Classical and empirical negation in subintuitionistic logic

M.J. De; Hitoshi Omori

Classical and empirical negation in subintuitionistic logic

M.J. De
, Hitoshi Omori

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

Abstract

Giovanna Corsi (1987) and Greg Restall (1994) investigate propositional subintuitionistic logics that result by weakening the frame conditions of the Kripke semantics for intuitionistic logic. Both Corsi and Restall confine their attention to the standard intuitionistic language. In this paper we consider two negation expansions of subintuitionistic logic, one by classical negation and the other with by what has been dubbed "empirical" negation. We provide an axiomatization of each expansion and show them sound and strongly complete. We conclude with some final remarks, including avenues for future research.

Original language	English
Title of host publication	Advances in Modal Logic
Editors	Lev Beklemishev, Stéphane Demri, András Máté
Publisher	College Publications
Pages	217-235
Volume	11
ISBN (Print)	978-1-84890-201-5
Publication status	Published - 2016

Keywords

Subintuitionistic logic
intuitionistic logic
classical negation
empiricalnegation

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http://www.aiml.net/volumes/volume11/

Cite this

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abstract = "Giovanna Corsi (1987) and Greg Restall (1994) investigate propositional subintuitionistic logics that result by weakening the frame conditions of the Kripke semantics for intuitionistic logic. Both Corsi and Restall confine their attention to the standard intuitionistic language. In this paper we consider two negation expansions of subintuitionistic logic, one by classical negation and the other with by what has been dubbed {"}empirical{"} negation. We provide an axiomatization of each expansion and show them sound and strongly complete. We conclude with some final remarks, including avenues for future research.",

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AB - Giovanna Corsi (1987) and Greg Restall (1994) investigate propositional subintuitionistic logics that result by weakening the frame conditions of the Kripke semantics for intuitionistic logic. Both Corsi and Restall confine their attention to the standard intuitionistic language. In this paper we consider two negation expansions of subintuitionistic logic, one by classical negation and the other with by what has been dubbed "empirical" negation. We provide an axiomatization of each expansion and show them sound and strongly complete. We conclude with some final remarks, including avenues for future research.

KW - Subintuitionistic logic

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KW - classical negation

KW - empiricalnegation

M3 - Chapter

SN - 978-1-84890-201-5

VL - 11

SP - 217

EP - 235

BT - Advances in Modal Logic

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A2 - Demri, Stéphane

A2 - Máté, András

PB - College Publications

ER -

Classical and empirical negation in subintuitionistic logic

Abstract

Keywords

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