Hypersequents and fuzzy logic.

Dov Gabbay; George Metcalfe; Nicola Olivetti

RACSAM (2004)

  • Volume: 98, Issue: 1, page 113-126
  • ISSN: 1578-7303

Abstract

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Fuzzy logics based on t-norms and their residua have been investigated extensively from a semantic perspective but a unifying proof theory for these logics has, until recently, been lacking. In this paper we survey results of the authors and others which show that a suitable proof-theoretic framework for fuzzy logics is provided by hypersequents, a natural generalization of Gentzen-style sequents. In particular we present hypersequent calculi for the logic of left-continuous t-norms MTL and related logics, and for logics based on the three fundamental continuous t-norms, Gödel logic G, Lukasiewicz logic L, and Product logic Π.

How to cite

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Gabbay, Dov, Metcalfe, George, and Olivetti, Nicola. "Hypersequents and fuzzy logic.." RACSAM 98.1 (2004): 113-126. <http://eudml.org/doc/41042>.

@article{Gabbay2004,
abstract = {Fuzzy logics based on t-norms and their residua have been investigated extensively from a semantic perspective but a unifying proof theory for these logics has, until recently, been lacking. In this paper we survey results of the authors and others which show that a suitable proof-theoretic framework for fuzzy logics is provided by hypersequents, a natural generalization of Gentzen-style sequents. In particular we present hypersequent calculi for the logic of left-continuous t-norms MTL and related logics, and for logics based on the three fundamental continuous t-norms, Gödel logic G, Lukasiewicz logic L, and Product logic Π.},
author = {Gabbay, Dov, Metcalfe, George, Olivetti, Nicola},
journal = {RACSAM},
keywords = {t-norm-based fuzzy logic; proof theory; hypersequents; hypersequent calculi; continuous t-norms},
language = {eng},
number = {1},
pages = {113-126},
title = {Hypersequents and fuzzy logic.},
url = {http://eudml.org/doc/41042},
volume = {98},
year = {2004},
}

TY - JOUR
AU - Gabbay, Dov
AU - Metcalfe, George
AU - Olivetti, Nicola
TI - Hypersequents and fuzzy logic.
JO - RACSAM
PY - 2004
VL - 98
IS - 1
SP - 113
EP - 126
AB - Fuzzy logics based on t-norms and their residua have been investigated extensively from a semantic perspective but a unifying proof theory for these logics has, until recently, been lacking. In this paper we survey results of the authors and others which show that a suitable proof-theoretic framework for fuzzy logics is provided by hypersequents, a natural generalization of Gentzen-style sequents. In particular we present hypersequent calculi for the logic of left-continuous t-norms MTL and related logics, and for logics based on the three fundamental continuous t-norms, Gödel logic G, Lukasiewicz logic L, and Product logic Π.
LA - eng
KW - t-norm-based fuzzy logic; proof theory; hypersequents; hypersequent calculi; continuous t-norms
UR - http://eudml.org/doc/41042
ER -

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