Many-valued logics—implications and semantic consequences

Many-valued logics – implications and semantic consequences

In this paper an application of the well-known matrix method to an extension of the classical logic to many-valued logic is discussed: we consider an n-valued propositional logic as a propositional logic language with a logical matrix over n truth-values. The algebra of the logical matrix has operations expanding the operations of the classical propositional logic. Therefore we look over the Lu...

Transporting many-valued sets along many-valued relations

The transport of L-sets along an L-relation R is considered, with L any residuated lattice, sometimes with further properties as to be a frame or an MV-algebra. Pairs of powerset operators related to R are considered and their basic properties are studied in a comprehensive discussion including some results already known. A few examples and suggestions for application and further development ar...

Neutrality and Many-Valued Logics

Preamble This book written by A. Schumann & F. Smarandache is devoted to advances of non-Archimedean multiple-validity idea and its applications to logical reasoning. Leibnitz was the first who proposed Archimedes' axiom to be rejected. He postulated infinitesimals (infinitely small numbers) of the unit interval [0, 1] which are larger than zero, but smaller than each positive real number. Robi...

Many-valued hybrid logic

In this paper we define a many-valued semantics for hybrid logic and we give a sound and complete tableau system which is prooftheoretically well-behaved, in particular, it gives rise to a decision procedure for the logic. This shows that many-valued hybrid logics is a natural enterprise and opens up the way for future applications.

Many - Valued Logics