Kolloquium des Graduiertenkolleg Wissensrepräsentation

Prof. Norman Foo

Research Program on Social Agents

Ideas from game theory (classical and evolutionary), social choice, economics, and behavioral psychology are coming together to provide new insights into how large communities of social agents interact. This talk will examine our contribution to this dialog using computational agents relying on the Answer Set Programming formalism. We will outline a long term agenda but also describe some short term work.

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Kolloquium des Graduiertenkolleg Wissensrepräsentation

Prof. Dr. Esparza

Fixed point equations in commutative semirings

Fixed point systems of equations over (omega-continuous) semirings can be seen as the mathematical foundation of interprocedural program analysis. Given a system x = f(x), the sequence 0, f(0), f(f(0) ... converges to the least fixed point mu_f, but convergence can be very slow. In LICS 99 Hopkins and Kozen presented an iteration scheme to accelerate the convergence, and proved that if the semiring is idempotent and commutative then the fixed point is reached after at most exponentially many iterations in the number of equations.

The talk presents some further results on the Hopkins-Kozen scheme. We first show that, in a certain formal sense, the scheme is nothing but Newton's method for computing a zero of a differentiable function. Then we show that the number of iterations needed to compute the solution is in fact much smaller than the Hopkins-Kozen bound: a system of n equations needs at most n iterations. Finally, we apply the Hopkins-Kozen acceleration to itself and study the resulting hierarchy of increasingly fast accelerations.

Joint work with Stefan Kiefer and Michael Luttenberger.

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Kolloquium des Graduiertenkolleg Wissensrepräsentation

Prof. Frank Wolter

"Conservative extensions, refinements, and modular ontologies"

A logical theory T is called a conservative extension of a logical theory S if, and only if, every consequence of T, formulated in the language of S, is already a consequence of S.

The notion of a conservative extension, which originated in mathematical logic and philosophy of scienc e, plays an important role in software engineering. For example, it is used to enable specifications in the large by supporting structured specifications, modularisation and segmentation of software. In this talk, I will argue that variants of the notion of a conservative extension should play an even more important role in ontology engineering. Firstly, they can be used to define the notion of a refinement of an ontology. Secondly, they can form a uniform basis for introducing the notion of a module of an ontology and modularised ontologies. And finally, first results indicate the feasibility of reasoning support for conservative extensions in ontology languages based on description logics such as OWL-DL.

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Kolloquium des Graduiertenkolleg Wissensrepräsentation

Prof. Marina de Vos

Answer Set Programming for Representing and Reasoning about Virtual Institutions

This presentation will focus on the use of ASP in multi-agent systems in general but more specifically we will look at virtual institutions.

It is recognised that institutions are potentially powerful means for making agent interactions effective and efficient, but institutions will only really be useful when, as in other safety-critical scenarios, it is possible to prove that particular properties do or do not hold for all possible encounters. In contrast to symbolic model-checking, answer set programming permits the statement of problems and queries in domain-specific terms as executable logic programs, thus eliminating the gap between specification and verification language. Furthermore, results are presented in the same terms.

We describe the use of answer set programs as an institutional modelling technique. We demonstrate that our institutional model can be intuitively be mapped into an answer set program such that the ordered event traces of the former can be obtained as the answer sets of the latter, allowing for an easy way to query properties of models.

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Kolloquium des Graduiertenkolleg Wissensrepräsentation

Prof. Th. Schwentick

Two variable logics in the presence of an equivalence relation

Mortimer showed more than 30 years ago that two-variable logics possesses the Finite Model Property and therefore has a decidable satisfiability problem. Since then, this result has been refined and extended in several ways. In particular, satisfiability on structures with specific properties has been investigated. Of course, the general decidability result can be directly transfered only if the property at hand can be axiomatized with two variables. Recently, the satisfiability problem for two-variable logics on structures with (one or more) equivalence relations has been investigated in more detail. Partially, these investigations were motivated by the fact that adding an equivalence relation to a structure has the same effect as associating a data value to each element and allowing for equality tests on these data values. After a survey of some general results, the focus of the talk will be on recent results for (finite and infinite) strings and trees with one equivalence relation.

