which the accessibility relation is well-founded. That’s why the usual counterexample showing the necessity of finite image property in Hennessy-Milner theorem (see [1]) doesn’t exist for them. However, we show that the analogous condition must still hold, by constructing two GL-models with worlds in them that are modally equivalent but not (...)
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  20.  8
    Filtration via Bisimulation.Valentin Shehtman - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 289-308.
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  21.  2
    Bisimulations and Boolean Vectors.Melvin Fitting - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 97-125.
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  22. From Bisimulation Quantifiers to Classifying Toposes.Silvio Ghilardi & Marek Zawadowski - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 193-220.
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  23.  42
    On intuitionistic modal and tense logics and their classical companion logics: Topological semantics and bisimulations.Jennifer M. Davoren - 2010 - Annals of Pure and Applied Logic 161 (3):349-367.
    We take the well-known intuitionistic modal logic of Fischer Servi with semantics in bi-relational Kripke frames, and give the natural extension to topological Kripke frames. Fischer Servi’s two interaction conditions relating the intuitionistic pre-order with the modal accessibility relation generalize to the requirement that the relation and its inverse be lower semi-continuous with respect to the topology. We then investigate the notion of topological bisimulation relations between topological Kripke frames, as introduced by Aiello and van Benthem, and show that (...)
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  24.  26
    A note on bisimulations of finite Kripke models.Ma Lgorzata Kruszelnicka - 2012 - Bulletin of the Section of Logic 41 (3/4):185-198.
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  25.  21
    The true bisimulations for 'since' and 'until'.Holger Sturm - 2002 - Logic and Logical Philosophy 10:173.
    The aim of this paper is to establish a new notion of equivalencebetween temporal models, so-called S-similarity, as the appropriate notionof bisimilarity for temporal logic with Since and Until. The main technicalresults of the paper provide semantical characterizations of the first-orderformulas that are equivalent to a temporal formula: Theorem 3.7 concernsthe equivalence of temporal and first-order formulas with respect to pointedtemporal models, whereas Theorem 4.4 takes the level of temporal modelsinto account.
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  26.  15
    Categorical Interpretation of Modal Structures under Bisimulation.Nino Guallart - 2019 - Kairos 22 (1):54-71.
    In this work we summarise the concept of bisimulation, widely used both in computational sciences and in modal logic, that characterises modal structures with the same behaviour in terms of accessibility relations. Then, we offer a sketch of categorical interpretation of bisimulation between modal structures, which comprise both the structure and the valuation from a propositional language.
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  27.  17
    Davide Sangiorgi. Introduction to bisimulation and coinduction. Cambridge University Press, 2012, 247 pp. - Advanced topics in bisimulation and coinduction, edited by Davide Sangiorgi and Jan Rutten, Cambridge Tracts in Theoretical Computer Science, vol. 52. Cambridge University Press, 2012, 326 pp. [REVIEW]Julian Gutierrez - 2013 - Bulletin of Symbolic Logic 19 (1):108-110.
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  28.  19
    Bimodal Logic with Contingency and Accident: Bisimulation and Axiomatizations.Jie Fan - 2021 - Logica Universalis 15 (2):123-147.
    In this paper, a suitable notion of bisimulation is proposed for the bimodal logic with contingency and accident. We obtain several van Benthem Characterization Theorems, and axiomatize the bimodal logic over the class of Eulidean frames and over some more restricted classes, showing their strong completeness via a novel strategy, thereby answering two open questions raised in the literature. With the new bisimulation notion, we also correct an error in the expressivity results in the literature.
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  29.  84
    Program constructions that are safe for bisimulation.Johan Van Benthem - 1998 - Studia Logica 60 (2):311-330.
    It has been known since the seventies that the formulas of modal logic are invariant for bisimulations between possible worlds models — while conversely, all bisimulation-invariant first-order formulas are modally definable. In this paper, we extend this semantic style of analysis from modal formulas to dynamic program operations. We show that the usual regular operations are safe for bisimulation, in the sense that the transition relations of their values respect any given bisimulation for their arguments. Our main (...)
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  30.  25
    Reviewed Work(s): Introduction to bisimulation and coinduction by Davide Sangiorgi; Advanced topics in bisimulation and coinduction by Davide Sangiorgi; Jan Rutten.Julian Gutierrez - forthcoming - Association for Symbolic Logic: The Bulletin of Symbolic Logic.
    Review by: Julian Gutierrez The Bulletin of Symbolic Logic, Volume 19, Issue 1, Page 108-110, March 2013.
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  31.  14
    On the crispness of and arithmetic with a bisimulation in a constructive naive set theory.S. Yatabe - 2014 - Logic Journal of the IGPL 22 (3):482-493.
  32.  80
    One Connection between Standard Invariance Conditions on Modal Formulas and Generalized Quantifiers.Dorit Ben Shalom - 2003 - Journal of Logic, Language and Information 12 (1):47-52.
