Proof routines for the propositional calculus.

Categorical proof theory of classical propositional calculus

We investigate semantics for classical proof based on the sequent calculus. We show that the propositional connectives are not quite well-behaved from a traditional categorical perspective, and give a more refined, but necessarily complex, analysis of how connectives may be characterised abstractly. Finally we explain the consequences of insisting on more familiar categorical behaviour.

A New Proof of Exponential Decidability for the Propositional -calculus with Program Converse

The propositional-Calculus (C) is a powerful propositional program logic with xpoints. C decidability with exponential upper bound was sketched for the rst time in 1988 by E. A. Emerson and Ch. S. Jutla on base of automata-theoretic technique, while a complete proof was published in 1999 only. Meanwhile M. Vardi sketched in 1998 an automata-theoretic proof of exponential decidability for the pr...

A Computational Structure for the Propositional Calculus

Despite the long history and descriptive simplicity of the propositional calculus, practical aspects of its implementation on the computer remain an active area of study. We propose a representation of the propositional calculus which is straightforward, yet compact and sufficiently flexible to circumvent the combinatorial difficulties posed by many problems. The methodology does not involve te...

A Propositional Proof System For

differential propositional calculus ∗

calculus Calculus circle Circle collection Collection combination Combination combinations Combinations component Component components Components cover Cover cut Cut divides Divides entire Entire even Even language Language number Number object Object objects Objects parallel Parallel range Range ranges Ranges rank Rank ranks Ranks place Place representation Representation represents Represents...