Kaiserslautern - Fachbereich Informatik
Refine
Year of publication
- 2006 (2) (remove)
Document Type
- Doctoral Thesis (2) (remove)
Has Fulltext
- yes (2)
Keywords
- Clustering (1)
- Umweltinformatik (1)
- VIACOBI (1)
- Visualisierung (1)
Faculty / Organisational entity
Die Computerisierung der Gesellschaft bedingt ein ständiges Zunehmen der Geschwindigkeit, mit der neue Daten erzeugt werden. Parallel zu dieser Entwicklung steigt der Bedarf an geeigneten Analyseverfahren, die in diesen großen und oftmals heterogenen Datenmengen Muster finden, Zusammenhänge entdecken und damit Wissen erzeugen. Das in dieser Arbeit entwickelte Verfahren findet die passende Struktur in einer ungeordneten, abstrakten Datenmenge, ordnet die zugrunde liegenden Informationen und bündelt diese somit für eine gezielte Anwendung. Dieser Prozess des Information Clustering ist zweistufig, es erfolgt zuerst ein generelles Clustering, an das sich eine interpretierende Visualisierung anschliesst. Für das Clustering wird das Verfahren der Voronoidiagramme erweitert. Durch den Einsatz einer generellen Distanzfunktion wird die Modellierung der durch die großen Datenmengen entstehenden multidimensionalen Parameter sowie weiterer Gewichte ermöglicht. Eine anschließende Visualisierung aus dem Bereich der Informationsvisualisierung unterstützt die Interpretation der neu gewonnenen Informationen. Für die praktische Anwendung wird die Stadtplanung betrachtet. In der Stadtplanung wird das Modell des Planungsablaufes eingesetzt, mit dem verschiedene Planungsalternativen erzeugt werden. Dieses Modell ist jedoch zu starr, um den dynamischen Anforderungen in der Realität gerecht zu werden. Das Information Clustering erweitert den klassischen Planungsablauf, die Flexibilität des Modells wird dadurch erhöht und die Komplexität reduziert. Das Ergebnis der Berechnung ist genau eine Planungsalternative, die sämtliche Eingabeparameter kanalisiert.
The validity of formulas w.r.t. a specification over first-order logic with a semantics based on all models is semi-decidable. Therefore, we may implement a proof procedure which finds a proof for every valid formula fully automatically. But this semantics often lacks intuition: Some pathological models such as the trivial model may produce unexpected results w.r.t. validity. Instead, we may consider just a class of special models, for instance, the class of all data models. Proofs are then performed using induction. But, inductive validity is not semi-decidable -- even for first-order logic. This theoretical drawback manifests itself in practical limitations: There are theorems that cannot be proved by induction directly but only generalizations can be proved. For their definition, we may have to extend the specification. Therefore, we cannot expect to prove interesting theorems fully automatically. Instead, we have to support user-interaction in a suitable way. In this thesis, we aim at developing techniques that enhance automatic proof control of (inductive) theorem provers and that enable user-interaction in a suitable way. We integrate our new proof techniques into the inductive theorem prover QuodLibet and validate them with various case studies. Essentially, we introduce the following three proof techniques: -We integrate a decision procedure for linear arithmetic into QuodLibet in a close way by defining new inference rules that perform the elementary steps of the decision procedure. This allows us to implement well-known heuristics for automatic proof control. Furthermore, we are able to provide special purpose tactics that support the manual speculation of lemmas if a proof attempt gets stuck. The integration improves the ability of the theorem prover to prove theorems automatically as well as its efficiency. Our approach is competitive with other approaches regarding efficiency; it provides advantages regarding the speculation of lemmas. -The automatic proof control searches for a proof by applying inference rules. The search space is not only infinite, but grows dramatically with the depth of the search. In contrast to this, checking and analyzing performed proofs is very efficient. As the search space also has a high redundancy, it is reasonable to reuse subproofs found during proof search. We define new notions for the contribution of proof steps to a proof. These notions enable the derivation of pruned proofs and the identification of superfluous subformulas in theorems. A proof may be reused in two ways: upward propagation prunes a proof by eliminating superfluous proof steps; sideward reuse closes an open proof obligation by replaying an already found proof. -For interactive theorem provers, it is essential not only to prove automatically as many lemmas as possible but also to restrict proof search in such a way that the proof process stops within a reasonable amount of time. We introduce different markings in the goals to be proved and the lemmas to be applied to restrict proof search in a flexible way: With a forbidden marking, we can simulate well-known approaches for applying conditional lemmas. A mandatory marking provides a new heuristics which is inspired by local contribution of proof steps. With obligatory and generous markings, we can fine-tune the degree of efficiency and extent of proof search manually. With an elaborate case study, we show the benefits of the different techniques, in particular the synergetic effect of their combination.