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T-norm-based logics with an independent involutive negation

T-norm-based logics with an independent involutive negation
T-norm-based logics with an independent involutive negation
In this paper we investigate the addition of arbitrary independent involutive negations to t-norm-based logics. We deal with several extensions of MTL and establish general completeness results. Indeed, we will show that, given any t-norm-based logic satisfying some basic properties, its extension by means of an involutive negation preserves algebraic and (finite) strong standard completeness. We will deal with both propositional and predicate logics. ?? 2006 Elsevier B.V. All rights reserved.
Involutive negations, Left-continuous t-norms, Many-valued logics, Predicate calculi, Standard completeness
0165-0114
3125-3144
Flaminio, Tommaso
10824669-cfbb-4724-aa74-e1b31574dae8
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96
Flaminio, Tommaso
10824669-cfbb-4724-aa74-e1b31574dae8
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96

Flaminio, Tommaso and Marchioni, Enrico (2006) T-norm-based logics with an independent involutive negation. Fuzzy Sets and Systems, 157 (24), 3125-3144. (doi:10.1016/j.fss.2006.06.016).

Record type: Article

Abstract

In this paper we investigate the addition of arbitrary independent involutive negations to t-norm-based logics. We deal with several extensions of MTL and establish general completeness results. Indeed, we will show that, given any t-norm-based logic satisfying some basic properties, its extension by means of an involutive negation preserves algebraic and (finite) strong standard completeness. We will deal with both propositional and predicate logics. ?? 2006 Elsevier B.V. All rights reserved.

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More information

e-pub ahead of print date: 7 August 2006
Keywords: Involutive negations, Left-continuous t-norms, Many-valued logics, Predicate calculi, Standard completeness

Identifiers

Local EPrints ID: 417220
URI: http://eprints.soton.ac.uk/id/eprint/417220
ISSN: 0165-0114
PURE UUID: 89b62d08-97a1-4eaa-bb40-4d80310dd348

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Date deposited: 25 Jan 2018 17:30
Last modified: 13 Mar 2019 19:04

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