Weak Completeness Theorem for Propositional Linear Time Temporal Logic

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...

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...

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...

Propositional Linear - Time Temporal Logi

Finitisation for Propositional Linear Time Logic

Currently known sequent systems for propositional linear time temporal logic either include a cut rule in some form or an infinitary rule, which is a rule with infinitely many premises. We strengthen the infinitary rule to require only a finite number of premises and show that this modification preserves soundness. This way we obtain a finitary cut-free sequent system which almost fulfills the ...