Logical Operations and Inference in the Complex s-Logic

Abstract

Imaginary propositional logic (i-logic) is being introduced through which the classical propositional logic (called in the present work real or r-logic) is extended to complex, summary (s-logic), in which the two logics above are interpreted. For this purpose a constraint (axiom) is added to the structures of the two logics—r and i, which connects heir variables and states. The s-logic received provides a possibility all logic equations to be solved which cannot be done in the frame of the classical propositional logic. It is proved that the s-logic has six states, non-equipotent between each other, i.e. it is a multi-valued logic. All possible truth tables for conjunction, disjunction, and implication between the six states and variables of the three logics—r, i, and s are received by the formalisms being introduced. A number of new results are discussed characteristic for the implication in the s-logic. On the base of the truth tables and the rules Modus Ponens and Modus Tollens a number of relations are received for the logical inference in the s-logic which is different in some aspect from those in the r-logic. Examples are given for s-logic application: solving problems in logical equations and the mental activity.