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We have developed a middleware framework for workgroup environments that can support distributed software development and a variety of other application domains requiring document management and change management for distributed projects. The framework enables hypermedia-based integration of arbitrary legacy and new information resources available via a range of protocols, not necessarily known in advance to us as the general framework developers nor even to the environment instance designers. The repositories in which such information resides may be dispersed across the Internet and/or an organizational intranet. The framework also permits a range of client models for user and tool interaction, and applies an extensible suite of collaboration services, including but not limited to multi-participant workflow and coordination, to their information retrievals and updates. That is, the framework is interposed between clients, services and repositories - thus "middleware". We explain how our framework makes it easy to realize a comprehensive collection of workgroup and workflow features we culled from a requirements survey conducted by NASA.

In recent years several computational systems and techniques fortheorem proving by analogy have been developed. The obvious prac-tical question, however, as to whether and when to use analogy hasbeen neglected badly in these developments. This paper addresses thisquestion, identifies situations where analogy is useful, and discussesthe merits of theorem proving by analogy in these situations. Theresults can be generalized to other domains.

Die Verfahren der Induktiven Logischen Programmierung (ILP) [Mug93] haben die Aufgabe, aus einer Menge von positiven Beispielen E+, einer Menge von negativen Beispielen E und dem Hintergrundwissen B ein logisches Programm P zu lernen, das aus einer Menge von definiten Klauseln C : l0 l1, : : : ,ln besteht. Da der Hypothesenraum für Hornlogik unendlich ist, schränken viele Verfahren die Hypothesensprache auf eine endliche ein. Auch wird oft versucht, die Hypothesensprache so einzuschränken, dass nur Programme gelernt werden können, für die die Konsistenz entscheidbar ist. Eine andere Motivation, die Hypothesensprache zu beschränken, ist, dass das Wissen über das Zielprogramm, das schon vorhanden ist, ausgenutzt werden soll. So sind für bestimmte Anwendungen funktionsfreie Hypothesenklauseln ausreichend, oder es ist bekannt, dass das Zielprogramm funktional ist.

Rules are an important knowledge representation formalism in constructive problem solving. On the other hand, object orientation is an essential key technology for maintaining large knowledge bases as well as software applications. Trying to take advantage of the benefits of both paradigms, we integrated Prolog and Smalltalk to build a common base architecture for problem solving. This approach has proven to be useful in the development of two knowledge-based systems for planning and configuration design (CAPlan and Idax). Both applications use Prolog as an efficient computational source for the evaluation of knowledge represented as rules.

We present the adaptation process in a CBR application for decision support in the domain of industrial supervision. Our approach uses explanations to approximate relations between a problem description and its solution, and the adaptation process is guided by these explanations (a more detailed presentation has been done in [4]).

The paper explores the role of artificial intelligence techniques in the development of an enhanced software project management tool, which takes account of the emerging requirement for support systems to address the increasing trend towards distributed multi-platform software development projects. In addressing these aims this research devised a novel architecture and framework for use as the basis of an intelligent assistance system for use by software project managers, in the planning and managing of a software project. This paper also describes the construction of a prototype system to implement this architecture and the results of a series of user trials on this prototype system.

Requirements engineering (RE) is a necessary part of the software development process, as it helps customers and designers identify necessary system requirements. If these stakeholders are separated by distance, we argue that a distributed groupware environment supporting a cooperative requirements engineering process must be supplied that allows them to negotiate software requirements. Such a groupware environment must support aspects of joint work relevant to requirements negotiation: synchronous and asynchronous collaboration, telepresence, and teledata. It should also add explicit support for a structured RE process, which includes the team's ability to discuss multiple perspectives during requirements acquisition and traceability. We chose the TeamWave software platform as an environment that supplied the basic collaboration capabilities, and tailored it to fit the specific needs of RE.

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.

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.

This paper addresses two modi of analogical reasoning. Thefirst modus is based on the explicit representation of the justificationfor the analogical inference. The second modus is based on the repre-sentation of typical instances by concept structures. The two kinds ofanalogical inferences rely on different forms of relevance knowledge thatcause non-monotonicity. While the uncertainty and non-monotonicity ofanalogical inferences is not questioned, a semantic characterization ofanalogical reasoning has not been given yet. We introduce a minimalmodel semantics for analogical inference with typical instances.

