Kolloquium/Ringvorlesung des Graduiertenkolleg Wissensrepräsentation

Default reasoning can be described as the art of drawing plausible conclusions from incomplete or contradictory information. From a generalized perspective, su ch default conclusions can be classified as being ASSOCIATIVE, representing properties implied by the given information and the available background knowledge, or REFLECTIVE, constituting explanations for contradictions or irregularities detected in the given information account. In this talk I will present a novel mathematical model of how the overall knowledge underlying the process may be represented and organized and how associative and reflective default conclusions are derived from that body of knowledge.

A distinctive feature of the approach is its incorporating in the basic formal framework the EVOLUTIONARY nature of knowledge and belief. Rather than focusing on a final state of belief ultimately generated from a given state of knowledge, as in the traditional approaches, we model the reasoner's belief stat e as undergoing a continuing evolution in response to a continuing evolution of th e reasoner's knowledge state. Apart from the ability to monitor the ongoing epistemic behavior of reactive reasoners, this evolutionary perspective allows one to formulate temporal defaults, detect and constrain inferential oscillation and divergence, and account for knowledge changes that occur _during_ inference.

Another distinctive feature of the approach is its employing the same formal language, mathematical logic, for specifying both the elements of the knowledge base and the particulars of the inference process. This methodological uniformit y grants the theory an advanced notion of INTROSPECTION, where the reasoner has knowledge of her entire epistemic history and can adapt her current reasoning in accordance with that knowledge.

In our approach there are two types of BELIEF REVISION that possibly arise in response to the arrival of new evidence, leading to a twofold notion of non-monotonicity. First, the new evidence may activate an item of background knowledge known to override a currently released item, causing the conclusions supported by the latter to be withdrawn from the belief stream and possibly replaced by new conclusions. Second, the new evidence may invalidate a currently pursued inferential thread, causing the entire thread to be dropped from the epistemic evolution and possibly replaced with a new thread. Both forms of revision may also occur due to internal epistemic processes, without any externa l change of evidence, and so constitute _per se_ the very process of default reasoning in our theory.

During the recent decades, reasoning about probabilities has started to play an important role in AI. In particular, model- theoretic probabilistic reasoning about interval restrictions for conditional probabilities, also called conditional constraints, has been a subject of extensive research efforts in the literature. In some sense, the model-theoretic notion of logical entailment in probabilistic logic is nonmonotonic, since it does not satisfy the property of subclass inheritance of purely probabilistic knowledge. However, in another sense, logical entailment is also monotonic, as it realizes some complete subclass inheritance of logical knowledge. The above observations suggest new notions of entailment beyond the classical notion of logical entailment. (A) If we add the inheritance of purely probabilistic knowledge together with a strategy for resolving inconsistencies due to this inheritance, then we arrive at new notions of entailment for probabilistic logic, which are generally stronger than logical entailment. They can especially be used for reasoning with statistical knowledge and degrees of belief. (B) If we add some strategy for resolving inconsistencies related to the inheritance of logical knowledge, then we arrive at new notions of entailment for probabilistic logic, which are weaker than logical entailment. They can especially be used for handling inconsistencies related to conditioning on events of probability zero. In this talk, I will give an overview on model-theoretic probabilistic reasoning and especially on probabilistic reasoning under the above new notions of entailment.

The aim of this lecture is to present a cluster of issues centered upon the distinction between two different approaches to logic. In one approach a logic is considered as a logical system thus a set of logical truth of the given logic. In the second approach the a logic is defined as a consequence relation (or operation) between sentences. I particular:

We will compare the approaches to logic proposed by Hilbert, Gentzen and Tarski.

We will present some results from the theory of logical consequence operation concerning to the logical matrices, an algebraic semantics, implicative logics and equivalential logic.

The above results will be applied to investigation of modal consequence operation, quantum - orthomodular logical consequence and relevant consequence operation.

Artificial agents employ reasoning techniques to devise plans and to act under incomplete information in partially known environments. The talk introduces FLUX as a declarative method for programming reasoning agents. Based on the axiomatic action theory of fluent calculus, FLUX uses efficient constraint techniques that scale up well to problems which require agents and robots to reason about the performance of several thousands of actions. Among the applications of FLUX are the high-level control of autonomous robots as well as personal software agents that surf the Semantic Web of the near future.

