A General Framework for Mathematical Fuzzy Logic. Chapter 2
Result description
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
Keywords
mathematical fuzzy logicweakly implicative logicsabstract algebraic logicnon-classical logicssemilinear logics
The result's identifiers
Result code in IS VaVaI
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
A General Framework for Mathematical Fuzzy Logic. Chapter 2
Original language description
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
Czech name
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Czech description
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Classification
Type
C - Chapter in a specialist book
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Book/collection name
Handbook of Mathematical Fuzzy Logic
ISBN
978-1-84890-039-4
Number of pages of the result
105
Pages from-to
103-207
Number of pages of the book
928
Publisher name
College Publications
Place of publication
London
UT code for WoS chapter
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Basic information
Result type
C - Chapter in a specialist book
CEP
BA - General mathematics
Year of implementation
2011