Hypersequents, logical consequence and intermediate logics for concurrency

Avron, Arnon

doi:10.1007/bf01531058

Cited by 146 publications

(131 citation statements)

References 11 publications

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“…For example, non-commutative logics, such as [Lambek, 1958, Abrusci andRuet, 1999], and proof systems based on hypersequents [Avron, 1991] do not appear to be captured by direct encodings into linear logic. Also, the inference rules for the "hybrid" conjunction Θ, ∆, A Θ, Γ, B Θ, ∆, Γ, A ∧ B (mixing the multiplicative and additive treatments of contexts) analyzed by Hughes [2005] does not seem possible to treat: here, additive and multiplicative behaviors are strictly separated.…”

Section: Smullyan's Analytic Cut Systemmentioning

confidence: 99%

A Framework for Proof Systems

Nigam

Miller

2010

J Autom Reasoning

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Linear logic can be used as a meta-logic to specify a range of object-level proof systems. In particular, we show that by providing different polarizations within a focused proof system for linear logic, one can account for natural deduction (normal and non-normal), sequent proofs (with and without cut), and tableaux proofs. Armed with just a few, simple variations to the linear logic encodings, more proof systems can be accommodated, including proof system using generalized elimination and generalized introduction rules. In general, most of these proof systems are developed for both classical and intuitionistic logics. By using simple results about linear logic, we can also give simple and modular proofs of the soundness and relative completeness of all the proof systems we consider.

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Section: Smullyan's Analytic Cut Systemmentioning

confidence: 99%

A Framework for Proof Systems

Nigam

Miller

2010

J Autom Reasoning

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“…In this section we survey some analytic calculi that have been recently proposed for MTL (e.g. see [Gabbay et al, 2004] for a survey) and some of its extensions using hypersequents, a natural generalization of Gentzen's sequents introduced by Avron [1991].…”

Section: Proof Theory For T-norm Based Fuzzy Logicsmentioning

confidence: 99%

Fuzzy-Set Based Logics — an History-Oriented Presentation of their Main Developments

Dubois¹,

Esteva²,

Godo³

et al. 2007

The Many Valued and Nonmonotonic Turn in Logic

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“…Avron's calculus HG for G ( [3], called HLC there) is defined by extending the hypersequent calculus HIL for intuitionistic logic with the following communication rule:…”

Section: Hypersequent Calculi For Gödel Logicsmentioning

confidence: 99%

Hypersequent Calculi for Godel Logics -- a Survey

Baaz¹,

Ciabattoni²,

Fermüller³

2003

Journal of Logic and Computation

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Hypersequent calculi arise by generalizing standard sequent calculi to refer to whole contexts of sequents instead of single sequents. We present a number of results using hypersequents to obtain a Gentzen-style characterization for the family of Gödel logics. We first describe analytic calculi for propositional finite and infinite-valued Gödel logics. We then show that the framework of hypersequents allows one to move straightforwardly from the propositional level to first-order as well as propositional quantification. A certain type of modalities, enhancing the expressive power of Gödel logic, is also considered.

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Hypersequents, logical consequence and intermediate logics for concurrency

Abstract: We give a calculus for reasoning about the first-order fragment of classical logic that is adequate for giving the truth conditions of intuitionistic Kripke frames, and outline a proof-theoretic soundness and completeness proof, which we believe is conducive to automation. Cut

Cited by 146 publications

References 11 publications

A Framework for Proof Systems

A Framework for Proof Systems

Fuzzy-Set Based Logics — an History-Oriented Presentation of their Main Developments

Hypersequent Calculi for Godel Logics -- a Survey

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