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An orthogonality-based classification of conjectures in ortholattices.

Enric Trillas;  Ana Pradera — 2006

Mathware and Soft Computing

A mathematical model for conjectures (including hypotheses, consequences and speculations), was recently introduced, in the context of ortholattices, by Trillas, Cubillo and Castiñeira (Artificial Intelligence 117, 2000, 255-257). The aim of the present paper is to further clarify the structure of this model by studying its relationships with one of the most important ortholattices' relation, the orthogonality relation. The particular case of orthomodular lattices -the framework for both Boolean...

Aggregation, Non-Contradiction and Excluded-Middle.

Ana Pradera;  Enric Trillas — 2006

Mathware and Soft Computing

This paper investigates the satisfaction of the Non-Contradiction (NC) and Excluded-Middle (EM) laws within the domain of aggregation operators. It provides characterizations both for those aggregation operators that satisfy NC/EM with respect to (w.r.t.) some given strong negation, as well as for those satisfying them w.r.t. any strong negation. The results obtained are applied to some of the most important known classes of aggregation operators.

Aggregation operators from the ancient NC and EM point of view

Ana Pradera;  Enric Trillas — 2006

Kybernetika

This paper deals with the satisfaction of the well-known Non-Contradiction (NC) and Excluded-Middle (EM) principles within the framework of aggregation operators. Both principles are interpreted in a non-standard way, based on self-contradiction (as in Ancient Logic) instead of falsity (as in Modern Logic). The logical negation is represented by means of strong negation functions, and conditions are given both for those aggregation operators that satisfy NC/EM with respect to (w.r.t.) some given...

On MPT-implication functions for fuzzy logic.

Enric Trillas;  Claudi Alsina;  Ana Pradera — 2004

RACSAM

This paper deals with numerical functions J : [0,1] x [0,1] → [0,1] able to functionally express operators →: [0,1] x [0,1] → [0,1] defined as (μ → σ)(x,y) = J(μ(x),σ(y)), and verifying either Modus Ponens or Modus Tollens, or both. The concrete goal of the paper is to search for continuous t-norms T and strong-negation functions N for which it is either T(a, J(a,b)) ≤ b (Modus Ponens) or T(N(b), J(a,b)) ≤ N(a) (Modus Tollens), or both, for all a,b in [0,1] and a given J. Functions J are taken among...

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