O método dos Tableaux Aplicado ao Cálculo Trivalente e Intuicionista I1

ABSTRACT

Sette and Carnielli introduced the axiomatic system I1 in 1995, which presents an intuitionistic character, in the same regard of the logical system developed by Arend Heyting (1898-1980), that is, as a logic underlying to the constructive mathematics, for instance, $\neg \neg A\to A$ is not an I1 tautology. On the other hand, this system is a 3-valued logic, in which presents in addition to the classical truth values, the truth-value F*, that can be understood as “false by lack of positive evidence”. In the semantic environment of this logic, there is only one distinguished value. In this work, we develop an alternative deductive method to the axiomatic for the system I1, namely, we introduce an analytic tableaux system for such logic. We establish, by means of a theorem, that every deduction obtained from the axiomatic system, will be also deduced by the tableaux system proposed.

Keywords:
intuitionistic logic; three-valued logic; method of analytic tableaux