2019
DOI: 10.1007/978-3-030-36755-8_3
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Countermodel Construction via Optimal Hypersequent Calculi for Non-normal Modal Logics

Abstract: We develop semantically-oriented calculi for the cube of nonnormal modal logics and some deontic extensions. The calculi manipulate hypersequents and have a simple semantic interpretation. Their main feature is that they allow for direct countermodel extraction. Moreover they provide an optimal decision procedure for the respective logics. They also enjoy standard proof-theoretical properties, such as a syntactical proof of cut-admissibility.

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Cited by 4 publications
(8 citation statements)
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“…The hypersequent calculi for NNMLs implemented by HYPNO are introduced in [4]. Their syntax is as follows: a block is a structure Σ , where Σ is a multiset of formulas of L. A sequent is a pair Γ ⇒ Δ, where Γ is a multiset of formulas and blocks, and Δ is a multiset of formulas.…”
Section: Axioms Semantics and Hypersequent Calculimentioning
confidence: 99%
See 3 more Smart Citations
“…The hypersequent calculi for NNMLs implemented by HYPNO are introduced in [4]. Their syntax is as follows: a block is a structure Σ , where Σ is a multiset of formulas of L. A sequent is a pair Γ ⇒ Δ, where Γ is a multiset of formulas and blocks, and Δ is a multiset of formulas.…”
Section: Axioms Semantics and Hypersequent Calculimentioning
confidence: 99%
“…The calculi implemented by HYPNO are a minor variant of the ones in [4]: they contain an additional arrow used to represent that the formulas on the left of entails the conjunction (rather than their disjunction) of the formulas on its right. By this modification, all rules of the calculi are at most binary; the equivalence of the modified calculi with the original ones in [4] is straightforward.…”
Section: Axioms Semantics and Hypersequent Calculimentioning
confidence: 99%
See 2 more Smart Citations
“…This upper bound is optimal the logics having C as theorem (if the conjecture made in [41] of Pspace-hardness is correct. The satisfiability problem for logics without C, instead, is in NP [41] and a coNP decision procedure based on hypersequents is presented in [7].…”
Section: Introductionmentioning
confidence: 99%