The symmetry rule in propositional logic

The Symmetry Rule in Propositional

Rewrite Rule Systems for Modal Propositional Logic

D This paper explains new results relating modal propositional logic and rewrite rule systems. More precisely, we give complete term rewriting systems for the modal propositional systems known as K, Q, T, and S5. These systems are presented as extensions of Hsiang’s system for classical propositional calculus. We have checked local confluence with the rewrite rule system K.B. (cf. the Knuth-Ben...

Equality propositional logic and its extensions

We introduce a new formal logic, called equality propositional logic. It has two basic connectives, $boldsymbol{wedge}$ (conjunction) and $equiv$ (equivalence). Moreover, the $Rightarrow$ (implication) connective can be derived as $ARightarrow B:=(Aboldsymbol{wedge}B)equiv A$. We formulate the equality propositional logic and demonstrate that the resulting logic has reasonable properties such a...

Propositional Lax Logic Propositional Lax Logic

We investigate a peculiar intuitionistic modal logic, called Propositional Lax Logic (PLL), which has promising applications to the formal veri cation of computer hardware. The logic has emerged from an attempt to express correctness `up to' behavioural constraints | a central notion in hardware veri cation | as a logical modality. As a modal logic it is special since it features a single modal...

Propositional Logic as a Propositional Fuzzy Logic

There are several ways to extend the classical logical connectives for fuzzy truth degrees, in such a way that their behavior for the values 0 and 1 work exactly as in the classical one. For each extension of logical connectives the formulas which are always true (the tautologies) changes. In this paper we will provide a fuzzy interpretation for the usual connectives (conjunction, disjunction, ...