For a (standard) Young tableau T on [k], say that a tableau T ′ on [n] contains T as a subtableau if the cells of T ′ containing the elements of [k] are arranged as in T . McKay, Morse, and Wilf recently introduced the idea of quasirandom permutations and used this to find the limiting probability (as n → ∞) that a tableau on [n] contains a given tableau on [k] as a subtableau. Stanley then use...

Rules that are admissible can be used in any derivations in any axiomatic system of a logic. In this paper we introduce a method for checking the admissibility of rules in the modal logic S4. Our method is based on a standard semantic ground tableau approach. In particular, we reduce rule admissibility in S4 to satisfiability of a formula in a logic that extends S4. The extended logic is charac...

Projection computation is a generalization of second-order quantifier elimination, which in turn is closely related to the computation of forgetting and of uniform interpolants. On the basis of a unified view on projection computation and knowledge compilation, we develop a framework for applying tableau methods to these tasks. It takes refinements from performance oriented systems into account...

Two prominent families of algorithms for the satisfiability test of DLs are automatabased algorithms (see e.g. [6]), which translate a concept C into an automaton AC accepting all (abstractions of) models for C, and tableau algorithms (TAs) [2], which incrementally create a tree-shaped (pre-) model for C using a set of completion rules. In short, the advantages of automata algorithms are on the...

Axiom pinpointing has been introduced in description logics (DLs) to help the user to understand the reasons why consequences hold and to remove unwanted consequences by computing minimal (maximal) subsets of the knowledge base that have (do not have) the consequence in question. The pinpointing algorithms described in the DL literature are obtained as extensions of the standard tableau-based r...

Tableau based proof systems have been designed for many logics extending classical rst order logic This paper proposes a sound tableau calculus for temporal logics of the rst order CTL family Until now a tableau calculus has only been presented for the propositional version of CTL The calculus considered operates with pre xed formulas and may be regarded as an instance of a labelled deductive s...

In this paper we improve a model checking algorithm based on the tableau method of Stifling and Walker. The algorithm proves whether a property expressed in the modal mu-calculus holds for a state in a finite transition system. It makes subsequent use of subtableaux which were calculated earlier in the proof run. These aubtab|eaux are reduced to expressions. Examples show that both size of tabl...

This paper studies the relationship between disjunctive form, a syntactic normal form for the modal μ calculus, and the alternation hierarchy. First it shows that all disjunctive formulas which have equivalent tableau have the same syntactic alternation depth. However, tableau equivalence only preserves alternation depth for the disjunctive fragment: there are disjunctive formulas with arbitrar...