Reactive Kripke Semantics

Gabbay, Dov M.

doi:10.1007/978-3-642-41389-6

Cited by 9 publications

(8 citation statements)

References 70 publications

(130 reference statements)

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“…One step up, at the middle level of our map, we find SML and the other logics inspired by it later, such as swap logic, bridging logic, and local sabotage logic in the sense of [1,3]. 32 From the cited publications, 30 Also relevant here is [21] on 'reactive logics', where the accessibility relation of modal models is changed during the interpretation process of formulas. 31 Here we disregard logics with Kleene * or fixed-point extensions, where things can be different.…”

Section: Landscape Of Logics For Model Changementioning

confidence: 91%

“…To make the preceding precise, we need to specify the semantics of µSML. This may seem obvious: one copies the standard definitions for the µ-calculus 21 and adds a clause for , noting that this new operator does not affect positive occurrence. The logic resulting from this obvious extension of the µ-calculus semantics has indeed been studied in [40].…”

Section: The Sabotage µ-Calculus: µSmlmentioning

confidence: 99%

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Modal logics of sabotage revisited

Aucher

Benthem

Grossi

2017

Journal of Logic and Computation

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Sabotage modal logic was proposed in 2003 as a format for analyzing games that modify graphs they are played on. We investigate some model-theoretic and proof-theoretic aspects of sabotage modal logic, which has come to be viewed as an early dynamic logic of graph change. Our first result is a characterization theorem for sabotage modal logic as a fragment of first-order logic which is invariant with respect to a natural notion of 'sabotage bisimulation'. Next, we offer a sound and complete tableau method and its associated labeled sequent calculus for analyzing reasoning in sabotage modal logic. Finally, we identify and briefly explore a number of open research problems concerning sabotage modal logic that illuminate its complexity, placing it within the current landscape of modal logics that analyze model update, and, returning to the original motivation of sabotage, fixed-point logics for network games.

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Section: Landscape Of Logics For Model Changementioning

confidence: 91%

Section: The Sabotage µ-Calculus: µSmlmentioning

confidence: 99%

Modal logics of sabotage revisited

Aucher

Benthem

Grossi

2017

Journal of Logic and Computation

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“…Hence, the separating connectives * and − * allow us to evaluate formulae in alternative models, which is a feature shared with many modal logics such as sabotage logics [67,50], logics of public announcements (see e.g., [51]), interval temporal logics [47], relation-changing logics [5,2,3], ambient logics or graph logics (see e.g. [18,11,27]), propositional team logics [43], second-order modal logics [37] or logics with reactive Kripke semantics [40].…”

Section: Introductionmentioning

confidence: 99%

The power of modal separation logics

Demri

Fervari

2019

Journal of Logic and Computation

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We introduce a modal separation logic MSL whose models are memory states from separation logic and the logical connectives include modal operators as well as separating conjunction and implication from separation logic. With such a combination of operators, some fragments of MSL can be seen as genuine modal logics whereas some others capture standard separation logics, leading to an original language to speak about memory states. We analyse the decidability status and the computational complexity of several fragments of MSL, obtaining surprising results by design of proof methods that take into account the modal and separation features of MSL. For example, the satisfiability problem for the fragment of MSL with $\Diamond $, the difference modality $\langle \neq \rangle $ and separating conjunction $\ast $ is shown Tower-complete whereas the restriction either to $\Diamond $ and $\ast $ or to $\langle \neq \rangle $ and $\ast $ is only NP-complete. We establish that the full logic MSL admits an undecidable satisfiability problem. Furthermore, we investigate variants of MSL with alternative semantics and we build bridges with interval temporal logics and with logics equipped with sabotage operators.

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“…An argument x can either attack another argument u, written x → u, or attack the attack of a second argument y attacking a third argument z, written x (y → z). The idea of nodes (arguments, possible worlds in modal logic) attacking other arrows (attacks in argumentation, accessibility arrows in modal logic) originates in Gabbay ( , 2008 in the context of Reactive Kripke Semantics. Such semantics is strictly stronger than traditional Kripke semantics and turned out to have a wide range of applications, not only in the usual application areas of modal logic, but also in many other areas such as automata theory (Crochemore and Gabbay 2011) and argumentation.…”

Section: Comparison With Related Papers 2005-2011mentioning

confidence: 99%

Temporal, numerical and meta-level dynamics in argumentation networks

Barringer¹,

Gabbay²,

Woods³

2012

Argument & Computation

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This paper studies general numerical networks with support and attack. Our starting point is argumentation networks with the Caminada labelling of three values 1 = in, 0 = out and 1 2 = undecided. This is generalised to arbitrary values in [01], which enables us to compare with other numerical networks such as predator-prey ecological networks, flow networks, logical modal networks and more. This new point of view allows us to see the place of argumentation networks in the overall landscape of networks and import and export ideas to and from argumentation networks. We make a special effort to make clear how general concepts in general networks relate to the special case of argumentation networks. We pay special attention to the handling of loops and to the special features of numerical support. We find surprising connections with the Dempster-Shafer rule and with the cross-ratio in projective geometry. This paper is an expansion of our 2005 paper and so we also consider higher level features such as numerical attacks on attacks, and propagation of numerical values.We conclude with a brief view of temporal numerical argumentation and with a detailed comparison with related papers published since 2005.

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Reactive Kripke Semantics

Cited by 9 publications

References 70 publications

Modal logics of sabotage revisited

Modal logics of sabotage revisited

The power of modal separation logics

Temporal, numerical and meta-level dynamics in argumentation networks

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