A propositional linear time logic with time flow isomorphic toω2

A propositional linear time logic with time flow isomorphic to ω2

Primarily guided with the idea to express zero-time transitions by means of temporal propositional language, we have developed a temporal logic where the time flow is isomorphic to ordinal ω 2 (concatenation of ω copies of ω). If we think of ω 2 as lexicographically ordered ω×ω, then any particular zero-time transition can be represented by states whose indices are all elements of some {n} × ω....

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 ...

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...

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