In order to improve the quality of software systems and to set up a more effective process for their development, many attempts have been made in the field of software engineering. Reuse of existing knowledge is seen as a promising way to solve the outstanding problems in this field. In previous work we have integrated the design pattern concept with the formal design language SDL, resulting in a certain kind of pattern formalization. For the domain of communication systems we have also developed a pool of SDL patterns with an accompanying process model for pattern application. In this paper we present an extension that combines the SDL pattern approach with the experience base concept. This extension supports a systematic method for empirical evaluation and continuous improvement of the SDL pattern approach. Thereby the experience base serves as a repository necessary for effective reuse of the captured knowledge. A comprehensive usage scenario is described which shows the advantages of the combined approach. To demonstrate its feasibility, first results of a research case study are given.

This paper focuses on the issues involved when multiple mobile agents interact in multiagent systems. The application is an intelligent agent market place, where buyer and seller agents cooperate and compete to process sales transactions for their owners. The market place manager acts as afacilitator by giving necessary information to agents and managing communication between agents, and also as a mediator by proposing solutions to agents or stopping them to get into infinite loops bargaining back and forth.The buyer and seller agents range from using hardcoded logic to rule-based inferencing in their negotiation strategies. However these agents must support some communication skills using KQML or FIPA-ACL.So in contrast with other approaches to multiagent negotiation, we introduce an explicit mediator (market place manager) into the negotiation, and we propose a negotiation strategy based on dependence theory [1] implemented by our best buyers and best sellers.

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)

This paper shows how a new approach to theorem provingby analogy is applicable to real maths problems. This approach worksat the level of proof-plans and employs reformulation that goes beyondsymbol mapping. The Heine-Borel theorem is a widely known result inmathematics. It is usually stated in R 1 and similar versions are also truein R 2 , in topology, and metric spaces. Its analogical transfer was proposedas a challenge example and could not be solved by previous approachesto theorem proving by analogy. We use a proof-plan of the Heine-Boreltheorem in R 1 as a guide in automatically producing a proof-plan of theHeine-Borel theorem in R 2 by analogy-driven proof-plan construction.

Most automated theorem provers suffer from the problem that theycan produce proofs only in formalisms difficult to understand even forexperienced mathematicians. Efforts have been made to transformsuch machine generated proofs into natural deduction (ND) proofs.Although the single steps are now easy to understand, the entire proofis usually at a low level of abstraction, containing too many tedioussteps. Therefore, it is not adequate as input to natural language gen-eration systems.To overcome these problems, we propose a new intermediate rep-resentation, called ND style proofs at the assertion level . After illus-trating the notion intuitively, we show that the assertion level stepscan be justified by domain-specific inference rules, and that these rulescan be represented compactly in a tree structure. Finally, we describea procedure which substantially shortens ND proofs by abstractingthem to the assertion level, and report our experience with furthertransformation into natural language.

We present an empirical study of mathematical proofs by diagonalization, the aim istheir mechanization based on proof planning techniques. We show that these proofs canbe constructed according to a strategy that (i) finds an indexing relation, (ii) constructsa diagonal element, and (iii) makes the implicit contradiction of the diagonal elementexplicit. Moreover we suggest how diagonal elements can be represented.

In this report we present a case study of employing goal-oriented heuristics whenproving equational theorems with the (unfailing) Knut-Bendix completion proce-dure. The theorems are taken from the domain of lattice ordered groups. It will bedemonstrated that goal-oriented (heuristic) criteria for selecting the next critical paircan in many cases significantly reduce the search effort and hence increase per-formance of the proving system considerably. The heuristic, goalADoriented criteriaare on the one hand based on so-called "measures" measuring occurrences andnesting of function symbols, and on the other hand based on matching subterms.We also deal with the property of goal-oriented heuristics to be particularly helpfulin certain stages of a proof. This fact can be addressed by using them in a frame-work for distributed (equational) theorem proving, namely the "teamwork-method".

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.

We transform a user-friendly formulation of aproblem to a machine-friendly one exploiting the variabilityof first-order logic to express facts. The usefulness of tacticsto improve the presentation is shown with several examples.In particular it is shown how tactical and resolution theoremproving can be combined.

Verfahren des Maschinellen Lernens haben heute eine Reife erreicht, die zu ersten erfolgreichen industriellen Anwendungen geführt hat. In der Prozessdiagnose und -steuerung ermöglichen Lernverfahren die Klassifikation und Bewertung von Betriebszuständen, d.h. eine Grobmodellierung eines Prozesses, wenn dieser nicht oder nur teilweise mathematisch beschreibbar ist. Ausserdem gestatten Lernverfahren die automatische Generierung von Klassifizierungsprozeduren, die deterministisch abgearbeitet werden und daher für die Belange der Echtzeitdiagnose und -steuerung u.U. zeiteffektiver als Inferenzmechanismen auf logischer bzw. Produktionsregelbasis sind, da letztere immer mit zeitaufwendigen Suchprozessen verbunden sind.

