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1

Tense Operators on MV-Algebras and Łukasiewicz-Moisil Algebras

Diaconescu D., Georgescu G.

Fundamenta Informaticae

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2007

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Vol. 81, nr 4

379-408

EN

We introduce tense LMn-algebras and tense MV-algebras as algebraic structures for some tense many-valued logics. A representation theorem for tense LMn-algebras is proved and the polynomial equivalence between tense LM3-algebras (resp. tense LM4-algebras) and tense MV3-algebras (resp. tense MV4-algebras) is established. We study the pairs of dually-conjugated operations on MV-algebras and we use their properties in order to investigate how the axioms of tense operators are preserved by the Dedekind-MacNeille completion of an Archimedean MV-algebra. A tense many-valued propositional calculus is developed and a completeness theorem is proved.

2

Concept lattices and similarity in non-commutative fuzzy logic

Georgescu G., Popescu A.

Fundamenta Informaticae

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2002

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Vol. 53, nr 1

23-54

EN

A classical (crisp) concept is given by its extent (a set of objects) and its intent (a set of properties). In commutative fuzzy logic, the generalization comes naturally, considering fuzzy sets of objects and properties. In both cases (the first being actually a particular case of the second), the situation is perfectly symmetrical: a concept is given by a pair (A,B), where A is the largest set of objects sharing the attributes from B and B is the largest set of attributes shared by the objects from A (with the necessary nuance when fuzziness is concerned). Because of this symmetry, working with objects is the same as working with properties, so there is no need to make any choice. In this paper, we define concepts in a "non-commutative fuzzy world", where conjunction of sentences is not necessarily commutative, which leads to the following non-symmetrical situation: a concept has one extent (because, at the end of the day, concepts are meant to embrace, using certain descriptions, diverse sets of objects), but two intents, given by the two residua (implications) of the non-commutative conjunction.

3

Some model theory for probability structures

Georgescu G.

Reports on Mathematical Logic

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2001

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No. 35

103-113

EN

In this paper we study some model theory for Gaifman probability structures. A classical result of Horn-Tarski concerning the extension of probabilities on Boolean algebras will allow us to prove some preservation theorems for probability structures, the model-companion of logical probability, etc. extending some classical results in eastern model theory.