SYLLOGISTICS, MODALITY, TRIVALENCE
Keywords:
Boolean semantics, modal semantics, modal syllogistics, closed or completed class of functionsAbstract
Both modal systems and syllogistics are pseudo-Boolean logic cases for which Boolean function class construction (FB) is insufficient. A complete and consistent trivalent comput-ing system can provide semantics for such Boolean logics, the developing strategy follow-ing two classes: the existing Boolean functions (FBE) and incomplete or partial (FBI) ones. In the first part of this paperwork we are dealing with a complete trivalent logic axiomatiza-tion, taking into consideration a complete class namely the trivalent function class (FT) as well as the closed classes of trivalent functions (in the way of Emil L. Post). In this second part, as we noticed that Venn’s diagram model is consistent, complete and non-ambiguous for building the immediate syllogistic inferences and Aristotelian syllogistic, we are trying to approach a modal interpretation of syllogistics. Finally, based on this Boolean semantics provided by syllogistic interpretation, we have in view to build modal computing systems starting with T minimal system.References
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