Sabotage Modal Logic: Some Model and Proof Theoretic Aspects

Benthem, Johan van; Grossi, Davide

doi:10.1007/978-3-662-48561-3_1

Cited by 12 publications

(10 citation statements)

References 14 publications

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“…A standard first-order translation for SML was sketched in [44] and [34]. Later on, a detailed translation was independently given in the proceedings version of this paper [9] and in [4]. In this section we describe the translation and its correctness in detail.…”

Section: A First-order Translation For Smlmentioning

confidence: 99%

“…In this section, we introduce a notion of 'sabotage bisimulation' for SML, a task left open in [34,33]. The invariance results enabled by this new notion of bisimulation (that is, Propositions 2 and 3 below) were independently proven in [9] and [4], albeit in slightly different formulations.…”

Section: Bisimulation For Smlmentioning

confidence: 99%

“…A main open problem mentioned in [34,33] is a bisimulation invariance characterization for SML. This was solved independently in the proceedings version of the present article [9] and in the work of an Argentinean team [4]. Also independently, both teams developed tableau systems to analyze the structure of validity in SML, cf.…”

Section: Introductionmentioning

confidence: 99%

“…Outline Our paper has two parts. The first, comprising Sections 2 to 5, extends the material in [9] with proofs left out there, while adding a labeled sequent calculus, several new examples and a few small novel observations. The two main contributions are a characterization result for SML (Section 4) as that fragment of first-order logic which is invariant for a natural notion of 'sabotage bisimulation' (Section 3) and a novel tableau system and matching sequent calculus in Section 5.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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: A First-order Translation For Smlmentioning

confidence: 99%

Section: Bisimulation For Smlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modal logics of sabotage revisited

Aucher

Benthem

Grossi

2017

Journal of Logic and Computation

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“…In [5] we studied local swap logic, in particular its decidability problem and its relation with first-order and hybrid logics. Global sabotage logic, together with some variants of relation-changing logics, have been investigated in [14,15]. In [6] a general framework for representing model updates is defined.…”

Section: Introductionmentioning

confidence: 99%

Satisfiability for relation-changing logics

Areces

Fervari

Hoffmann

et al. 2018

Journal of Logic and Computation

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Relation-changing modal logics are extensions of the basic modal logic with dynamic operators that modify the accessibility relation of a model during the evaluation of a formula. These languages are equipped with dynamic modalities that are able, for example, to delete, add, and swap edges in the model, both locally and globally. We study the satisfiability problem for some of these logics. We first show that they can be translated into hybrid logic. As a result, we can transfer some results from hybrid logics to relation-changing modal logics. We discuss in particular, decidability for some fragments. We then show that satisfiability is, in general, undecidable for all the languages introduced, via translations from memory logics.

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An Auxiliary Logic on Trees: on the Tower-Hardness of Logics Featuring Reachability and Submodel Reasoning

Mansutti

2020

Lecture Notes in Computer Science

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We describe a set of simple features that are sufficient in order to make the satisfiability problem of logics interpreted on trees TOWER-hard. We exhibit these features through an Auxiliary Logic on Trees (ALT), a modal logic that essentially deals with reachability of a fixed node inside a forest and features modalities from sabotage modal logic to reason on submodels. After showing that ALT admits a TOWER-complete satisfiability problem, we prove that this logic is captured by four other logics that were independently found to be TOWER-complete: twovariables separation logic, quantified computation tree logic, modal logic of heaps and modal separation logic. As a by-product of establishing these connections, we discover strict fragments of these logics that are still non-elementary.

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Sabotage Modal Logic: Some Model and Proof Theoretic Aspects

Cited by 12 publications

References 14 publications

Modal logics of sabotage revisited

Modal logics of sabotage revisited

Satisfiability for relation-changing logics

An Auxiliary Logic on Trees: on the Tower-Hardness of Logics Featuring Reachability and Submodel Reasoning

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