Partial cut elimination for propositional discrete 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...

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...

Cut Elimination in Multifocused Linear Logic

We study cut elimination for a multifocused variant of linear logic in the sequent calculus. The multifocused normal form of proofs yields problems that do not appear in the standard focused system, related to the constraints in grouping rule instances inside focusing phases. We show that cut elimination can be performed in a sensible way even though the proof requires specific lemmas to deal w...

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 ...