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Parametrized prime implicant-implicate computations for regular logics.

Anavai Ramesh, Neil V. Murray (1997)

Mathware and Soft Computing

Prime implicant-implicate generating algorithms for multiple-valued logics (MVL's) are introduced. Techniques from classical logic not requiring large normal forms or truth tables are adapted to certain regular'' multiple-valued logics. This is accomplished by means of signed formulas, a meta-logic for multiple valued logics; the formulas are normalized in a way analogous to negation normal form. The logic of signed formulas is classical in nature. The presented method is based on path dissolution,...

Polyadic algebras over nonclassical logics

Don Pigozzi, Antonino Salibra (1993)

Banach Center Publications

The polyadic algebras that arise from the algebraization of the first-order extensions of a SIC are characterized and a representation theorem is proved. Standard implicational calculi (SIC)'s were considered by H. Rasiowa [19] and include classical and intuitionistic logic and their various weakenings and fragments, the many-valued logics of Post and Łukasiewicz, modal logics that admit the rule of necessitation, BCK logic, etc.

Probabilistic propositional calculus with doubled nonstandard semantics

Ivan Kramosil (1999)

Kybernetika

The classical propositional language is evaluated in such a way that truthvalues are subsets of the set of all positive integers. Such an evaluation is projected in two different ways into the unit interval of real numbers so that two real-valued evaluations are obtained. The set of tautologies is proved to be identical, in all the three cases, with the set of classical propositional tautologies, but the induced evaluations meet some natural properties of probability measures with respect to nonstandard...

Putting together Lukasiewicz and product logics.

Francesc Esteva, Lluis Godo (1999)

Mathware and Soft Computing

In this paper we investigate a propositional fuzzy logical system LΠ which contains the well-known Lukasiewicz, Product and Gödel fuzzy logics as sublogics. We define the corresponding algebraic structures, called LΠ-algebras and prove the following completeness result: a formula φ is provable in the LΠ logic iff it is a tautology for all linear LΠ-algebras. Moreover, linear LΠ-algebras are shown to be embeddable in linearly ordered abelian rings with a strong unit and cancellation law.

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