## Fachbereich Informatik

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- AG-RESY (1)
- Automatic Theorem Provi (1)
- Case-Based Reasoning (1)
- CoMo-Kit (1)
- Completion (1)
- Distribution and Combination of Theorem Provers (1)
- Functional Programs (1)
- Inductive Theorem Proving (1)
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SPIN-NFDS Learning and Preset Knowledge for Surface Fusion - A Neural Fuzzy Decision System -
(1993)

In this paper we present an interpreter which allows to support the validation of conceptual models in early stages of the development. We compare hypermedia and expert system approaches to knowledge processing and show how an integrated approach eases the creation of expert systems. Our knowledge engineering tool CoMo-Kit allows a "smooth" transition from initial protocols via a semi-formal specification based on a typed hypertext up to an running expert system. The interpreter uses the intermediate hypertext representation for the interactive solution of problems. Thereby, tasks are distributed to agents via an local area network. This means that the specification of an expert system can directly be used to solve real world problems. If there exist formal (operational) specifications for subtasks then these are delegated to computers. Therefore, our approach allows to specify and validate distributed, cooperative systems where some subtasks are solved by humans and other subtasks are solved automatically by computers.

The composition of Bézier curves and tensor product Bézier surfaces, polynomial as well as rational, is applied to exactly and explicitely represent trim curves of tensor product Bézier surfaces. Trimming curves are assumed to be defined as Bézier curves in surface parameter domain. A Bézier spline approximation of lower polynomial degree is built up as weil which is based on the exact trim curve representation in coordinate space.

Shadow-Mapping
(1993)

Most radiosity techniques store radiosities in certain sample points, typically the vertices of polyhedral scenes. As diffuse radiosities are view independent they can be used for an interactive 'walk-through'. This paper presents an algorithm for storing radiosities independent of the representation of the object. A distributed rendering system, which uses this shadow-mapping technique is described. The basic thermophysical definitions, needed to derive a sum formula for a form factor calculation of polygons, are explained.

Four different initialization methods for parallel Branch-and-bound algorithms are described and compared with reference to several criteria. A formal analysis of their idle times and efficiency follows. It indicates that the efficiency of three methods depends on the branching factor of the search tree. Furthermore, the fourth method offers the best efficiency of the overall algorithm when a centralized OPEN set is used. Experimental results by a PRAM simulation support these statements.

We investigate restricted termination and confluence properties of term rewritADing systems, in particular weak termination and innermost termination, and theirinterrelation. New criteria are provided which are sufficient for the equivalenceof innermost / weak termination and uniform termination of term rewriting sysADtems. These criteria provide interesting possibilities to infer completeness, i.e.termination plus confluence, from restricted termination and confluence properADties.Using these basic results we are also able to prove some new results aboutmodular termination of rewriting. In particular, we show that termination ismodular for some classes of innermost terminating and locally confluent termrewriting systems, namely for nonADoverlapping and even for overlay systems. Asan easy consequence this latter result also entails a simplified proof of the factthat completeness is a decomposable property of soADcalled constructor systems.Furthermore we show how to obtain similar results for even more general cases of(nonADdisjoint) combined systems with shared constructors and of certain hierarADchical combinations of systems with constructors. Interestingly, these modularityresults are obtained by means of a proof technique which itself constitutes a modADular approach.

Case-based problem solving can be significantly improved by applying domain knowledge (in opposition to problem solving knowledge), which can be acquired with reasonable effort, to derive explanations of the correctness of a case. Such explanations, constructed on several levels of abstraction, can be employed as the basis for similarity assessment as well as for adaptation by solution refinement. The general approach for explanation-based similarity can be applied to different real world problem solving tasks such as diagnosis and planning in technical areas. This paper presents the general idea as well as the two specific, completely implemented realizations for a diagnosis and a planning task.

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

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.