The language for describing inconsistency is underdeveloped. If a knowledgebase (a set of formulae) is inconsistent, we need more illuminating ways to say how inconsistent it is, or to say whether one knowledgebase is ``more inconsistent" than another. To address this, we provide a general characterization of inconsistency, based on quasi-classical logic (a form of paraconsistent logic with a more expressive semantics than Belnap's four-valued logic; unlike other paraconsistent logics, this logic allows the connectives to behave as classical connectives). We analyse inconsistent knowledge by considering the conflicts arising in the minimal quasi-classical models for that knowledge. This is used for a measure of coherence for each knowledgebase, and for a preference ordering, called the compromise relation, over knowledgebases. In this talk, we will look at this framework, and consider applications in managing heterogeneous sources of knowledge.

Nested logic programs have recently been introduced in order to allow for arbitrarily nested Boolean expressions in the heads and bodies of logic program rules under the answer set semantics. Previous results show that nested logic programs can be transformed into standard (unnested) disjunctive logic programs, albeit leading to an exponential increase of program size in the worst case. Hence, in general, such a translation is not suitable for implementation purposes. In this talk, we present two different kinds of translations of nested programs, both of which are guaranteed to be polynomial in the size of the input program. The first translation deals with a reduction of nested logic programs into quantified Boolean formulas, and the second one maps nested programs into disjunctive programs such that the resultant function is not only polynomial but also modular and strongly faithful. Both translations have been implemented as a front-end to existing state-of-the art solvers for quantified Boolean formulas and disjunctive logic programs under the answer set semantics, respectively. As a side result, we also determine precise complexity bounds for the main reasoning tasks associated with nested logic programs.

Der Erfolg einer Web Site wird nicht gemessen anhand der ausgefuehrten Zugriffe, sondern in Bezug auf die unternehmerischen Ziele, die durch die Web Praesenz erfuellt werden sollen. Im Bereich des web-basierten Handels wird der Erfolg anhand der getaetigten Kaeufe gemessen; dabei ist die Konvertierungseffizienz als Erfolgsindikator zu betrachten. In anderen Anwendungsdomaenen wird der Erfolg durch die Anzahl der abgeschlossenen Vertraege (Banken, Versicherungen) oder der Kontaktaufnahmen (Versicherungen, Krankenhaeuser) widerspiegelt.

In diesem Vortrag besprechen wir einen allgemeinen Rahmen fuer die Modellierung des Erfolges einer Web-Site. Zuerst werden die Aktivitaeten der Nutzer auf anwendungsbezogene "Aufgaben" abgebildet. Dann werden generische, schablonen-basierte Navigationsstrategien identifiziert, die eine erfolgreiche Nutzung der Site darstellen, z.B. den Kauf von Produkten oder die Kontaktaufnahme mit einer Beratungsstelle. Diese Strategien haengen sowohl von den Aufgaben als auch von den Verhaltensunterschieden zwischen Nutzergruppen ab, so dass mehrere Strategien per Nutzergruppe beruecksichtigt werden sollen. Eine Mining-Sprache wird dann verwendet, um die Navigationsstrategien als Schablonen darzustgellen und die entsprechenden Navigationsmuster zu entdecken. Erste Ergebnisse dieser Methode werden im Rahmen einer Fallstudie praesentiert.

Die Begriffliche Wissensverarbeitung ordnet und gliedert Gegenstände an hand ihrer Merkmale. Das mathematische Modell welches hierfür von der Formalen Begriffsanalyse vorgeschlagen wird ist symmetrisch aufgebaut Gegenstände und Merkmale werden separat aber auf die gleiche Weise behandelt und können grundsätzlich in ihren Rollen vertauscht werden ("Dualitätsprinzip"). Beim umgangssprachlichen Gebrauch hingegen werden feine Unterschiede gemacht. Während die Hierarchie von Begriffen auf der Seite der Gegenstände eher mittels der Teilmengenbeziehung formuliert wird ("alle Säugetiere sind Wirbeltiere"), drückt man einen entsprechenden Sachverhalt merkmalseitig eher als Implikation aus ("Übergewicht bedeutet Infarktgefahr"). Das Zusammenspiel zwischen Implikationen und den Begriffsinhalten hat deshalb in der Formalen Begriffsanalyse stets eine wichtige Rolle gespielt zumal sich die Struktur eines Begriffsverbandes durch die in ihm geltenden Implikationen beschreiben läßt. Allerdings ist die Menge aller Implikationen eines gegebenen Kontextes gewöhnlich sehr groß und hochredundant. Eine der Grundaufgaben ist es deshalb eine handliche Implikationenbasis zu finden d.h. eine möglichst übersichtliche Menge von Implikationen aus denen alle anderen in einem zu präzisierenden Sinne "folgen". Für den Fall einwertiger Kontexte ohne Zusatzbedingungen ist dies gut gelöst und Grundlage von praktikablen Wissensakquisitionsverfahren.

