A General Framework for Mathematical Fuzzy Logic. Chapter 2

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

A General Framework for Mathematical Fuzzy Logic. Chapter 2

Popis výsledku v původním jazyce

The aim of this chapter is to present a marriage of Mathematical Fuzzy Logic and (Abstract) Algebraic Logic in order to provide a general background for the rest of the handbook. We use the notions and techniques from the latter to create a new frameworkwhere we can develop in a natural way a particular technical notion corresponding to the intuition of fuzzy logics as the logics of chains. Our framework is the class of weakly implicative semilinear logics, roughly speaking logics with implication connective which are complete with respect to the class of linear ordered matrices. We choose the term `semilinear' instead of `fuzzy', because the term `fuzzy' is too heavily charged with many conflicting potential meanings. The chapter is structured as follows. In Section 1 we introduce the necessary notions from (Abstract) Algebraic Logic, the definition of weakly implicative logic and some refinements thereof and provide three increasingly stronger completeness theorems for them. Moreove

Název v anglickém jazyce

A General Framework for Mathematical Fuzzy Logic. Chapter 2

Popis výsledku anglicky

The aim of this chapter is to present a marriage of Mathematical Fuzzy Logic and (Abstract) Algebraic Logic in order to provide a general background for the rest of the handbook. We use the notions and techniques from the latter to create a new frameworkwhere we can develop in a natural way a particular technical notion corresponding to the intuition of fuzzy logics as the logics of chains. Our framework is the class of weakly implicative semilinear logics, roughly speaking logics with implication connective which are complete with respect to the class of linear ordered matrices. We choose the term `semilinear' instead of `fuzzy', because the term `fuzzy' is too heavily charged with many conflicting potential meanings. The chapter is structured as follows. In Section 1 we introduce the necessary notions from (Abstract) Algebraic Logic, the definition of weakly implicative logic and some refinements thereof and provide three increasingly stronger completeness theorems for them. Moreove

Druh

C - Kapitola v odborné knize

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2011

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název knihy nebo sborníku

Handbook of Mathematical Fuzzy Logic

ISBN

978-1-84890-039-4

Počet stran výsledku

105

Strana od-do

103-207

Počet stran knihy

928

Název nakladatele

College Publications

Místo vydání

London

Kód UT WoS kapitoly

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