Система на пропозиционалната логика с добавен Т-оператор
System of Propositional Logic with an added T-operator

Summary/Abstract: The paper proposes an extension of the propositional logic with the addition of a new T-operator. The T-operator is similar to the necessity operator Ÿ in modal logic and its meaning is that the expression it prefixes is a tautology. Т and Ÿ differ substantially, which excludes T’s treatment via Kripke’s possible world semantics. In general terms, the difference consists in the fact that while Ÿ is reduced to universality of cases (truth in every one of a set of possible worlds), T is reduced to logical consistency, (if Тр is true, then p’s negation contains contradiction). The paper also introduces a new semantic method for determining the logical validity of expressions in the propositional logic with an added T-operator (alternative to possible world semantics) and presents an axiomatic system whose completeness with respect to the proposed semantic method is proved. The introduction of T removes the paradoxes of logical entailment (strict implication) encountered even in the strongest of standard modal systems.

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