Focused and Synthetic Nested Sequents

Chaudhuri, Kaustuv; Marin, Sonia; Straßburger, Lutz

doi:10.1007/978-3-662-49630-5_23

Cited by 11 publications

(20 citation statements)

References 23 publications

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“…Proof By a straightforward induction, observing that the operations , and in (7) are associative, and that and are also commutative.…”

Section: Theorem 33mentioning

confidence: 99%

“…We have now access to a systematic treatment of modal logics in display calculus [32], calculus of structures [26,14], labeled systems [25,22], hyper sequents [3,18], and nested sequents [5,28,20]. There are focused proof systems for classical and intuitionistic modal logics [7,8], and we understand the relation between display calculus and nested sequents [10] and hyper sequents [11].…”

Section: Introductionmentioning

confidence: 99%

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On Combinatorial Proofs for Modal Logic

Acclavio¹,

Straßburger²

2019

Lecture Notes in Computer Science

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In this paper we extend Hughes' combinatorial proofs to modal logics. The crucial ingredient for modeling the modalities is the use of a self-dual non-commutative operator that has first been observed by Retoré through pomset logic. Consequently, we had to generalize the notion of skew fibration from cographs to Guglielmi's relation webs. Our main result is a sound and complete system of combinatorial proofs for all normal and non-normal modal logics in the S4-tesseract. The proof of soundness and completeness is based on the sequent calculus with some added features from deep inference.

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“…Proof By a straightforward induction, observing that the operations , and in (7) are associative, and that and are also commutative.…”

Section: Theorem 33mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Combinatorial Proofs for Modal Logic

Acclavio¹,

Straßburger²

2019

Lecture Notes in Computer Science

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“…In the nested system proposed in [Chaudhuri et al 2016a] all the existing right boxes can be processed in parallel (and this is invertible) and then the left boxes can be transferred one by one to all the nestings. A derivation then proceeds by running all the possible traces in parallel, and finish whenever one or more of them succeed.…”

Section: Block Forms Versus Focused Derivationsmentioning

confidence: 99%

Modularisation of Sequent Calculi for Normal and Non-normal Modalities

Lellmann

Pimentel

2019

ACM Trans. Comput. Logic

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In this work we explore the connections between (linear) nested sequent calculi and ordinary sequent calculi for normal and non-normal modal logics. By proposing local versions to ordinary sequent rules we obtain linear nested sequent calculi for a number of logics, including to our knowledge the first nested sequent calculi for a large class of simply dependent multimodal logics, and for many standard non-normal modal logics. The resulting systems are modular and have separate left and right introduction rules for the modalities, which makes them amenable to specification as bipole clauses. While this granulation of the sequent rules introduces more choices for proof search, we show how linear nested sequent calculi can be restricted to blocked derivations, which directly correspond to ordinary sequent derivations. ACM Reference Format:Björn Lelllmann and Elaine Pimentel, 2016. Modularisation of sequent calculi for normal and non-normal modalities.

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“…In the last decade, nested sequent calculi have been successfully used to define cut-free deductive systems for various normal modal logics (classical [3], intuitionistic [17,23], constructive [1] and tense logics [10]) and non-normal modal logics [14]. For some variants there also exist focused calculi [5,6].…”

Section: Introductionmentioning

confidence: 99%

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

Girlando

Straßburger

2020

Lecture Notes in Computer Science

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We present a simple Prolog prover for intuitionistic modal logics based on nested sequent proof systems. We have implemented single-conclusion systems (Gentzen-style) and multi-conclusion systems (Maehara-style) for all logics in the intuitionistic modal IS5-cube. While the single-conclusion system are better investigated and have an internal cut-elimination, the multi-conclusion systems can provide a countermodel in case the proof search fails. To our knowledge this is the first automated theorem prover for intuitionistic modal logics. For wider usability, we also implemented classical normal modal logics in the S5cube.

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Focused and Synthetic Nested Sequents

Cited by 11 publications

References 23 publications

On Combinatorial Proofs for Modal Logic

On Combinatorial Proofs for Modal Logic

Modularisation of Sequent Calculi for Normal and Non-normal Modalities

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

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