Chair for Automata Theory of the Institute for Theoretical Computer Science, Faculty of Computer Science at TU Dresden

Technical Reports

2011


Franz Baader, Nguyen Thanh Binh, Stefan Borgwardt, and Barbara Morawska. Unification in the Description Logic EL Without the Top Concept. LTCS-Report 11-01, Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universität Dresden, Dresden, Germany, 2011. See http://lat.inf.tu-dresden.de/research/reports.html.
Bibtex entry  Paper (PDF)

Abstract

Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. The inexpressive Description Logic EL is of particular interest in this context since, on the one hand, several large biomedical ontologies are defined using EL. On the other hand, unification in EL has recently been shown to be NP-complete, and thus of considerably lower complexity than unification in other DLs of similarly restricted expressive power. However, EL allows the use of the top concept, which represents the whole interpretation domain, whereas the large medical ontology SNOMED CT makes no use of this feature. Surprisingly, removing the top concept from EL makes the unification problem considerably harder. More precisely, we will show in this paper that unification in EL without the top concept is PSpace-complete.


Stefan Borgwardt and Rafael Peñaloza. Complementation and Inclusion of Weighted Automata on Infinite Trees: Revised Version. LTCS-Report 11-02, Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universität Dresden, Dresden, Germany, 2011. See http://lat.inf.tu-dresden.de/research/reports.html.
Bibtex entry  Paper (PDF)

Abstract

Weighted automata can be seen as a natural generalization of finite state automata to more complex algebraic structures. The standard reasoning tasks for unweighted automata can also be generalized to the weighted setting. In this report we study the problems of intersection, complementation, and inclusion for weighted automata on infinite trees and show that they are not harder than reasoning with unweighted automata. We also present explicit methods for solving these problems optimally.


Rafael Peñaloza. Towards a Tableau Algorithm for Fuzzy ALC with Product T-norm. LTCS-Report 11-03, Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universität Dresden, Dresden, Germany, 2011. See http://lat.inf.tu-dresden.de/research/reports.html.
Bibtex entry  Paper (PDF)

Abstract

Very recently, the tableau-based algorithm for deciding consistency of general fuzzy DL ontologies over the product t-norm was shown to be incorrect, due to a very weak blocking condition. In this report we take the first steps towards a correct algorithm by modifying the blocking condition, such that the (finite) structure obtained through the algorithm uniquely describes an infinite system of quadratic constraints. We show that this procedure terminates, and is sound and complete in the sense that the input is consistent iff the corresponding infinite system of constraints is satisfiable.


Stefan Borgwardt and Barbara Morawska. Finding Finite Herbrand Models. LTCS-Report 11-04, Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universität Dresden, Dresden, Germany, 2011. See http://lat.inf.tu-dresden.de/research/reports.html.
Bibtex entry  Paper (PDF)

Abstract

We show that finding finite Herbrand models for a restricted class of first-order clauses is ExpTime-complete. A Herbrand model is called finite if it interprets all predicates by finite subsets of the Herbrand universe. The restricted class of clauses consists of anti-Horn clauses with monadic predicates and terms constructed over unary function symbols and constants. The decision procedure can be used as a new goal-oriented algorithm to solve linear language equations and unification problems in the description logic FL_0. The new algorithm has only worst-case exponential runtime, in contrast to the previous one which was even best-case exponential.


Franz Baader, Stefan Borgwardt, and Barbara Morawska. Unification in the Description Logic EL w.r.t. Cycle-Restricted TBoxes. LTCS-Report 11-05, Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universität Dresden, Dresden, Germany, 2011. See http://lat.inf.tu-dresden.de/research/reports.html.
Bibtex entry  Paper (PDF)

Abstract

Unification in Description Logics (DLs) has been proposed as an inference service that can, for example, be used to detect redundancies in ontologies. The inexpressive Description Logic EL is of particular interest in this context since, on the one hand, several large biomedical ontologies are defined using EL. On the other hand, unification in EL has recently been shown to be NP-complete, and thus of significantly lower complexity than unification in other DLs of similarly restricted expressive power. However, the unification algorithms for EL developed so far cannot deal with general concept inclusion axioms (GCIs). This paper makes a considerable step towards addressing this problem, but the GCIs our new unification algorithm can deal with still need to satisfy a certain cycle restriction.


Stefan Borgwardt and Rafael Peñaloza. Undecidability of Fuzzy Description Logics. LTCS-Report 11-06, Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universität Dresden, Dresden, Germany, 2011. See http://lat.inf.tu-dresden.de/research/reports.html.
Bibtex entry  Paper (PDF)

Abstract

Fuzzy description logics (DLs) have been investigated for over two decades, due to their capacity to formalize and reason with imprecise concepts. Very recently, it has been shown that for several fuzzy DLs, reasoning becomes undecidable. Although the proofs of these results differ in the details of each specific logic considered, they are all based on the same basic idea. In this report, we formalize this idea and provide sufficient conditions for proving undecidability of a fuzzy DL. We demonstrate the effectiveness of our approach by strengthening all previously-known undecidability results and providing new ones. In particular, we show that undecidability may arise even if only crisp axioms are considered.


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