This paper introduces a new decision procedure for PLTL based on labelled superposition. Its main idea is to treat temporal formulas as infinite sets of purely propositional clauses over an extended signature. These infinite sets are then represented by finite sets of labelled propositional clauses. The new representation enables the replacement of the complex temporal resolution rule, suggeste...

In this paper we present a new labelled sequent calculus for modal logic. The proof method works with a more “liberal” modal language which allows inferential steps where different formulas refer to different labels without moving to a particular world and there computing if the consequence holds. World-paths can be composed, decomposed and manipulated through unification algorithms and formula...

Labelled tableaux are extensions of semantic tableaux with annotations (labels, indices) whose main function is to enrich the modal object language with semantic elements. This paper consists of three parts. In the first part we consider some options for labels: simple constant labels vs labels with free variables, logic depended inference rules vs labels manipulation based on a label algebra. ...

We present an approach to providing natural deduction style proof systems for a large class of quantiied modal logics with varying, increasing, decreasing or constant domains of quantiication. The systems we develop are modular both in the behavior of the accessibility relation and quantiication relative to the semantics, and in the proofs of soundness and completeness relative to that semantic...