In this paper we generalize the existing tableau methods for modal logics. First of all, while usual modal tableaux are based on trees, our basic structures are rooted directed acyclic graphs (RDAG). This allows natural tableau rules for some modal logics that are diicult to capture in the usual way (such as those having an accessibility relation that is dense or connuent). Second, tableau rule...

The paper presents a tableau calculus for a linear time tem poral logic for reasoning about processes and events in concurrent sys tems The logic is based on temporal connectives in the style of Transac tion Logic BK and explicit quanti cation over states The language extends rst order logic with sequential and parallel conjunction parallel disjunction and temporal implication Explicit quanti c...

Like the LR-tableau, a socle tableau is given as skew diagram with certain entries. Unlike in entries are weakly increasing each row, strictly column and satisfy modified lattice permutation property. In study of embeddings subgroup finite abelian p $p$ -group, tableaux occur isomorphism invariants, they by series subgroup. We show that can be realized some embedding. Moreover, an embedding LR-...

In this paper we present a tableau calculus for a temporal extension of the description logic ALC, called T L ALC. This logic is based on the temporal language with`Until' interpreted over the natural numbers with expanding ALC-domains. The tableau calculus forms an elaborated combination of Wolper's tableau calculus for propositional linear temporal logic, the standard tableau-algorithm for AL...

An alternative version of the tableau decision making algorithm defined in the ”Handbook of Description Logics” (Baader et col.) is presented. It is a version of semi-decidable tableau formal system that corresponds with that one of first order logic and shares its semantic soundness and completeness. In examples the advantages of the transparent tree-style representation algorithm, comparing w...

We describe a general and uniform tableau methodology for multi-modal logics arising from Gabbay’s methodology of fibring and Governatori’s tableau system KEM.

A tableau calculus is proof confluent if every partial tableau proof for an unsatisfiable formula can be extended to a closed tableau. A rule application may be redundant but it can never prevent the construction of a proof; there are no “dead ends” in the proof search. Proof confluence is a prerequisite of (a) backtrackingfree proof search and (b) the generation of counter examples to non-theo...

In [15,19] we showed how to combine propositional multimodal logics using Gabbay’s fibring methodology. In this paper we extend the above mentioned works by providing a tableau-based proof technique for the combined/fibred logics. To achieve this end we first make a comparison between two types of tableau proof systems, (graph & path), with the help of a scenario (The Friend’s Puzzle). Having d...

In this article a modiied form of tableau calculus, called Tableau Graph Calculus, is presented for overcoming the well-known ineeciencies of the traditional tableau calculus to a large extent. This calculus is based on a compact representation of analytic tableaux by using graph structures called tableau graphs. These graphs are obtained from the input formula in linear time and incorporate mo...

We present a sound, complete and relatively straightforward tableau method for deciding valid formulas in the propositional version of computation tree logic CTL*. This is the first such tableau. CTL* is an exceptionally important temporal logic with applications from hardware design to agent reasoning but there is no easy automated reasoning approach to CTL*. The tableau here is a traditional ...