## SEKI Report

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#### Keywords

- Knowledge acquisition (3)
- Deduction (2)
- HOT (2)
- MOLTKE-Projekt (2)
- Term rewriting systems (2)
- Wissensakquisition (2)
- analogy (2)
- combined systems with sha (2)
- confluence (2)
- disjoint union (2)

- 89,9
- Knowledge acquisition in the domain of CNC machining centers: the Moltke approach (1999)
- MOLTKE is a research project dealing with a complex technical application. After describing the domain of CNCmachining centers and the applied KA methods, we summarize the concrete KA problems which we have to handle. Then we describe a KA mechanism which supports an engineer in developing a diagnosis system. In chapter 6 weintroduce learning techniques operating on diagnostic cases and domain knowledge for improving the diagnostic procedure of MOLTKE. In the last section of this chapter we outline some essential aspects of organizationalknowledge which is heavily applied by engineers for analysing such technical systems (Qualitative Engineering). Finally we give a short overview of the actual state of realization and our future plans.

- 90,21
- Multiple knowledge acquisition strategies in MOLTKE (1999)
- In this paper we will present a design model (in the sense of KADS) for the domain of technical diagnosis. Based on this we will describe the fully implemented expert system shell MOLTKE 3.0, which integrates common knowledge acquisition methods with techniques developed in the fields of Model-Based Diagnosis and Machine Learning, especially Case-Based Reasoning.

- 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.

- 97,5
- An Abstraction for Proof Planning: The S-Abstraction (1999)
- 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.

- 98,5
- Semantical Investigation of Simultaneous Skolemization for First-Order Sequent Calculus (1998)
- Simultaneous quantifier elimination in sequent calculus is an improvement over the well-known skolemization. It allows a lazy handling of instantiations as well as of the order of certain reductions. We prove the soundness of a sequent calculus which incorporates a rule for simultaneous quantifier elimination. The proof is performed by semantical arguments and provides some insights into the dependencies between various formulas in a sequent.

- 93,6
- Distributing equational theorem proving (1999)
- In this paper we show that distributing the theorem proving task to several experts is a promising idea. We describe the team work method which allows the experts to compete for a while and then to cooperate. In the cooperation phase the best results derived in the competition phase are collected and the less important results are forgotten. We describe some useful experts and explain in detail how they work together. We establish fairness criteria and so prove the distributed system to be both, complete and correct. We have implementedour system and show by non-trivial examples that drastical time speed-ups are possible for a cooperating team of experts compared to the time needed by the best expert in the team.

- 93,11
- Informal Proceedings of the Annual Meeting of "GI-Fachgruppe Deduktionssysteme" (1993)
- This report contains a collection of abstracts for talks given at the "Deduktionstreffen" held at Kaiserslautern, October 6 to 8, 1993. The topics of the talks range from theoretical aspects of term rewriting systems and higher order resolution to descriptions of practical proof systems in various applications. They are grouped together according the following classification: Distribution and Combination of Theorem Provers, Termination, Completion, Functional Programs, Inductive Theorem Proving, Automatic Theorem Proving, Proof Presentation. The Deduktionstreffen is the annual meeting of the Fachgruppe Deduktionssysteme in the Gesellschaft für Informatik (GI), the German association for computer science.

- 93,3
- Canonical Conditional Rewrite Systems Containing Extra Variables (1993)
- We study deterministic conditional rewrite systems, i.e. conditional rewrite systemswhere the extra variables are not totally free but 'input bounded'. If such a systemR is quasi-reductive then !R is decidable and terminating. We develop a critical paircriterion to prove confluence if R is quasi-reductive and strongly deterministic. In thiscase we prove that R is logical, i.e./!R==R holds. We apply our results to proveHorn clause programs to be uniquely terminating.This research was supported by the Deutsche Forschungsgemeinschaft, SFB 314, Project D4

- 95,3
- A Reduction Ordering for Higher-Order Terms (1999)
- We investigate one of the classical problems of the theory ofterm rewriting, namely termination. We present an ordering for compar-ing higher-order terms that can be utilized for testing termination anddecreasingness of higher-order conditional term rewriting systems. Theordering relies on a first-order interpretation of higher-order terms anda suitable extension of the RPO.

- 95,14
- Theorem Proving in Hierarchical Clausal Specifications (1999)
- In this paper we are interested in an algebraic specification language that (1) allowsfor sufficient expessiveness, (2) admits a well-defined semantics, and (3) allows for formalproofs. To that end we study clausal specifications over built-in algebras. To keep thingssimple, we consider built-in algebras only that are given as the initial model of a Hornclause specification. On top of this Horn clause specification new operators are (partially)defined by positive/negative conditional equations. In the first part of the paper wedefine three types of semantics for such a hierarchical specification: model-theoretic,operational, and rewrite-based semantics. We show that all these semantics coincide,provided some restrictions are met. We associate a distinguished algebra A spec to ahierachical specification spec. This algebra is initial in the class of all models of spec.In the second part of the paper we study how to prove a theorem (a clause) valid in thedistinguished algebra A spec . We first present an abstract framework for inductive theoremprovers. Then we instantiate this framework for proving inductive validity. Finally wegive some examples to show how concrete proofs are carried out.This report was supported by the Deutsche Forschungsgemeinschaft, SFB 314 (D4-Projekt)