Lattice-valued modal propositional logic and its completeness

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...

α-Resolution Method for Lattice-valued Horn Generalized Clauses in Lattice-valued Propositional Logic Systems

In this paper, an α-resolution method for a set of lattice-valued Horn generalized clauses is established in lattice-valued propositional logic systemL P(X) based on lattice implication algebra. Firstly, the notions of lattice-valued Horn generalized clause, normal lattice-valued Horn generalized clause and unit latticevalued Horn generalized clause are given in L P(X). Then, the α-resolution o...

Remarks on completeness of lattice-valued Cauchy spaces

We study different completeness definitions for two categories of lattice-valued Cauchy spaces and the relations between these definitions. We also show the equivalence of a so-called completion axiom and the existence of a completion.

Completeness in modal logic

Propositional Abduction in Modal Logic

In this work, the problem of performing abduction in modal logics is addressed, along the lines of 3], where a proof theoretical abduction method for full rst order classical logic is deened, based on tableaux and Gentzen-type systems. This work applies the same methodology to face modal abduction. The non-classical context enforces the value of analytical proof systems as tools to face the met...