    The language of standard propositional modal logic has one operator (? or ?), that can be thought of as being determined by the quantifiers ? or ?, respectively: for example, a formula of the form ?F is true at a point s just in case all the immediate successors of s verify F.This paper uses a propositional modal language with one operator determined by a generalized quantifier to discuss a simple connection between standard invariance conditions on modal formulas and generalized (...)
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  33.  54
    Strong Noncontingency: On the Modal Logics of an Operator Expressively Weaker Than Necessity.Jie Fan - 2019 - Notre Dame Journal of Formal Logic 60 (3):407-435.
    Operators can be compared in at least two respects: expressive strength and deductive strength. Inspired by Hintikka’s treatment of question embedding verbs, the variations of noncontingency operator, and also the various combinations of modal operators and Boolean connectives, we propose a logic with strong noncontingency operator as the only primitive modality. The novel operator is deductively but not expressively stronger than both noncontingency operator and essence operator, and expressively but not deductively weaker than the necessity operator. The frame-definability power of (...)
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  34.  20
    On the Modal Definability of Simulability by Finite Transitive Models.David Fernández Duque - 2011 - Studia Logica 98 (3):347-373.
    We show that given a finite, transitive and reflexive Kripke model 〈 W , ≼, ⟦ ⋅ ⟧ 〉 and $${w \in W}$$ , the property of being simulated by w (i.e., lying on the image of a literalpreserving relation satisfying the ‘forth’ condition of bisimulation) is modally undefinable within the class of S4 Kripke models. Note the contrast to the fact that lying in the image of w under a bi simulation is definable in the standard modal language (...)
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  35.  4
    Logics of True Belief.Yuanzhe Yang - 2024 - Notre Dame Journal of Formal Logic 65 (1):55-80.
    In epistemic logic, the beliefs of an agent are modeled in a way very similar to knowledge, except that they are fallible. Thus, the pattern of an agent’s true beliefs is an interesting subject to study. In this paper, we conduct a systematic study on a novel modal logic with the bundled operator ⊡ϕ:=□ϕ∧ϕ as the only primitive modality, where ⊡ captures the notion of true belief. With the help of a novel notion of ⊡-bisimulation, we characterize the expressivity (...)
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  36. Extensive games as process models.Johan van Benthem - 2002 - Journal of Logic, Language and Information 11 (3):289-313.
    We analyze extensive games as interactive process models, using modallanguages plus matching notions of bisimulation as varieties of gameequivalences. Our technical results show how to fit existing modalnotions into this new setting.
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  37.  59
    Expressive Power of “Now” and “Then” Operators.Igor Yanovich - 2015 - Journal of Logic, Language and Information 24 (1):65-93.
    Natural language provides motivation for studying modal backwards-looking operators such as “now”, “then” and “actually” that evaluate their argument formula at some previously considered point instead of the current one. This paper investigates the expressive power over models of both propositional and first-order basic modal language enriched with such operators. Having defined an appropriate notion of bisimulation for first-order modal logic, I show that backwards-looking operators increase its expressive power quite mildly, contrary to beliefs widespread among philosophers of language (...)
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  38.  73
    Action emulation.Jan Eijck, Ji Ruan & Tomasz Sadzik - 2012 - Synthese 185 (S1):131-151.
    The effects of public announcements, private communications, deceptive messages to groups, and so on, can all be captured by a general mechanism of updating multi-agent models with update action models, now in widespread use. There is a natural extension of the definition of a bisimulation to action models. Surely enough, updating with bisimilar action models gives the same result (modulo bisimulation). But the converse turns out to be false: update models may have the same update effects without being (...)
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  39. Action emulation.Jan van Eijck - 2012 - Synthese 185 (1):131-151.
    The effects of public announcements, private communications, deceptive messages to groups, and so on, can all be captured by a general mechanism of updating multi-agent models with update action models, now in widespread use. There is a natural extension of the definition of a bisimulation to action models. Surely enough, updating with bisimilar action models gives the same result (modulo bisimulation). But the converse turns out to be false: update models may have the same update effects without being (...)
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  40.  39
    Action Emulation between Canonical Models.Floor Sietsma & Jan van Eijck - 2013 - Journal of Philosophical Logic 42 (6):905-925.
    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. (...)
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  41.  42
    Hybrid counterfactual logics David Lewis meets Arthur prior again.Katsuhiko Sano - 2009 - Journal of Logic, Language and Information 18 (4):515-539.
    The purpose of this paper is to argue that the hybrid formalism fits naturally in the context of David Lewis’s counterfactual logic and that its introduction into this framework is desirable. This hybridization enables us to regard the inference “The pig is Mary; Mary is pregnant; therefore the pig is pregnant” as a process of updating local information (which depends on the given situation) by using global information (independent of the situation). Our hybridization also has the following technical advantages: (i) (...)
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  42.  40
    How True It Is = Who Says It’s True.Melvin Fitting - 2009 - Studia Logica 91 (3):335 - 366.
