## 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)

- 92,18
- Classification and Learning of Similarity Measures (1999)
- 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.

- 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.

- 89,12
- Some Aspects of Analogy in Mathematical Reasoning (1999)
- An important research problem is the incorporation of "declarative" knowledge into an automated theorem prover that can be utilized in the search for a proof. An interesting pro-posal in this direction is Alan Bundy's approach of using explicit proof plans that encapsulatethe general form of a proof and is instantiated into a particular proof for the case at hand. Wegive some examples that show how a "declarative" highlevel description of a proof can be usedto find proofs of apparently "similiar" theorems by analogy. This "analogical" information isused to select the appropriate axioms from the database so that the theorem can be proved.This information is also used to adjust some options of a resolution theorem prover. In orderto get a powerful tool it is necessary to develop an epistemologically appropriate language todescribe proofs, for which a large set of examples should be used as a testbed. We presentsome ideas in this direction.

- 90,19
- How to Prove Higher Order Theorems in First Order Logic (1999)
- In this paper we are interested in using a firstorder theorem prover to prove theorems thatare formulated in some higher order logic. Tothis end we present translations of higher or-der logics into first order logic with flat sortsand equality and give a sufficient criterion forthe soundness of these translations. In addi-tion translations are introduced that are soundand complete with respect to L. Henkin's gen-eral model semantics. Our higher order logicsare based on a restricted type structure in thesense of A. Church, they have typed functionsymbols and predicate symbols, but no sorts.

- 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.

- 91,1
- Similarity, uncertainty and case-based reasoning in PATDEX (1999)
- Patdex is an expert system which carries out case-based reasoning for the fault diagnosis of complex machines. It is integrated in the Moltke workbench for technical diagnosis, which was developed at the university of Kaiserslautern over the past years, Moltke contains other parts as well, in particular a model-based approach; in Patdex where essentially the heuristic features are located. The use of cases also plays an important role for knowledge acquisition. In this paper we describe Patdex from a principal point of view and embed its main concepts into a theoretical framework.

- 91,6
- Useful Properties of a Frame-Based Representation of Mathematical Knowledge (1999)
- To prove difficult theorems in a mathematical field requires substantial know-ledge of that field. In this paper a frame-based knowledge representation formalismis presented, which supports a conceptual representation and to a large extent guar-antees the consistency of the built-up knowledge bases. We define a semantics ofthe representation by giving a translation into the underlaying logic.

- 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.

- 91,14
- Termination Proofs of Rewriting Systems (1999)
- 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.

- 91,17
- A Guide to UNICOM, an Inductive Theorem Prover Based on Rewriting and Completion Techniques (1999)
- We provide an overview of UNICOM, an inductive theorem prover for equational logic which isbased on refined rewriting and completion techniques. The architecture of the system as well as itsfunctionality are described. Moreover, an insight into the most important aspects of the internalproof process is provided. This knowledge about how the central inductive proof componentof the system essentially works is crucial for human users who want to solve non-trivial prooftasks with UNICOM and thoroughly analyse potential failures. The presentation is focussedon practical aspects of understanding and using UNICOM. A brief but complete description ofthe command interface, an installation guide, an example session, a detailed extended exampleillustrating various special features and a collection of successfully handled examples are alsoincluded.