A growing share of all software development project work is being done by geographically distributed teams. To satisfy shorter product design cycles, expert team members for a development project may need to be r ecruited globally. Yet to avoid extensive travelling or r eplacement costs, distributed project work is preferred. Current-generation software engineering tools and ass ociated systems, processes, and methods were for the most part developed to be used within a single enterprise. Major innovations have lately been introduced to enable groupware applications on the Internet to support global collaboration. However, their deployment for distributed software projects requires further research. In partic ular, groupware methods must seamlessly be integrated with project and product management systems to make them attractive for industry. In this position paper we outline the major challenges concerning distributed (virtual) software projects. Based on our experiences with software process modeling and enactment environments, we then propose approaches to solve those challenges.

A non-trivial real-time requirement obeying a pattern that can be foundin various instantiations in the application domain building automation, and which is therefore called generic, is investigated in detail. Starting point is a description of a real-time problem in natural language augmented by a diagram, in a style often found in requirements documents. Step by step, this description is made more precise and finally transformed into a surprisingly concise formal specification, written in real-time temporal logic with customized operators. Wereason why this formal specification precisely captures the original description- as far as this is feasible due to the lack of precision of natural language.

The development of software products has become a highly cooperative and distributed activity involving working groups at geographically distinct places. These groups show an increasing mobility and a very flexible organizational structure. Process methodology and technology have to take such evolutions into account. A possible direction for the emergence of new process technology and methodology is to take benefit from recent advances within multiagent systems engineering : innovative methodologies for adaptable and autonomous architectures; they exhibit interesting features to support distributed software processes.

SmallSync, an internet event synchronizer, is intended to provide a monitoring and visualization methodology for permitting simultaneous analysis and control of multiple remote processes on the web. The current SmallSync includes: (1) a mechanism to multicast web window-based commands, message passing events and process execution events among processes; (2) an event synchronizer to allow concurrent execution of some functions on multiple machines; (3) a means to report when these events cause errors in the processes; and (4) ad hoc visualization of process states using existing visualizers.

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.

Reusing Proofs
(1999)

We develop a learning component for a theorem prover designed for verifying statements by mathematical induction. If the prover has found a proof, it is analyzed yielding a so-called catch. The catch provides the features of the proof which are relevant for reusing it in subsequent verification tasks and may also suggest useful lemmata. Proof analysis techniques for computing the catch are presented. A catch is generalized in a certain sense for increasing the reusability of proofs. We discuss problems arising when learning from proofs and illustrate our method by several examples.

This paper describes a declarative approach forencoding the plan operators in proof planning,the so-called methods. The notion of methodevolves from the much studied concept of a tac-tic and was first used by A. Bundy. Signific-ant deductive power has been achieved withthe planning approach towards automated de-duction; however, the procedural character ofthe tactic part of methods hinders mechanicalmodification. Although the strength of a proofplanning system largely depends on powerfulgeneral procedures which solve a large class ofproblems, mechanical or even automated modi-fication of methods is necessary, since methodsdesigned for a specific type of problems willnever be general enough. After introducing thegeneral framework, we exemplify the mechan-ical modification of methods via a particularmeta-method which modifies methods by trans-forming connectives to quantifiers.

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).

Der Wissenserwerb erschwert bisher häufig den Einsatz wissensbasierter Systeme der Arbeitsplanerstellung in der industriellen Praxis. Die meisten Anwendungen gestatten nur das Erfassen und Editieren des durch aufwendige Erhebung, Systematisierung und Formulierung gewonnenen fachspezifischen Planungswissens. Im Rahmen eines DFG-Projektes soll die Anwendbarkeit bekannter maschineller Lernverfahren auf technologische Reihenfolge- und Zuordnungsprobleme im Rahmen der generierenden Arbeitsplanerstellung von Teilefertigungsprozessen im Maschinenbau nachgewiesen werden. Dazu wird ein Prototyp mit Hilfe eines verfügbaren Softwarewerkzeuges entwickelt, der das maschinelle Lernen aus vorgegebenen Beispielen ermöglichen und mit einem existierenden Prototypen der wissensbasierten Arbeistplanung kommunizieren soll. Der folgende Beitrag gibt einen Überblick über das mit Lernverfahren zu behandelnde Planungswissen und stellt mögliche Repräsentationsmöglichkeiten des Wissens zur Diskussion.