    This is a largely expository paper in which the following simple idea is pursued. Take the truth value of a formula to be the set of agents that accept the formula as true. This means we work with an arbitrary (finite) Boolean algebra as the truth value space. When this is properly formalized, complete modal tableau systems exist, and there are natural versions of bisimulations that behave well from an algebraic point of view. There remain significant problems concerning the proper (...)
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  43.  35
    Extended full computation-tree logics for paraconsistent model checking.Norihiro Kamide - 2007 - Logic and Logical Philosophy 15 (3):251-276.
    It is known that the full computation-tree logic CTL * is an important base logic for model checking. The bisimulation theorem for CTL* is known to be useful for abstraction in model checking. In this paper, the bisimulation theorems for two paraconsistent four-valued extensions 4CTL* and 4LCTL* of CTL* are shown, and a translation from 4CTL* into CTL* is presented. By using 4CTL* and 4LCTL*, inconsistency-tolerant and spatiotemporal reasoning can be expressed as a model checking framework.
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  44.  74
    Carnap’s Problem for Modal Logic.Denis Bonnay & Dag Westerståhl - 2023 - Review of Symbolic Logic 16 (2):578-602.
    We take Carnap’s problem to be to what extent standard consequence relations in various formal languages fix the meaning of their logical vocabulary, alone or together with additional constraints on the form of the semantics. This paper studies Carnap’s problem for basic modal logic. Setting the stage, we show that neighborhood semantics is the most general form of compositional possible worlds semantics, and proceed to ask which standard modal logics (if any) constrain the box operator to be interpreted as in (...)
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  45. Weakly Aggregative Modal Logic: Characterization and Interpolation.Jixin Liu, Yanjing Wang & Yifeng Ding - 2019 - In Patrick Blackburn, Emiliano Lorini & Meiyun Guo (eds.), Logic, Rationality, and Interaction 7th International Workshop, LORI 2019, Chongqing, China, October 18–21, 2019, Proceedings. Springer. pp. 153-167.
    Weakly Aggregative Modal Logic (WAML) is a collection of disguised polyadic modal logics with n-ary modalities whose arguments are all the same. WAML has some interesting applications on epistemic logic and logic of games, so we study some basic model theoretical aspects of WAML in this paper. Specifically, we give a van Benthem-Rosen characterization theorem of WAML based on an intuitive notion of bisimulation and show that each basic WAML system Kn lacks Craig Interpolation.
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  46.  39
    Counting to Infinity: Graded Modal Logic with an Infinity Diamond.Ignacio Bellas Acosta & Yde Venema - 2024 - Review of Symbolic Logic 17 (1):1-35.
    We extend the languages of both basic and graded modal logic with the infinity diamond, a modality that expresses the existence of infinitely many successors having a certain property. In both cases we define a natural notion of bisimilarity for the resulting formalisms, that we dub $\mathtt {ML}^{\infty }$ and $\mathtt {GML}^{\infty }$, respectively. We then characterise these logics as the bisimulation-invariant fragments of the naturally corresponding predicate logic, viz., the extension of first-order logic with the infinity quantifier. Furthermore, (...)
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  47.  38
    A Lindström Theorem in Many-Valued Modal Logic over a Finite MTL-chain.Guillermo Badia & Grigory Olkhovikov - forthcoming - Fuzzy Sets and Systems.
    We consider a modal language over crisp frames and formulas evaluated on a finite MTL-chain (a linearly ordered commutative integral residuated lattice). We first show that the basic modal abstract logic with constants for the values of the MTL-chain is the maximal abstract logic satisfying Compactness, the Tarski Union Property and strong invariance for bisimulations. Finally, we improve this result by replacing the Tarski Union Property by a relativization property.
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  48.  21
    Some Formal Semantics for Epistemic Modesty.Christopher Steinsvold - 2020 - Logic and Logical Philosophy 29 (3):381-413.
    Given the frequency of human error, it seems rational to believe that some of our own rational beliefs are false. This is the axiom of epistemic modesty. Unfortunately, using standard propositional quantification, and the usual relational semantics, this axiom is semantically inconsistent with a common logic for rational belief, namely KD45. Here we explore two alternative semantics for KD45 and the axiom of epistemic modesty. The first uses the usual relational semantics and bisimulation quantifiers. The second uses a topological (...)
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  49.  63
    A Tractarian Universe.Albert Visser - 2012 - Journal of Philosophical Logic 41 (3):519-545.
    In this paper we develop a reconstruction of the Tractatus ontology. The basic idea is that objects are unsaturated and that Sachlagen are like molecules. Bisimulation is used for the proper individuation of the Sachlagen. We show that the ordering of the Sachlagen is a complete distributive, lattice. It is atomistic , i.e., each Sachlage is the supremum of the Sachverhalte below it. We exhibit three normal forms for Sachlagen: the bisimulation collapse, the canonical unraveling and the canonical (...)
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  50.  45
    Public announcement logic with distributed knowledge: expressivity, completeness and complexity.Yì N. Wáng & Thomas Ågotnes - 2013 - Synthese 190 (S1).
    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 (...)
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