We have seen that the language of propositional logic allows us to build up expressions from propositional variables A, B, C, \ldots using propositional connectives like \to, \wedge, \vee, and \neg.

We attempt to define the classical propositional logic by use of appropriate derivability conditions called Cn-definitions. The conditions characterize basic properties of propositional connectives.

Girard introduced phase semantics as a complete set-theoretic semantics of linear logic, and Okada modified phase-semantic completeness proofs to obtain normalform theorems. On the basis of these ...

Abstract: We provide the foundations of automated deduction in the propositional Gδdel logic. The propositional Gδdel logic is one of the simplest infinitely valued fuzzy logics, which generalizes ...

Modal logic, an extension of classical logic, investigates the modes of truth such as necessity and possibility. Its development has been closely intertwined with advances in proof theory, a field ...

This is an introductory course in Discrete Mathematics oriented towards Computer Science. It covers the principles of mathematics from the foundation of computing. By the end of this course, students ...

Abstract: Logic is the foundation of most computer programming and now is an integral part of the development of New Age Artificial Intelligence. Logic helps AI and ML in fields with very little or ...