Contribución al estudio del razonamiento ordinario y la computación con palabras

Abstract

This work is a contribution to enlarge the Conjectures, Hypotheses and Consequences (CHC) models, which try to formalize commonsense reasoning. Its main contribution is to introduce in these models the possibility to use the imprecision typical of language. The first paper collected in this work deals with the problem of the meaning of words, that can be framed in the field of Computing with Words. It mainly tries to analyze, which intrinsic properties of a predicate P and collectives originated by it, are required for obtaining a mathematical representation of it through a function, defined from the universe of discourse, where the predicate is stated, to a scale. That allows to compute the extent up to which x is P in language, for all x in the universe of discourse. The paper focuses on the design of scale used explaining the case of: the Zadeh's fuzzy sets, the interval-valued, the intuitionistic, and the type-2 fuzzy sets. Continuing with the problem of meaning, it is analyzed a new interpretation of the Aristotelian principles of non-contradiction and excluded-middle based on the concept of self-contradiction. This is the aim of the second paper collected in the current work. It deals with the 'principles' verification in the case of the unit interval of the real line. Such verification is done in the unit interval for three different preorders, being the first one the restriction to usual orden on the real line to the unit interval, what allows to extend this study to characterize the case of fuzzy sets. In the third paper of this work, CHC models are defined in a preordered set. So, the results obtained are applied to the case of fuzzy sets endowed with the usual pointwise ordering. The model departs from a structure of consequence defined by an operator in the sense of Tarski, adding a family of subsets which controls the consistence of premises and consequences depending on different interpretations of non-inconsistency (not admitting any premise false, or self-contradictory, or any pair of premises contradictories,...). From them, the corresponding sets of conjectures, hypotheses, speculations and refutations are considered. Finally, the last contribution of this work considers CHC models not coming from a consequence operator, the set of conjectures is built depending on different interpretation of being not-inconsistent with the information conveyed by the set of premises, and then consequences, hypotheses and speculations are obtained