A cut-free calculus for second-order Gödel logic

Lahav, Ori; Avron, Arnon

doi:10.1016/j.fss.2015.01.017

Cited by 2 publications

(2 citation statements)

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“…Second-Order Intuitionistic Logic with Dummett's Axiom At the time of this writing, there is no known cut-free sequent calculus for second-order intuitionistic logic with Dummett's Axiom, which we call LC 2 . Even if there were one, the situation would be similar to what happens in the hypersequent calculus for second-order Gödel-Dummett logic [27]: there is no known cut-elimination procedure, only a semantical proof that valid statements can be proved without cuts. Why?…”

Section: Normal Form Property and Herbrand's Disjunction Extractionmentioning

confidence: 99%

On Natural Deduction for Herbrand Constructive Logics I: Curry-Howard Correspondence for Dummett's Logic LC

Aschieri¹

2017

Logical Methods in Computer Science

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Abstract. Dummett's logic LC is intuitionistic logic extended with Dummett's axiom: for every two statements the first implies the second or the second implies the first. We present a natural deduction and a Curry-Howard correspondence for first-order and secondorder Dummett's logic. We add to the lambda calculus an operator which represents, from the viewpoint of programming, a mechanism for representing parallel computations and communication between them, and from the viewpoint of logic, Dummett's axiom. We prove that our typed calculus is normalizing and show that proof terms for existentially quantified formulas reduce to a list of individual terms forming an Herbrand disjunction.

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Section: Normal Form Property and Herbrand's Disjunction Extractionmentioning

confidence: 99%

On Natural Deduction for Herbrand Constructive Logics I: Curry-Howard Correspondence for Dummett's Logic LC

Aschieri¹

2017

Logical Methods in Computer Science

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“…Overall, the impact and relevance of such a line of research is to be measured directly by its foundational character with respect to a better and deeper understanding of meaning in logics modeling complex phenomena and, of necessity, suitable general forms of compositional reasoning. Some highlights of the GeTFun project, covering topics such as truth-values, valuation semantics, bivalence, proof-systems and focusing, controlled nondeterminism, distance-based reasoning, information sources, paraconsistency, labeled and hybrid logic, inter alia, can be found in [2,10,12,20,19,21,24,25,29,32,45,44,55,56,58,74,50,7,3,27,26,59,11,47,57,43,49,60,54,1,66].…”

Section: The Contextmentioning

confidence: 99%

Compositional Meaning in Logic

Caleiro

Viganò

2017

Log. Univers.

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The Fregean-inspired Principle of Compositionality of Meaning (PoC) for formal languages asserts that the meaning of a compound expression is analysable in terms of the meaning of its constituents, taking into account the mode in which these constituents are combined so as to form the compound expression. From a logical point of view, this amounts to prescribing a constraint-that may or may not be respected-on the internal mechanisms that build and give meaning to a given formal system. Within the domain of formal semantics and of the structure of logical derivations, the PoC is often directly reflected by metaproperties such as truth-functionality and analyticity, characteristic of computationally well-behaved logical systems.

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A cut-free calculus for second-order Gödel logic

Cited by 2 publications

References 16 publications

On Natural Deduction for Herbrand Constructive Logics I: Curry-Howard Correspondence for Dummett's Logic LC

On Natural Deduction for Herbrand Constructive Logics I: Curry-Howard Correspondence for Dummett's Logic LC

Compositional Meaning in Logic

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