One of the obstacles against the use of tableau-based theorem provers for non-standard logics is the ineeciency of tableau systems in practical applications, though they are highly intuitive and extremely exible from a proof theoretical point of view. We present a method for increasing the eeciency of tableau systems in the case of multiple-valued logics by introducing a generalized notion of s...

for a composition $lambda$ of $n$ our aim is to obtain reduced forms ‎for all the elements in the kazhdan-lusztig (right) cell containing ‎$w_{j(lambda)}$‎, ‎the longest element of the standard parabolic‎ ‎subgroup of $s_n$ corresponding to $lambda$‎. ‎we investigate how far this is possible to achieve by looking at‎ ‎elements of the form $w_{j(lambda)}d$‎, ‎where $d$ is a prefix of ‎an element...

3T AP is an acronym for 3–valued tableau–based theorem prover. It is based on the method of analytic tableaux. 3T AP has been developed at the University of Karlsruhe in cooperation with the Institute for Knowledge Based Systems of IBM Germany in Heidelberg. Despite its name 3T AP is able to deal with “classical” — i.e. two– valued — first–order predicate logic as well as with any finite–valued...

We connect generalized permutahedra with Schubert calculus. Thereby, we give sufficient vanishing criteria for intersection numbers of the flag variety. Our argument utilizes recent developments in study Schubitopes, which are Newton polytopes polynomials. The resulting tableau test executes polynomial time.

We describe the automated theorem prover \Deep Thought" (d DT). The prover can be used for arbitrary multiple-valued rst-order logics, provided the connec-tives can be deened by truth tables and the quantiiers are generalizations of the classical universal resp. ex-istential quantiiers. d DT has been tested with many interesting multiple-valued logics as well as classical rst-order predicate lo...

Automated reasoning systems often su er from redundancy: similar parts of derivations are repeated again and again. This leads us to the problem of loopdetection, which clearly is undecidable in general. Nevertheless, we tackle this problem by extending the hyper-tableau calculus as proposed in [Baumgartner, 1998] by generalized terms with exponents, that can be computed by means of computer al...

Using the collective field theory approach of large–N generalized two–dimensional Yang–Mills theory on cylinder, it is shown that the classical equation of motion of collective field is a generalized Hopf equation. Then, using the Itzykson–Zuber integral at the large–N limit, it is found that the classical Young tableau density, which satisfies the saddle–point equation and determines the large...

Borozan and Cornuéjols introduced a semi-infinite relaxation for mixed-integer linear programs, derived from the simplex tableau relative to a fractional vertex f of the linear relaxation. They showed that any minimal valid inequality for such relaxation is determined by a maximal lattice-free convex set containing f . In this note we show that, for the purpose of generating cuts for the origin...

A non-clausal connection calculus for classical first-order logic is presented that does not require the translation of input formulae into any clausal form. The definition of clauses is generalized, which may now also contain (sub-) matrices. Copying of appropriate (sub-)clauses in a dynamic way, i.e. during the actual proof search, is realized by a generalized extension rule. Thus, the calcul...