Navigationsaufgaben enthalten eine Reihe interessanter Probleme für die Orientierung und die Navigation kognitiver Agenten (Menschen, Roboter, Softwareagenten) und für die Kommunikation zwischen kognitiven Agenten. Im Rahmen des DFG-Sonderforschungsbereichs SFB/TR8 Spatial Cognition: Reasoning, Action, Interaction verwenden wir u.a. Navigationsaufgaben als Untersuchungsgegenstand frü die Entwicklung unterschiedlicher KI-Repräsentationstechniken und deren Integration. Die Techniken sind kognitiv motiviert, d.h. auf reale Anforderungen natürlicher und künstlicher kognitiver Agenten abgestimmt. Dies bedeutet insbesondere, dass sie Entscheidungen in reichhaltigen Umwelten mit vergleichsweise magerem (d.h. unvollständigem, ungenauem, unscharfem und möglicherweise konfligierendem) Wissen unterstützen und die Kommunikation mit Menschen unterstützen sollen. Wir untersuchen Möglichkeiten, räumliches Wissen über schematische räumliche Strukturen (diagrammatisch) zu vermitteln und mit Ansätzen des qualitativen räumlichen Schliessens zu verarbeiten. In dem Vortrag wird ein Experimentierparadigma vorgestellt, an dem wir vielfältige Fragestellungen der Raumkognition untersuchen und miteinander in Verbindung setzen können.

GermaNet ist ein lexikalisch--semantisches Netz fuer das Deutsche im Stile des Princeton WordNet, das die haeufigsten und wichtigsten Woerter des deutschen Grundwortschatzes und ihre bedeutungstragenden Beziehungen zu anderen Woertern in der Sprache abbildet. Im deutschen Wortnetz sind Nomen, Verben und Adjektive modelliert und anhand der semantischen Relationen der Synonymie, Hyponymie, Antonymie, Meronymie, Kausation miteinander verknuepft. Im Rahmen eines europaeischen Projektes sind GermaNet--Module in das polylinguale EuroWordNet integriert worden. GermaNet wird als Hintergrundressource in sprachtechnologischen Verfahren im Bereich der Informationserschließung und semantischen Annotierung eingesetzt. Der Vortrag gibt einen Ueberblick ueber die wesentlichen Aufbauprinzipien und den aktuellen Stand des GermaNet und thematisiert neuere Entwicklungen zu webfaehigen Formaten.

Kunze, C. (2001), Lexikalisch-semantische Wortnetze. In: Carstensen, K.-U. et al. (Hrsg.), Computerlinguistik und Sprachtechnologie: eine Einfuehrung. Heidelberg; Berlin: Spektrum Akademischer Verlag, S. 386--393.

Logic programs without negation have a very satisfactory declarative semantics which can be characterized as the least fixed point of a semantic operator which is both monotonic and order continuous. Attempts to carry over this result to logic programs with negation fail for various reasons, including the fact that reasonable generalizations of the mentioned operator fail to be order continuous, or even monotonic. The quest for understanding and rectifying this situation has driven research in logic programming and nonmonotonic reasoning throughout the last two decades. In this presentation we will study properties of semantic operators for logic programs with negation, starting from topological investigations concerning their iterative behaviour. We will touch very diverse topics such as termination analysis under Prolog, quantitative domain theory, a novel uniform approach to different semantics in nonmonotonic reasoning, and connectionism.

Belief merging is the process of defining a belief base representing the beliefs of a group of agents, from the belief bases encoding the beliefs of each agent.

We first consider the requirements that one can put on such process. This axiomatic characterization shows that the problem of merging belief bases is close to the preference aggregation problem.

Then, we explore the two main ways that have been proposed to address this problem : The model-based operators that compute the most credible worlds, given the set of belief bases. And the syntax-based operators that select some (maximal consistent subset of) formulae in the union of all the belief bases. These two approaches have their pros and cons.

Finally we propose a new approach to belief merging, that resolves nicely the drawbacks of the two other approaches.

Systematic approaches like the family of Action Description Languages have been designed for the formal assessments of action calculi. We assess the fluent calculus for knowledge and sensing with the help of the recently developed, high-level action language A_k. As the main result, we present a provably correct embedding of this language into fluent calculus. As a spinoff, the action programming language FLUX, which is based on fluent calculus, provides a system for answering queries to A_k domains. Conversely, the action description language may serve as a high-level surface language for specifying action domains in FLUX.