Many-valued Logics

On elementary equivalence in Fuzzy Predicate Logics

Publication Type:

Journal Article

Authors:

Pilar Dellunde; Francesc Esteva

Source:

Archive for Mathematical Logic, Springer-Verlag (In Press)

Keywords:

Mathematical Logic and Foundations; Model Theory; Fuzzy Predicate Logics; Elementary Extensions; Witnessed Models; Quasi-witnessed Models

Abstract:

Our work is a contribution to the model theory of fuzzy predicate logics. In
this paper we characterize elementary equivalence between models of fuzzy predicate
logic using elementary mappings. Re ning the method of diagrams we give a solution
to an open problem of P. Hajek and P. Cintula (Conjectures 1 and 2 of [HaCi06]).
We investigate also the properties of elementary extensions in witnessed and quasiwitnessed
theories, generalizing some results of Section 7 of [HaCi06] and of Section 4
of [CeEs11] to non-exhaustive models.

Many-valued Semantics for Vague Counterfactuals

Publication Type:

Book Chapter

Authors:

Marco Cerami; Pere Pardo

Source:

Understanding Vagueness - Logical, Philosophical, and Linguistic Perspectives, College Publications, Number 36, p.341-362 (2011)

Keywords:

Many-valued Logics; Counterfactuals

First-order SMTL Logic and quasi-witnessed models

Publication Type:

Conference Paper

Authors:

Marco Cerami; Francesc Esteva

Source:

XV Congreso Español sobre Tecnologías y Lógica Fuzzy ESTYLF 2010, Huelva, p.145-150 (2010)

From Classical Description Logic to n-graded Fuzzy Description logics

Publication Type:

Conference Paper

Authors:

Angel García-Cerdaña; Marco Cerami; Francesc Esteva

Source:

FUZZ-IEEE2010, IEEE, Barcelona, p.1506-1513. (2010)

Fuzzy Description Logics and t-norm based Fuzzy Logics

Publication Type:

Journal Article

Authors:

Angel García-Cerdaña; Eva Armengol; Francesc Esteva

Source:

International Journal of Approximate reasoning, Elsevier, Volume 51, Issue 6, p.632 -- 655 (2010)

Keywords:

Description Logics; Fuzzy Description Logics; Many-valued Logics; Propositional and Predicate t-norm based Fuzzy Logics; Truth-constantsReceived 22 May 2009

Abstract:

Description Logics (DLs) are knowledge representation languages built on the basis of classical logic. DLs allow the creation of knowledge bases and provide ways to reason on the contents of these bases. Fuzzy Description Logics (FDLs) are natural extensions of DLs for
dealing with vague concepts, commonly present in real applications. Ha?jek proposed to
deal with FDLs taking as basis t-norm based fuzzy logics with the aim of enriching the
expressive possibilities in FDLs and to capitalize on recent developments in the field of
Mathematical Fuzzy Logic. From this perspective we define a family of description lan-
guages, denoted by
ALC

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