Satisfiability for relation-changing logics

Areces, Carlos; Fervari, Raul; Hoffmann, G. W.; Martel, Mauricio

doi:10.1093/logcom/exy022

Cited by 12 publications

(8 citation statements)

References 29 publications

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“…This gives us a proof that MSL g (Q, gsb ) is NP-complete over the class of models with finite and functional models. On the other hand, it is known that the satisfiability problem of MSL g (Q, gsb ) (over arbitrary models) is undecidable [4]. Therefore, the minimal modal separation logic over arbitrary models MSL g ( * , Q) is also undecidable.…”

Section: Msl Over General Modelsmentioning

confidence: 99%

“…• Along the paper, we also investigate variants of MSL (or some of its fragments) by slightly modifying the semantics or by adding other modal connectives. For instance, we provide a translation from formulae of global sabotage logic [4] into MSL( * , Q) formulae. As a consequence, the satisfiability problem for the global sabotage logic over MSL models is NP-complete, whereas the satisfiability problem for MSL g ( * , Q) (i.e.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Msl Over General Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The power of modal separation logics

Demri

Fervari

2019

Journal of Logic and Computation

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“…This article is also relevant to other work studying graph games with modal logics, such as [9,14,18,20]. Technically, the logic SLL has resemblances to several recent logics with model modifiers, such as [2,3,4]. Besides, instead of updating links, [21] considers a logic of stepwise point deletion, which sheds light on the long-standing open problem of how to axiomatize the sabotage-style modal logics.…”

Section: Discussionmentioning

confidence: 99%

On the Right Path: A Modal Logic for Supervised Learning

Baltag

Pedersen

2019

Logic, Rationality, and Interaction

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Formal learning theory formalizes the process of inferring a general result from examples, as in the case of inferring grammars from sentences when learning a language. Although empirical evidence suggests that children can learn a language without responding to the correction of linguistic mistakes, the importance of Teacher in many other paradigms is significant. Instead of focusing only on learner(s), this work develops a general framework-the supervised learning game (SLG)-to investigate the interaction between Teacher and Learner. In particular, our proposal highlights several interesting features of the agents: on the one hand, Learner may make mistakes in the learning process, and she may also ignore the potential relation between different hypotheses; on the other hand, Teacher is able to correct Learner's mistakes, eliminate potential mistakes and point out the facts ignored by Learner. To reason about strategies in this game, we develop a modal logic of supervised learning (SLL). Broadly, this work takes a small step towards studying the interaction between graph games, logics and formal learning theory.

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“…In a similar spirit to reactive automata, there are also interesting studies [35][36][37] carried out in modal logic -initiated by van Benthem's swap logic -to model dynamic changes in transition relations (or accessibility relations as they are known in the modal logic literature) of the underlying Kripke structure. The expressivity of such Kripke structures extended with model update functions (cf.…”

Section: Dynamic Modal Logicmentioning

confidence: 99%

Conditional transition systems with upgrades

Beohar

König

Küpper

et al. 2020

Science of Computer Programming

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We introduce a variant of transition systems, where activation of transitions depends on conditions of the environment and upgrades during runtime potentially create additional transitions. Using a cornerstone result in lattice theory, we show that such transition systems can be modelled in two ways: as conditional transition systems (CTS) with a partial order on conditions, or as lattice transition systems (LaTS), where transitions are labelled with the elements from a distributive lattice. We define equivalent notions of bisimilarity for both variants and characterise them via a bisimulation game. We explain how conditional transition systems are related to featured transition systems for the modelling of software product lines. Furthermore, we show how to compute bisimilarity symbolically via BDDs by defining an operation on BDDs that approximates an element of a Boolean algebra into a lattice. We have implemented our procedure and provide runtime results. This is an extended version of the TASE 2017 paper [1], including all proofs, additional examples, an extension of the formalism to account for deactivation of updates and detailed runtime results.

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Satisfiability for relation-changing logics

Cited by 12 publications

References 29 publications

The power of modal separation logics

The power of modal separation logics

On the Right Path: A Modal Logic for Supervised Learning

Conditional transition systems with upgrades

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