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Kolloquium des Graduiertenkolleg Wissensrepräsentation

Prof. Dr. Gabriele Kern-Isberner

Probabilistic Abduction without Priors

This talk considers the simple problem of abduction in the framework of Bayes theorem, when the prior probability of the hypothesis is not available, either because there are no statistical data to rely on, or simply because a human expert is reluctant to provide a subjective assessment of this prior probability. This abduction problem remains an open issue since a simple sensitivity analysis on the value of the unknown prior yields empty results. In the talk, some general criteria are proposed which a solution to this problem should satisfy. We then survey and comment on various existing or new solutions to this problem: the use of likelihood functions (as in classical statistics), the use of information principles like maximum entropy, Shapley value, maximum likelihood. Finally, we present a novel maximum likelihood solution by making use of conditional event theory. The formal setting includes de Finetti's coherence approach, which does not exclude conditioning on contingent events with zero probability.

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Kolloquium des Graduiertenkolleg Wissensrepräsentation

Anders Søgaard

LOGIC AND THE ADEQUACY OF LINGUISTIC THEORIES

Certain mathematical properties have been proposed as upper and lower bounds on what is considered a possible natural language and therefore on adequate linguistic theories. A classic is recognizability. Learnability is another. In principle, any property can help us weed out inadequate theories. Of course empirical evidence that natural languages must have or cannot possibly have this particular property, is needed. In this lecture, it is shown how logic may help us obtain results about the mathematical properties of linguistic theories. This is so for many reasons: (i) Logical axiomatizations enable us to derive new theorems about our theories. (ii) Many results can be directly imported from logic once linguistic theories are translated into logical systems. In particular, this holds for upper bounds on complexity. Logic also provides a new vocabulary of possible interest. For instance, notions such as tree model property and polysize model property seem relevant in linguistics. It goes without saying that logic benefits from its application to new fields, and linguistics is no exception. Some linguistic theories translate into standard logics, but others don't, and new extensions must be considered.

In the talk, I consider only a subclass of linguistic theories, namely so-called "attribute-value grammars". I show how results from logic have helped linguists (me, in particular) in evaluating such theories. If time permits, I will also give an example of a family of logics (polyadic dynamic logics) that was developed to model non-standard linguistic theories.

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Kolloquium des Graduiertenkolleg Wissensrepräsentation

Prof. U. Moulines

Zur Frage einer vereinheitlichenden Ontologie der Wissenschaften

Es soll die These vertreten werden, dass eine gut fundierte und wissenschaftlich orientierte Ontologie Semantik, Epistemologie und (formale) modelltheoretische Ontologie in kohaärenter Weise miteinander kombinieren sollte; und zwar in einer Weise, die der Tatsache Rechnung trägt, dass die Ontologie entwickelter Wissenschaften (wie etwa der Physik) zugleich durch den systematisch-experimentellen Zugang zur Realität und ihre mathematische Verarbeitung bestimmt wird. Die Begriffe /Datenmodell/ und /theoretisches Modell/ spielen dabei eine zentrale Rolle. Auch die Frage der intertheoretischen Verbindungen sollte in diesem Zusammenhang herangezogen werden. Das Konzept einer formal-ontologischen Reduktion ist dafür einschlägig.

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Kolloquium des Graduiertenkolleg Wissensrepräsentation

Dipl. Inform. Dr. med. Jörg Niggemann

Ontologische Besonderheiten der Neuroanatomie

Die Neuroanatomie ist zunächst wie die generelle Anatomie in Disziplinen gegliedert: Die systematische, die deskriptive (morphologische und topographische) und die funktionelle Neuroanatomie. Letztere zeichnet sich dadurch aus, dass sie nicht dieselben Objekte beschreibt wie die beiden anderen Sichten, nur eben aus der Perspektive der Funktion. Stattdessen beschreibt sie die Verbindungen von (namenlosen) Gruppen von Nervenzellen innerhalb der morphologisch definierten Objekte. Diese Gruppen sind z.T. ausschließlich über die gemeinsame Funktion der enthaltenen Nervenzellen definiert, eine Ontologie der funktionellen Neuroanatomie setzt also eine Ontologie der Funktionen voraus. Von den Gruppen ausgehend wird eine Reihe weiterer Besonderheiten der Neuroanatomie beleuchtet wie das Problem der Lateralität ("Das Auge" versus rechtes/linkes Auge und das Konzept(?) "Paarige Struktur"), das Problem der Granularität und die Erscheinung der "Scheinobjekte". Zusammenfassend zeigt sich, dass die Neuroanatomie aus der "conceptualist" Sicht sehr viel besser zu beschreiben ist als aus der "realist" Sichtweise. In der Diskussion sollen Ideen dafür gesammelt werden, wie die genannten Besonderheiten mit den neuen Mitteln der GFO und der Ontologie der Funktionen dargestellt werden können.

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