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- Representação holista de números reaisPublication . Abrantes, MárioO propósito deste artigo é a definição e a caracterização de uma certa representação híbrida de números reais, aqui designada por representação holista, salientando-se um conjunto de propriedades que a tornam interessante na classe das representações híbridas equiponderadas apresentada no texto.
- An abductive paraconsistent semantics – MHPPublication . Abrantes, Mário; Pereira, Luís MonizIn this paper we present a paraconsistent abdutive semantics for extended normal logic programs, the paraconsistent minimal hypotheses semantics MHP . The MHP is a semantics of total paraconsistent models wich combines the merits of two already existing semantics: it inherits the existence property of the abductive minimal hypotheses semantics MH [1], which is a semantics of total models, and the property of detection of support on contradiction of the paraconsistent well-founded semantics with explicit negation WFSXP [2], which is a semantics of partial paraconsistent models. The MHP enjoys also the property of simple relevance, which permits top-down query answering for brave reasoning purposes. Besides, the MHP lends itself to various types of skeptical and brave reasoning, which include the possibility of drawing conclusions from inconsistent models in a nontrivial way. The MHP coincides with the MH on normal logic programs, and with the WFSXP on stratified extended programs.
- Moeda universalPublication . Abrantes, MárioAtravés de um só lançamento de uma moeda equilibrada, podemos realizar uma escolha aleatória com dois resultados possíveis e equiprováveis. Neste texto é apresentado um algoritmo que generaliza este procedimento para o caso em que os dois resultados possíveis têm probabilidades quaisquer p e q, p+q=1. Designamos o algoritmo por Moeda Universal. A sua execução procede por sucessivos lançamentos de uma moeda equilibrada, com a particularidade de o número de lançamentos necessários para efectuar a escolha ser independente das probabilidades envolvidas, o que confere ao algoritmo uma certa naturalidade enquanto generalização do processo de escolha com dois resultados possíveis equiprováveis, que requer sempre um só lançamento.
- Revision based total semantics for extended normal logic programsPublication . Abrantes, Mário; Pereira, Luís Moniz; Rocha, Isabel OitavemThe purpose of this thesis is the development of a formal semantical approach for extended normal logic programs, where contradictions are tackled by means of a reduction ad absurdum with respect to default negation mechanism, in the fashion of arti cial intelligence belief revision, that leads to a set of implicit revisions. We ful lled these objectives in two steps. The rst one was the implementation of a total paraconsistent models semantics for extended normal logic programs MHP , that combines the merits of two already existing semantics: it inherits the existence property of the abductive minimal hypotheses semantics MH, a semantics of total models, and the property of detection of support on contradiction of the paraconsistent well-founded semantics with explicit negation WFSXP , a semantics of partial paraconsistent models. As for the second step, we developed a revision procedure for inconsistent constrained theories, that tackles inconsistencies arising from contradictions with respect to explicit negation, i.e., L and :L in the same model, and stepping beyond, also tackles inconsistencies arising in more general constrained theories (i.e., theories containing constraints of the type ? A; not B, where A is a conjunction of objective literals and not B stands for a conjunction of default literals). An algorithm for inconsistency propagation detection was also developed. A characterization of the MHP with respect to the semantic formal properties of relevance and cumulativity is furnished, by resorting to a set of results that arose from a detailed study of these properties for a class of 2-valued conservative extensions of the stable models semantics.