## SEKI Report

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#### Dokumenttyp

- Preprint (85)
- Wissenschaftlicher Artikel (6)
- Bericht (1)

#### Schlagworte

- Knowledge acquisition (3)
- resolution (3)
- Case-Based Reasoning (2)
- Deduction (2)
- HOT (2)
- MOLTKE-Projekt (2)
- Term rewriting systems (2)
- Wissensakquisition (2)
- analogy (2)
- combined systems with sha (2)

98,1

Top-down and bottom-up theorem proving approaches have each specific ad-vantages and disadvantages. Bottom-up provers profit from strong redundancycontrol and suffer from the lack of goal-orientation, whereas top-down provers aregoal-oriented but have weak calculi when their proof lengths are considered. Inorder to integrate both approaches our method is to achieve cooperation betweena top-down and a bottom-up prover: The top-down prover generates subgoalclauses, then they are processed by a bottom-up prover. We discuss theoreticaspects of this methodology and we introduce techniques for a relevancy-basedfiltering of generated subgoal clauses. Experiments with a model eliminationand a superposition-based prover reveal the high potential of our cooperation approach.The author was supported by the Deutsche Forschungsgemeinschaft (DFG).

98,2

We examine an approach for demand-driven cooperative theorem proving.We briefly point out the problems arising from the use of common success-driven cooperation methods, and we propose the application of our approachof requirement-based cooperative theorem proving. This approach allows for abetter orientation on current needs of provers in comparison with conventional co-operation concepts. We introduce an abstract framework for requirement-basedcooperation and describe two instantiations of it: Requirement-based exchangeof facts and sub-problem division and transfer via requests. Finally, we reporton experimental studies conducted in the areas superposition and unfailing com-pletion.The author was supported by the Deutsche Forschungsgemeinschaft (DFG).

98,3

HOT is an automated higher-order theorem prover based on HTE, an extensional higher-order tableaux calculus (Kohlhase 95). The first part of the paper introduces a variant of the calculus which closely corresponds to the proof procedure implemented in HOT. The second part discusses HOT's design that can be characterized as a concurrent Blackboard architecture. We show the usefulness of the implementation by including benchmark results for over one hundred solved problems from logic and set theory.

91,14

Orderings on polynomial interpretations of operators represent a powerful technique for proving thetermination of rewriting systems. One of the main problems of polynomial orderings concerns thechoice of the right interpretation for a given rewriting system. It is very difficult to develop techniquesfor solving this problem. Here, we present three new heuristic approaches: (i) guidelines for dealingwith special classes of rewriting systems, (ii) an algorithm for choosing appropriate special polynomialsas well as (iii) an extension of the original polynomial ordering which supports the generation ofsuitable interpretations. All these heuristics will be applied to examples in order to illustrate theirpractical relevance.

92,18

The background of this paper is the area of case-based reasoning. This is a reasoning technique where one tries to use the solution of some problem which has been solved earlier in order to obta in a solution of a given problem. As example of types of problems where this kind of reasoning occurs very often is the diagnosis of diseases or faults in technical systems. In abstract terms this reduces to a classification task. A difficulty arises when one has not just one solved problem but when there are very many. These are called "cases" and they are stored in the case-base. Then one has to select an appropriate case which means to find one which is "similar" to the actual problem. The notion of similarity has raised much interest in this context. We will first introduce a mathematical framework and define some basic concepts. Then we will study some abstract phenomena in this area and finally present some methods developed and realized in a system at the University of Kaiserslautern.

97,3

We present a cooperation concept for automated theorem provers that isbased on a periodical interchange of selected results between several incarnationsof a prover. These incarnations differ from each other in the search heuristic theyemploy for guiding the search of the prover. Depending on the strengths' andweaknesses of these heuristics different knowledge and different communicationstructures are used for selecting the results to interchange.Our concept is easy to implement and can easily be integrated into alreadyexisting theorem provers. Moreover, the resulting cooperation allows the dis-tributed system to find proofs much faster than single heuristics working alone.We substantiate these claims by two case studies: experiments with the DiCoDesystem that is based on the condensed detachment rule and experiments with theSPASS system, a prover for first order logic with equality based on the super-position calculus. Both case studies show the improvements by our cooperationconcept.

97,5

This paper presents a new kind of abstraction, which has been developed for the purpose of proofplanning. The basic idea of this paper is to abstract a given theorem and to find an abstractproof of it. Once an abstract proof has been found, this proof has to be refined to a real proofof the original theorem. We present a goal oriented abstraction for the purpose of equality proofplanning, which is parameterized by common parts of the left- and right-hand sides of the givenequality. Therefore, this abstraction technique provides an abstract equality problem which ismore adequate than those generated by the abstractions known so far. The presented abstractionalso supports the heuristic search process based on the difference reduction paradigm. We give aformal definition of the abstract space including the objects and their manipulation. Furthermore,we prove some properties in order to allow an efficient implementation of the presented abstraction.

97,6

This report is a first attempt of formalizing the diagonalization proof technique.We give a strategy how to systematically construct diagonalization proofs: (i) findingan indexing relation, (ii) constructing a diagonal element, and (iii) making the implicitcontradiction of the diagonal element explicit. We suggest a declarative representationof the strategy and describe how it can be realized in a proof planning environment.

97,7

We examine different possibilities of coupling saturation-based theorem pro-vers by exchanging positive/negative information. We discuss which positive ornegative information is well-suited for cooperative theorem proving and show inan abstract way how this information can be used. Based on this study, we in-troduce a basic model for cooperative theorem proving. We present theoreticalresults regarding the exchange of positive/negative information as well as practi-cal methods and heuristics that allow for a gain of efficiency in comparison withsequential provers. Finally, we report on experimental studies conducted in theareas condensed detachment, unfailing completion, and superposition.The author was supported by the Deutsche Forschungsgemeinschaft (DFG).

91,7

Case-based knowledge acquisition, learning and problem solving for diagnostic real world tasks
(1999)

Within this paper we focus on both the solution of real, complex problems using expert system technology and the acquisition of the necessary knowledge from a case-based reasoning point of view. The development of systems which can be applied to real world problems has to meet certain requirements. E.g., all available information sources have to be identified and utilized. Normally, this involves different types of knowledge for which several knowledge representation schemes are needed, because no scheme is equally natural for all sources. Facing empirical knowledge it is important to complement the use of manually compiled, statistic and otherwise induced knowledge by the exploitation of the intuitive understandability of case-based mechanisms. Thus, an integration of case-based and alternative knowledge acquisition and problem solving mechanisms is necessary. For this, the basis is to define the "role" which case-based inference can "play" within a knowledge acquisition workbench. We will discuss a concrete casebased architecture, which has been applied to technical diagnosis problems, and its integration into a knowledge acquisition workbench which includes compiled knowledge and explicit deep models, additionally.