![]() ![]() The tautologies of / L, \Pi, and G are coNP complete, and thus not harder than the classical prop. ![]() ![]() Thus one can view M as a minimal complete core of Gentzen's LK. In turn, every continuous t-norm can be represented as the ordinal sum of the / Lukasiewicz, Product and Godel t-norms. A minimality theorem holds for the propositional fragment Mp: any propositional sequent calculus S (within a standard class of right-sided calculi) is complete if and only if S contains Mp (that is, each rule of Mp is derivable in S). It studies the logical values of propositions when taken as a whole and logical relationships when connected using logical connectives (such as logical AND, logical OR. It is also known as sentential logic or sentential calculus. Triangular logics have attracted a lot of research in recent years, since on the one hand they retain an appealing theory akin to the theory of Boolean algebras in classical logic, while on the other hand they subsume major fuzzy formalisms such as / Lukasiewicz logic / L, Product logic \Pi, and Godel logic G. The area of mathematical logic that deals with propositions are called Propositional Logic or Propositional Calculus. A triangular logic is a propositional fuzzy logics whose truth functions are defined by continuous triangular norms (t-norms) a formal definition is given in section 2. In this paper we show that the problem of recognizing t-tautologies is coNP complete, and thus decidable. A t-tautology (triangular tautology) is a propositional formula which is a tautology in all fuzzy logics defined by continuous triangular norms.
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