MOIN: A Nested Sequent Theorem Prover for Intuitionistic Modal Logics (System Description)

Girlando, Marianna; Straßburger, Lutz

doi:10.1007/978-3-030-51054-1_25

Cited by 9 publications

(4 citation statements)

References 16 publications

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“…[11,22,33]) to provide decision procedures for logics within the class considered. Our primary concern will be to establish the decidability of transitive extensions of IK, which has remained a longstanding open problem [15,31].…”

Section: Discussionmentioning

confidence: 99%

Nested Sequents for Intuitionistic Modal Logics via Structural Refinement

Lyon

2021

Lecture Notes in Computer Science

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We employ a recently developed methodology-called structural refinement-to extract nested sequent systems for a sizable class of intuitionistic modal logics from their respective labelled sequent systems. This method can be seen as a means by which labelled sequent systems can be transformed into nested sequent systems through the introduction of propagation rules and the elimination of structural rules, followed by a notational translation. The nested systems we obtain incorporate propagation rules that are parameterized with formal grammars, and which encode certain frame conditions expressible as first-order Horn formulae that correspond to a subclass of the Scott-Lemmon axioms. We show that our nested systems are sound, cut-free complete, and admit hp-admissibility of typical structural rules.

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Section: Discussionmentioning

confidence: 99%

Nested Sequents for Intuitionistic Modal Logics via Structural Refinement

Lyon

2021

Lecture Notes in Computer Science

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“…There are also some computational issues: although the exact complexity of CK and CCDL has not been explicitly stated, we strongly conjecture that both are in PSPACE, in this hypothesis, the calculi G4.CK and G4.CCDL would not be optimal, since a derivation may have an exponential size, the same happens within Dyckhoff's G4ip ; this naturally leads to the issue of studying refinements of our calculi, following the line of [6] which would match (and establish) the PSPACE upper bound. Moreover, we believe that our terminating calculi are very suitable for implementation: a theorem prover based on them would expand the realm of intuitionistic modal theorem proving, in addition to the recent prover presented in [10]. Following Iemhoff [14] we also intend to use our terminating calculi to prove constructively the uniform interpolation property for both CK and CCDL.…”

Section: Discussionmentioning

confidence: 99%

Terminating Calculi and Countermodels for Constructive Modal Logics

Dalmonte¹,

Grellois²,

Olivetti³

2021

Lecture Notes in Computer Science

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We investigate terminating sequent calculi for constructive modal logics CK and CCDL in the style of Dyckhoff's calculi for intuitionistic logic. We first present strictly terminating calculi for these logics. Our calculi provide immediately a decision procedure for the respective logics and have good proof-theoretical properties, namely they allow for a syntactic proof of cut admissibility. We then present refutation calculi for non-provability in both logics. Their main feature is that they support direct countermodel extraction: each refutation directly defines a finite countermodel of the refuted formula in a natural neighbourhood semantics for these logics.

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“…However, the questions of whether these logics enjoy the finite model property remained open for twenty years or more: in the case of CS4 since at least 2001 [11], and of IS4 at least since 1994 [10]. The question for IS4 was recently resolved in the positive in [12]. In this paper we do the same for CS4, solving the other principle open problem concerning nonclassical variants of S4.…”

Section: Introductionmentioning

confidence: 92%