An axiomatic formulation of a logic called LPS4 appears in [3]. Here that logic is proved sound and complete with respect to the weak semantics of [7]. Also a tableau system for LPS4 is introduced, and also proved sound and complete with respect to the semantics, thus establishing both cut elimination and equivalence with the axiomatic formulation.

In this paper we present new time and size bounds for satissability in modal K. This is done by means of a simpliied SAT based procedure. Then, as a direct consequence, we provide theoretical support to the claim of superior eeciency for the SAT based decision procedures, with respect to the \classic" tableau based procedures.

Satallax is an automatic higher-order theorem prover that generates propositional clauses encoding (ground) tableau rules and uses MiniSat to test for unsatisfiability. We describe the implementation, focusing on flags that control search and examples that illustrate how the

In this paper we reduce the question of validity of a first-order intuitionistic formula without equality to generating ground instances of this formula and then checking whether the instances are deducible in a propositional intuitionistic tableaux calculus, provided that the propositional proof is compatible with the way how the instances were generated. This result can be seen as a form of t...

The cdebruted ri-we-Rdinson-ThraU (Canad. J. Math. 6 (1954) 316-324) hook-lengths formula, counting the foung tableaux of a specified shape, is given a shart bijective proof. This proof was obtained by translating the elegant Greene-Nijenhuis-Wilf proof (Adv. in Math. 31 (1979) f&l-109) into bijective language. 1 GjG&) satisfying qj <*+lj and ej C= Rj+l (whenever applicable) such that every int...

The fruitful relation between the theory of symmetric functions and that of D-finite power series was first introduced by Goulden and Jackson in 1980, and later extended by Gessel, who stated two important results that provide closure properties of D-finite symmetric series under the scalar and inner products. These products are very important from the computational and combinatorial points of ...