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#### Faculty / Organisational entity

- Fachbereich Informatik (178) (remove)

We present an inference system for clausal theorem proving w.r.t. various kinds of inductivevalidity in theories specified by constructor-based positive/negative-conditional equations. The reductionrelation defined by such equations has to be (ground) confluent, but need not be terminating. Our con-structor-based approach is well-suited for inductive theorem proving in the presence of partially definedfunctions. The proposed inference system provides explicit induction hypotheses and can be instantiatedwith various wellfounded induction orderings. While emphasizing a well structured clear design of theinference system, our fundamental design goal is user-orientation and practical usefulness rather thantheoretical elegance. The resulting inference system is comprehensive and relatively powerful, but requiresa sophisticated concept of proof guidance, which is not treated in this paper.This research was supported by the Deutsche Forschungsgemeinschaft, SFB 314 (D4-Projekt)

We describe a hybrid architecture supporting planning for machining workpieces. The archi- tecture is built around CAPlan, a partial-order nonlinear planner that represents the plan already generated and allows external control decision made by special purpose programs or by the user. To make planning more efficient, the domain is hierarchically modelled. Based on this hierarchical representation, a case-based control component has been realized that allows incremental acquisition of control knowledge by storing solved problems and reusing them in similar situations.

We describe a hybrid case-based reasoning system supporting process planning for machining workpieces. It integrates specialized domain dependent reasoners, a feature-based CAD system and domain independent planning. The overall architecture is build on top of CAPlan, a partial-order nonlinear planner. To use episodic problem solving knowledge for both optimizing plan execution costs and minimizing search the case-based control component CAPlan/CbC has been realized that allows incremental acquisition and reuse of strategical problem solving experience by storing solved problems as cases and reusing them in similar situations. For effective retrieval of cases CAPlan/CbC combines domain-independent and domain-specific retrieval mechanisms that are based on the hierarchical domain model and problem representation.

While most approaches to similarity assessment are oblivious of knowledge and goals, there is ample evidence that these elements of problem solving play an important role in similarity judgements. This paper is concerned with an approach for integrating assessment of similarity into a framework of problem solving that embodies central notions of problem solving like goals, knowledge and learning.

Contrary to symbolic learning approaches, which represent a learned concept explicitly, case-based approaches describe concepts implicitly by a pair (CB; sim), i.e. by a measure of similarity sim and a set CB of cases. This poses the question if there are any differences concerning the learning power of the two approaches. In this article we will study the relationship between the case base, the measure of similarity, and the target concept of the learning process. To do so, we transform a simple symbolic learning algorithm (the version space algorithm) into an equivalent case- based variant. The achieved results strengthen the hypothesis of the equivalence of the learning power of symbolic and case-based methods and show the interdependency between the measure used by a case-based algorithm and the target concept.

One of the problems of autonomous mobile systems is the continuous tracking of position and orientation. In most cases, this problem is solved by dead reckoning, based on measurement of wheel rotations or step counts and step width. Unfortunately dead reckoning leads to accumulation of drift errors and is very sensitive against slippery. In this paper an algorithm for tracking position and orientation is presented being nearly independent from odometry and its problems with slippery. To achieve this results, a rotating range-finder is used, delivering scans of the environmental structure. The properties of this structure are used to match the scans from different locations in order to find their translational and rotational displacement. For this purpose derivatives of range-finder scans are calculated which can be used to find position and orientation by crosscorrelation.

A map for an autonomous mobile robot (AMR) in an indoor environment for the purpose ofcontinuous position and orientation estimation is discussed. Unlike many other approaches, this map is not based on geometrical primitives like lines and polygons. An algorithm is shown , where the sensordata of a laser range finder can be used to establish this map without a geometrical interpretation of the data. This is done by converting single laser radar scans to statistical representations of the environ-ment, so that a crosscorrelation of an actu al converted scan and this representative results into the actual position and orientation in a global coordinate system. The map itsel f is build of representative scansfor the positions where the AMR has been, so that it is able to find its position and orientation by c omparing the actual scan with a scan stored in the map.

We tested the GYROSTAR ENV-05S. This device is a sensor for angular velocity. There- fore the orientation must be calculated by integration of the angular velocity over time. The devices output is a voltage proportional to the angular velocity and relative to a reference. The test where done to find out under which conditions it is possible to use this device for estimation of orientation.

Problem specifications for classical planners based on a STRIPS-like representation typically consist of an initial situation and a partially defined goal state. Hierarchical planning approaches, e.g., Hierarchical Task Network (HTN) Planning, have not only richer representations for actions but also for the representation of planning problems. The latter are defined by giving an initial state and an initial task network in which the goals can be ordered with respect to each other. However, studies with a specification of the domain of process planning for the plan-space planner CAPlan (an extension of SNLP) have shown that even without hierarchical domain representation typical properties called goal orderings can be identified in this domain that allow more efficient and correct case retrieval strategies for the case-based planner CAPlan/CbC. Motivated by that, this report describes an extension of the classical problem specifications for plan-space planners like SNLP and descendants. These extended problem specifications allow to define a partial order on the planning goals which can interpreted as an order in which the solution plan should achieve the goals. These goal ordering can theoretically and empirically be shown to improve planning performance not only for case-based but also for generative planning. As a second but different way we show how goal orderings can be used to address the control problem of partial order planners. These improvements can be best understood with a refinement of Barrett's and Weld's extended taxonomy of subgoal collections.

