The Axiomatization of Propositional Linear Time Temporal Logic

The Axiomatization of Propositional Linear Time Temporal Logic

The article introduces propositional linear time temporal logic as a formal system. Axioms and rules of derivation are defined. Soundness Theorem and Deduction Theorem are proved [9]. The terminology and notation used in this paper have been introduced in the In this paper a, b, c denote boolean numbers. Next we state three propositions: (1) (a ⇒ b ∧ c) ⇒ (a ⇒ b) = 1. (2) (a ⇒ (b ⇒ c)) ⇒ (a ∧ b...

Tableau-Like Automata-Based Axiomatization for Propositional Linear Temporal Logic

Propositional Linear Temporal Logic (PLTL) is a very popular formalism for specification and verification of computer programs and systems. This extended abstract sketches a tableau-like axiomatization for PLTL based on automata-theoretic decision procedure coupled with tableau for local model checking of the propositional μ-Calculus. Propositional Linear Temporal Logic (PLTL) is a very popular...

Weak Completeness Theorem for Propositional Linear Time Temporal Logic

We prove weak (finite set of premises) completeness theorem for extended propositional linear time temporal logic with irreflexive version of until-operator. We base it on the proof of completeness for basic propositional linear time temporal logic given in [20] which roughly follows the idea of the Henkin-Hasenjaeger method for classical logic. We show that a temporal model exists for every fo...

Propositional Linear - Time Temporal Logi

Propositional Scopes in Linear Temporal Logic

In this paper, we address the problem of specifying a property in LTL over a subset of the states of a system under test, ignoring the rest of the states. A modern LTL semantics that applies for both finite and infinite traces is considered. We introduce specialized operators (syntax and semantic) that help specifying properties over propositional scopes, where each scope constitute a subset of...