Emerging technologies such as the Internet, the World Wide Web, JavaTM technology, and software components, are changing the software business. Activities that have in the past been constrained by the need for intense information management increasingly involve cooperating organizations. Information management tools and techniques do not scale well in the face of this organizational complexity. An informal approach to information sharing, based largely on manual copying of information, cannot meet the demands of the task as size and complexity increase. Formal approaches to sharing information are based on groupware tools, but cooperating organizations do not always enjoy the trust or commonality of sophisticated infrastructure, methods, and skills that this approach requires. Bridging the gap requires a simple, loosely coupled, highly flexible strategy for information sharing. Extensive information relevant to different parts of the software life cycle should be interconnected in a simple, easily described way; such connections should permit selective information sharing by a variety of tools and in a variety of collaboration modes that vary in the amount of organizational coupling they require.

A lot of the human ability to prove hard mathematical theorems can be ascribedto a problem-specific problem solving know-how. Such knowledge is intrinsicallyincomplete. In order to prove related problems human mathematicians, however,can go beyond the acquired knowledge by adapting their know-how to new relatedproblems. These two aspects, having rich experience and extending it by need, can besimulated in a proof planning framework: the problem-specific reasoning knowledge isrepresented in form of declarative planning operators, called methods; since these aredeclarative, they can be mechanically adapted to new situations by so-called meta-methods. In this contribution we apply this framework to two prominent proofs intheorem proving, first, we present methods for proving the ground completeness ofbinary resolution, which essentially correspond to key lemmata, and then, we showhow these methods can be reused for the proof of the ground completeness of lockresolution.

This paper addresses analogy-driven auto-mated theorem proving that employs a sourceproof-plan to guide the search for a proof-planof the target problem. The approach presen-ted uses reformulations that go beyond symbolmappings and that incorporate frequently usedre-representations and abstractions. Severalrealistic math examples were successfully pro-cessed by our analogy-driven proof-plan con-struction. One challenge example, a Heine-Borel theorem, is discussed here. For this ex-ample the reformulaitons are shown step bystep and the modifying actions are demon-strated.

This paper outlines an implemented system called PROVERB that explains machine -found natural deduction proofs in natural language. Different from earlier works, we pursue a reconstructive approach. Based on the observation that natural deduction proofs are at a too low level of abstraction compared with proofs found in mathematical textbooks, we define first the concept of so-called assertion level inference rules. Derivations justified by these rules can intuitively be understood as the application of a definition or a theorem. Then an algorithm is introduced that abstracts machine-found ND proofs using the assertion level inference rules. Abstracted proofs are then verbalized into natural language by a presentation module. The most significant feature of the presentation module is that it combines standard hierarchical text planning and techniques that locally organize argumentative texts based on the derivation relation under the guidance of a focus mechanism. The behavior of the system is demonstrated with the help of a concrete example throughout the paper.

This paper outlines the linguistic part of an implemented system namedPROVERB[3] that transforms, abstracts, and verbalizes machine-found proofs innatural language. It aims to illustrate, that state-of-the-art techniques of natural language processing are necessary to produce coherent texts that resemble those found in typical mathematical textbooks, in contrast to the belief that mathematical texts are only schematic and mechanical.The verbalization module consists of a content planner, a sentence planner, and a syntactic generator. Intuitively speaking, the content planner first decides the order in which proof steps should be conveyed. It also some messages to highlight global proof structures. Subsequently, thesentence planner combines and rearranges linguistic resources associated with messages produced by the content planner in order to produce connected text. The syntactic generat or finally produces the surface text.

This paper describes the linguistic part of a system called PROVERB, which transforms, abstracts,and verbalizes machine-found proofs into formatedtexts. Linguistically, the architecture of PROVERB follows most application oriented systems, and is a pipelined control of three components. Its macroplanner linearizes a proof and plans mediating communicative acts by employing a combination of hierarchical planning and focus-guided navigation. The microplanner then maps communicative acts and domain concepts into linguistic resources, paraphrases and aggregates such resources to producethe final Text Structure. A Text Structure contains all necessary syntactic information, and can be executed by our realizer into grammatical sentences. The system works fully automatically and performs particularly well for textbook size examples.

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.

