The completeness of Stoic propositional logic.

The completeness of Stoic propositional logic

On the Completeness of Propositional Hoare Logic

As shown by Cook [5], Hoare logic is relatively complete for partial correctness assertions (PCAs) over while programs whenever the underlying assertion language is sufficiently expressive. The expressiveness conditions in Cook’s formulation provide for the expression of weakest preconditions. These conditions holds for first-order logic over , for example, because of the coding power of first-...

On the polynomial-space completeness of intuitionistic propositional logic

We present an alternative, purely semantical and relatively simple, proof of the Statman’s result that both intuitionistic propositional logic and its implicational fragment are PSPACE -complete.

Deterministic Propositional Dynamic Logic: Finite Models, Complexity, and Completeness

Let p be a formula in deterministic propositional dynamic logic. A decision procedure for the satisliability of p is given along with a construction of a finite model for every satisfiable p. The decision procedure runs in deterministic time 2’” and the size of the model is bounded by nz . 4”, where n is the length of p. Finally, a complete axiomatization for deterministic propositional dynamic...

A Hierarchical Completeness Proof for Propositional Temporal Logic

We present a new proof of axiomatic completeness for Proposition Temporal Logic (PTL) for discrete, linear time for both finite and infinite time (without past-time). This makes use of a natural hierarchy of logics and notions and is an interesting alternative to the proofs in the literature based on tableaux, filtration, game theory and other methods. In particular we exploit the deductive com...