Real world planning tasks like manufacturing process planning often don't allow to formalize all of the relevant knowledge. Especially, preferences between alternatives are hard to acquire but have high influence on the efficiency of the planning process and the quality of the solution. We describe the essential features of the CAPlan planning architecture that supports cooperative problem solving to narrow the gap caused by absent preference and control knowledge. The architecture combines an SNLP-like base planner with mechanisms for explict representation and maintenance of dependencies between planning decisions. The flexible control interface of CAPlan allows a combination of autonomous and interactive planning in which a user can participate in the problem solving process. Especially, the rejection of arbitrary decisions by a user or dependency-directed backtracking mechanisms are supported by CAPlan.

Software development is becoming a more and more distributed process, which urgently needs supporting tools in the field of configuration management, software process/w orkflow management, communication and problem tracking. In this paper we present a new distributed software configuration management framework COMAND. It offers high availabilit y through replication and a mechanism to easily change and adapt the project structure to new business needs. To better understand and formally prove some properties of COMAND, we have modeled it in a formal technique based on distributed graph transformations. This formalism provides an intuitive rule-based description technique mainly for the dynamic behavior of the system on an abstract level. We use it here to model the replication subsystem.

An important property and also a crucial point ofa term rewriting system is its termination. Transformation or-derings, developed by Bellegarde & Lescanne strongly based on awork of Bachmair & Dershowitz, represent a general technique forextending orderings. The main characteristics of this method aretwo rewriting relations, one for transforming terms and the otherfor ensuring the well-foundedness of the ordering. The centralproblem of this approach concerns the choice of the two relationssuch that the termination of a given term rewriting system can beproved. In this communication, we present a heuristic-based al-gorithm that partially solves this problem. Furthermore, we showhow to simulate well-known orderings on strings by transformationorderings.

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.

It is generally agreed that one of the most challenging issues facing the case-based reasoning community is that of adaptation. To date the lion's share of CBR research has concentrated on the retrieval of similar cases, and the result is a wide range of quality retrieval techniques. However, retrieval is just the first part of the CBR equation, because once a similar case has been retrieved it must be adapted. Adaptation research is still in its earliest stages, and researchers are still trying to properly understand and formulate the important issues. In this paper I describe a treatment of adaptation in the context of a case-based reasoning system for software design, called Deja Vu. Deja Vu is particularly interesting, not only because it performs automatic adaptation of retrieved cases, but also because it uses a variety of techniques to try and reduce and predict the degree of adaptation necessary.

The multiple-view modeling of a product in a design context is discussed in this paper. We study the existing approaches for multiple-view modeling of a product and we give a brief analysis of them. Then we propose our approach which incorporates the multiple-model approach in STEP standard current works based on a single model. We propose a meta-model inspired by this approach for a multiple-view design environment. Next, we validate this meta-model with a case study. Finally we conclude and give some perspectives of this work. Keywords: product data modeling, multiple-view modeling, product data integration, STEP, functional model.

We present a mathematical knowledge base containing the factual know-ledge of the first of three parts of a textbook on semi-groups and automata,namely "P. Deussen: Halbgruppen und Automaten". Like almost all math-ematical textbooks this textbook is not self-contained, but there are somealgebraic and set-theoretical concepts not being explained. These concepts areadded to the knowledge base. Furthermore there is knowledge about the nat-ural numbers, which is formalized following the first paragraph of "E. Landau:Grundlagen der Analysis".The data base is written in a sorted higher-order logic, a variant of POST ,the working language of the proof development environment OmegaGamma mkrp. We dis-tinguish three different types of knowledge: axioms, definitions, and theorems.Up to now, there are only 2 axioms (natural numbers and cardinality), 149definitions (like that for a semi-group), and 165 theorems. The consistency ofsuch knowledge bases cannot be proved in general, but inconsistencies may beimported only by the axioms. Definitions and theorems should not lead to anyinconsistency since definitions form conservative extensions and theorems areproved to be consequences.

The paper shows that characterizing the causal relationship between significant events is an important but non-trivial aspect for understanding the behavior of distributed programs. An introduction to the notion of causality and its relation to logical time is given; some fundamental results concerning the characterization of causality are pre- sented. Recent work on the detection of causal relationships in distributed computations is surveyed. The relative merits and limitations of the different approaches are discussed, and their general feasibility is analyzed.

We first show that ground term-rewriting systems can be completed in apolynomial number of rewriting steps, if the appropriate data structure for termsis used. We then apply this result to study the lengths of critical pair proofs innon-ground systems, and obtain bounds on the lengths of critical pair proofsin the non-ground case. We show how these bounds depend on the types ofinference steps that are allowed in the proofs.

We will answer a question posed in [DJK91], and will show that Huet's completion algorithm [Hu81] becomes incomplete, i.e. it may generate a term rewriting system that is not confluent, if it is modified in a way that the reduction ordering used for completion can be changed during completion provided that the new ordering is compatible with the actual rules. In particular, we will show that this problem may not only arise if the modified completion algorithm does not terminate: Even if the algorithm terminates without failure, the generated finite noetherian term rewriting system may be non-confluent. Most existing implementations of the Knuth-Bendix algorithm provide the user with help in choosing a reduction ordering: If an unorientable equation is encountered, then the user has many options, especially, the one to orient the equation manually. The integration of this feature is based on the widespread assumption that, if equations are oriented by hand during completion and the completion process terminates with success, then the generated finite system is a maybe non terminating but locally confluent system (see e.g. [KZ89]). Our examples will show that this assumption is not true.