Cooperation between Top-Down and Bottom-Up Theorem Provers

Top-down and bottom-up theorem proving approaches each have specific advantages and disadvantages. Bottom-up provers profit from strong redundancy control but suffer from the lack of goal-orientation, whereas top-down provers are goal-oriented but often have weak calculi when their proof lengths are considered. In order to integrate both approaches, we try to achieve cooperation between a top-down and a bottom-up prover in two different ways: The first technique aims at supporting a bottom-up with a top-down prover. A top-down prover generates subgoal clauses, they are then processed by a bottom-up prover. The second technique deals with the use of bottom-up generated lemmas in a top-down prover. We apply our concept to the areas of model elimination and superposition. We discuss the ability of our techniques to shorten proofs as well as to reorder the search space in an appropriate manner. Furthermore, in order to identify subgoal clauses and lemmas which are actually relevant for the proof task, we develop methods for a relevancy-based filtering. Experiments with the provers SETHEO and SPASS performed in the problem library TPTP reveal the high potential of our cooperation approaches

Fixed point resolution in extended WZW-models

A formula is derived for the fixed point resolution matrices of simple current extended WZW-models and coset conformal field theories. Unlike the analogous matrices for unextended WZW-models, these matrices are in general not symmetric, and they may have field-dependent twists. They thus provide non-trivial realizations of the general conditions presented in earlier work with Fuchs and Schweigert.Comment: 21 pages, Phyzz

Real dimension groups

We show the characterization analogous to dimension groups of partially ordered real vector spaces with interpolation works, but sequential direct limits of simplicial vector spaces only under strong assumptions. We also provide and generalize a proof of a result of Fuchs asserting that the real polynomial algebra with pointwise ordering coming from an interval satisfies Riesz interpolatio

Remarks on deixis

The prevailing conception of deixis is oriented to the idea of 'concrete' physical and perceptual characteristics of the situation of speech. Signs standardly adduced as typical deictics are I, you, here, now, this, that. I and you are defined as meaning "the person producing the utterance in question" and "the person spoken to", here and now as meaning "where the speaker is at utterance time" and "at the moment the utterance is made" (also, "at the place/time of the speech exchange"); similarly, the meanings of this and that are as a rule defined via proximity to speaker's physical location. The elements used in such definitions form the conceptual framework of most of the general characterisations of deixis in the literature. [...] There is much in the literature, of course, that goes far beyond this framework . A great variety of elements, mostly with very abstract meanings, have been found to share deictic characteristics although they do not fit into the personnel-place-time-of-utterance schema. The adequacy of that schema is also called into question by many observations to the effect that the use of such standard deictics as here, now, this, that cannot really be accounted for on its basis, and by the far-reaching possibilities of orienting deictics to reference points in situations other than the situation of speech, to 'deictic centers' other than the speaker. [...] Analyses along the lines of the standard conception regularly acknowledge the existence of deviations from the assumed basic meanings. One traditional solution attributes them to speaker's "subjectivity", or to differences between "physical" and "psychological" space or time; in a similar vein, metaphorical extensions may be said to be at play, or a distinction between prototypical and non-prototypical meanings invoked. Quite apart from the question of the relative merits of these explanatory principles, which I do not wish to discuss here, the problem with all such accounts is that the definitions of the assumed basic meanings themselves are founded on axiom rather than analysis of situated use. The logical alternative, of course, is to set out for more abstract and comprehensive meaning definitions from the start. In fact, a number of recent, discourse-oriented, treatments of the demonstratives proceed this way; they view those elements as processing instructions rather than signs with inherently spatial denotation (Isard 1975, Hawkins 1978, Kirsner 1979, Linde 1979 , Ehlich 1982.

Structural Relaxations in a Simple Model Molten Salt

The structural relaxations of a dense, binary mixture of charged hard spheres are studied using the Mode Coupling Theory (MCT). Qualitative differences to non--ionic systems are shown to result from the long--range Coulomb interaction and charge ordering in dense molten salts. The presented non--equilibrium results are determined by the equilibrium structure, which is input using the well studied Mean Spherical Approximation.Comment: 6 pages, 4 Postscript figures, uses epsfig.sty, rotate.sty, here.st

Braiding in Conformal Field Theory and Solvable Lattice Models

Braiding matrices in rational conformal field theory are considered. The braiding matrices for any two block four point function are computed, in general, using the holomorphic properties of the blocks and the holomorphic properties of rational conformal field theory. The braidings of $SU(N)_k$ with the fundamental are evaluated and are used as examples. Solvable interaction round the face lattice models are constructed from these braiding matrices, and their Boltzmann weights are given. This allows, in particular, for the derivation of the Boltzmann weights of such solvable height models.Comment: 18p

A classifying algebra for boundary conditions

We introduce a finite-dimensional algebra that controls the possible boundary conditions of a conformal field theory. For theories that are obtained by modding out a Z_2 symmetry (corresponding to a so-called D_odd-type, or half-integer spin simple current, modular invariant), this classifying algebra contains the fusion algebra of the untwisted sector as a subalgebra. Proper treatment of fields in the twisted sector, so-called fixed points, leads to structures that are intriguingly close to the ones implied by modular invariance for conformal field theories on closed orientable surfaces.Comment: 12 pages, LaTe