The expressive power of modal logic with inclusion atoms

Hella, Lauri; Stumpf, Johanna Beate

doi:10.4204/eptcs.193.10

Cited by 15 publications

(20 citation statements)

References 13 publications

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“…Then one can proceed with the parameterised complexity of validity and entailment in these logics. In [12], Hella and Stumpf posed an interesting question to determine the complexity of satisfiability for modal inclusion logic with only unary inclusion atoms. In Theorem 18 we proved that the fixed-arity fragment of PIN C has the same complexity for SAT as PL (NP-complete).…”

Section: Discussionmentioning

confidence: 99%

Parameterised Complexity of Propositional Inclusion and Independence Logic

Mahmood¹,

Virtema²

2021

Preprint

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In this work we analyse the parameterised complexity of propositional inclusion (PIN C) and independence logic (PIN D). The problems of interest are model checking (MC) and satisfiability (SAT). The complexity of these problems is well understood in the classical (non-parameterised) setting. Mahmood and Meier (FoIKS 2020) recently studied the parameterised complexity of propositional dependence logic (PDL). As a continuation of their work, we classify inclusion and independence logic and thereby come closer to completing the picture with respect to the parametrised complexity for the three most studied logics in the propositional team semantics setting. We present results for each problem with respect to 8 different parameterisations. It turns out that for a team based logic L such that L-atoms can be evaluated in polynomial time, the MC parameterised by teamsize is FPT. As a corollary, we get an FPT-membership under the following parameterisations: formula-size, formula-depth, treewidth, and number of variables. The parameter teamsize shows interesting behavior for SAT. For PIN C the parameter teamsize is not meaningful, whereas for PDL and PIN D the satisfiability is paraNP-complete. Finally, we prove that when parameterised by arity, both MC and SAT are paraNP-complete for each of the considered logics.

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Section: Discussionmentioning

confidence: 99%

Parameterised Complexity of Propositional Inclusion and Independence Logic

Mahmood¹,

Virtema²

2021

Preprint

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“…Theorem 43 ( [20]). A class C of team-pointed Kripke models is definable by a single formula of EMIN C iff C is union closed, closed under team k-bisimulation, for some k ∈ N, and admits the empty team property.…”

Section: Extensions Of Modal Logic With Atomic Dependency Notionsmentioning

confidence: 99%

“…Hella et al [19] established that exactly the properties of teams that have the so-called empty team property, are downward closed and closed under the so-called team k-bisimulation, for some finite k, are definable in EMDL. Kontinen et al [25] have shown that exactly the properties of teams that are closed under the team k-bisimulation are definable in the so-called modal team logic, whereas Hella and Stumpf established [20] that the so-called extended modal inclusion logic is characterised by the empty team property, union closure, and closure under team k-bisimulation. See the survey [7] for a detailed exposition on the expressive power and computational complexity of related logics.…”

Section: Introductionmentioning

confidence: 99%

Characterising modal definability of team-based logics via the universal modality

Sano

Virtema

2019

Annals of Pure and Applied Logic

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We study model and frame definability of various modal logics. Let ML( u + ) denote the fragment of modal logic extended with the universal modality in which the universal modality occurs only positively. We show that a class of Kripke models is definable in ML( u + ) if and only if the class is elementary and closed under disjoint unions and surjective bisimulations. We also characterise the definability of ML( u + ) in the spirit of the well-known Goldblatt-Thomason theorem. We show that an elementary class F of Kripke frames is definable in ML( u + ) if and only if F is closed under taking generated subframes and bounded morphic images, and reflects ultrafilter extensions and finitely generated subframes. In addition we study frame definability relative to finite transitive frames and give an analogous characterisation of ML( u + )-definability relative to finite transitive frames. Finally, we initiate the study of model and frame definability in team-based logics. We study (extended) modal dependence logic, (extended) modal inclusion logic, and modal team logic. We establish strict linear hierarchies with respect to model definability and frame definability, respectively. We show that, with respect to model and frame definability, the before mentioned team-based logics, except modal dependence logic, either coincide with ML( u + ) or plain modal logic ML. Thus as a corollary we obtain model theoretic characterisation of model and frame definability for the team-based logics.This article subsumes and extends the conference articles [30] and [31].

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“…By analogously adding the independence atom α ⊥ β γ, we obtain modal independence logic MIL [19], and with the inclusion atom α ⊆ β, we have modal inclusion logic MInc [14]. Adding both the inclusion and exclusion atom results in modal inclusion/exclusion logic MIncEx, the modal analogon to Galliani's I/E-logic [5].…”

Section: Dependence Independence Inclusion and Exclusion Logicmentioning

confidence: 99%

Axiomatizations of team logics

Lück

2018

Annals of Pure and Applied Logic

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In a modular approach, we lift Hilbert-style proof systems for propositional, modal and first-order logic to generalized systems for their respective team-based extensions. We obtain sound and complete axiomatizations for the dependence-free fragment FO(∼) of Väänänen's firstorder team logic TL, for propositional team logic PTL, quantified propositional team logic QPTL, modal team logic MTL, and for the corresponding logics of dependence, independence, inclusion and exclusion.As a crucial step in the completeness proof, we show that the above logics admit, in a particular sense, a semantics-preserving elimination of modalities and quantifiers from formulas.

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The expressive power of modal logic with inclusion atoms

Cited by 15 publications

References 13 publications

Parameterised Complexity of Propositional Inclusion and Independence Logic

Parameterised Complexity of Propositional Inclusion and Independence Logic

Characterising modal definability of team-based logics via the universal modality

Axiomatizations of team logics

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