Proof planning is an alternative methodology to classical automated theorem prov-ing based on exhausitve search that was first introduced by Bundy [8]. The goal ofthis paper is to extend the current realm of proof planning to cope with genuinelymathematical problems such as the well-known limit theorems first investigated for au-tomated theorem proving by Bledsoe. The report presents a general methodology andcontains ideas that are new for proof planning and theorem proving, most importantlyideas for search control and for the integration of domain knowledge into a general proofplanning framework. We extend proof planning by employing explicit control-rules andsupermethods. We combine proof planning with constraint solving. Experiments showthe influence of these mechanisms on the performance of a proof planner. For instance,the proofs of LIM+ and LIM* have been automatically proof planned in the extendedproof planner OMEGA.In a general proof planning framework we rationally reconstruct the proofs of limittheorems for real numbers (IR) that were first computed by the special-purpose programreported in [6]. Compared with this program, the rational reconstruction has severaladvantages: It relies on a general-purpose problem solver; it provides high-level, hi-erarchical representations of proofs that can be expanded to checkable ND-proofs; itemploys declarative contol knowledge that is modularly organized.

This paper outlines an implemented system named PROVERBthat transforms and abstracts machine-found proofs to natural deduction style proofs at an adequate level of abstraction and then verbalizesthem in natural language. The abstracted proofs, originally employedonly as an intermediate representation, also prove to be useful for proofplanning and proving by analogy.

Planverfahren
(1999)

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.

This paper presents a new way to use planning in automated theorem provingby means of distribution. To overcome the problem that often subtasks fora proof problem can not be detected a priori (which prevents the use of theknown planning and distribution techniques) we use a team of experts that workindependently with different heuristics on the problem. After a certain amount oftime referees judge their results using the impact of the results on the behaviourof the expert and a supervisor combines the selected results to a new startingpoint.This supervisor also selects the experts that can work on the problem inthe next round. This selection is a reactive planning task. We outline whichinformation the supervisor can use to fulfill this task and how this informationis processed to result in a plan or to revise a plan. We also show that the useof planning for the assignment of experts to the team allows the system to solvemany different examples in an acceptable time with the same start configurationand without any consultation of the user.Plans are always subject to changeShin'a'in proverb

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.

Abstraction is one of the most promising approaches to improve the performance of problem solvers. Abstraction by dropping sentences of a domain description - as used in most hierarchical planners - is known to be very representation dependent. To overcome these drawbacks, we propose a more general view of abstraction involving the change of representation language. We have developed a new abstraction methodology and a related sound and complete learning algorithm that allows the complete change of representation language of planning cases from concrete to abstract.

Due to the large variety of modern applications and evolving network technologies, a small number of general-purpose protocol stacks will no longer be sufficient. Rather, customization of communication protocols will play a major role. In this paper, we present an approach that has the potential to substantially reduce the effort for designing customized protocols. Our approach is based on the concept of design patterns, which is well-established in object oriented software development. We specialize this concept to communication protocols, and - in addition - use formal description techniques (FDTs) to specify protocol design patterns as well as rules for their instantiation and composition. The FDTs of our choice are SDL-92 and MSCs, which offer suitable language support. We propose an SDL pattern description template and relate pattern-based configuring of communication protocols to existing SDL methodologies. Particular SDL patterns and the configuring of a customized resource reservation protocol are presented in detail.

Im Bereich der Expertensysteme ist das Problemlösen auf der Basis von bekannten Fallbeispielen ein derzeit sehr aktuelles Thema. Auch für Diagnoseaufgaben gewinnt der fallbasierte Ansatz immer mehr an Bedeutung. In diesem Papier soll der im Rahmen des Moltke -Projektes1 an der Universität Kaiserslautern entwickelte fallbasierte Problemlöser Patdex/22 vorgestellt werden. Ein erster Prototyp, Patdex/1, wurde bereits 1988 entwickelt.

We argue in this paper that sophisticated mi-croplanning techniques are required even formathematical proofs, in contrast to the beliefthat mathematical texts are only schematicand mechanical. We demonstrate why para-phrasing and aggregation significantly en-hance the flexibility and the coherence ofthe text produced. To this end, we adoptedthe Text Structure of Meteer as our basicrepresentation. The type checking mecha-nism of Text Structure allows us to achieveparaphrasing by building comparable combi-nations of linguistic resources. Specified interms of concepts in an uniform ontologicalstructure called the Upper Model, our se-mantic aggregation rules are more compactthan similar rules reported in the literature.