Knjiga apstrakata - Mathematical Institute of the Serbian Academy of ...

Probability description language P − ALCNTatjana StojanovićUniversity of Kragujevac, Faculty of Science,tanjat@kg.ac.rsDescriptive logics (DL) are commonly used languages for representing ontologies. Classical DL are a part of first-orderlogic, and as such do not alow representation of uncertainty of any kind. Some authors introduced a possibility in DL [3,7]. Others work with statistical probability in DL [3, 4]. Last year Lutz and Scrhöder [5] published their result introducingsubjective probability in descriptive language ALC and some weaker languages. They used a Halpern’s approaches forfirst-order logic [2] and they obtained probabilistic DLs with two-dimensional semantics similar to popular combinationsof DL with temporal logic.Our main task is to expand this language with more DL concept operators. We will start with classical ALCN descriptivelanguage, i.e. with sets of atomic concepts N C = {C 0 , C 1 , . . .}, atomic roles N R = {R 0 , R 1 , . . .} and individuals N O ={a 0 , a 1 , . . .}, and define concepts, using classical concept constructors (⊓, ⊔, ¬, ∃, ∀, n, n), and formulas, C = D, a : C,aRb. Probability formulas are going to be P s a : C and P s aRb (s ∈ Q ∩ [0, 1]). In that way we will create formulas ¬φ andφ ∧ ψ (φ and ψ are both probability formulas or both classical DL formulas).Main result of that work will be to prove that this formal system is sound and complete, and then to describe algorithmfor checking consistency of a set of formulas. For all of that we will use the same technique as used in [6] for first-orderlanguage. Since, for the classical DL language ALCN checking consistency is ExpTime-complete, we expect that thisformal system will have same complexity.References[1] F. Baader, D. L. McGuinness, D. N. Peter, F. Patel-Schneider, THE DESCRIPTION LOGIC HANDBOOK: Theory,implementation, and applications, Cambridge University Press, (2002).[2] J. Y. Halpern, An Analysis of First-Order Logics of Probability, Artif. Intell. (AI), 46(3) (1990), 311–350.[3] J. Heinsohn, Probabilistic Description Logics, Procedings UAI’94,(1994), 311–318.[4] T. Lukasiewicz, Expressive probabilistic description logics, Artif. Intell., 172(6-7) (2008), 852–883.[5] C. Lutz, L. Schröder, Probabilistic Description Logics for Subjective Uncertainty, KR (2010).[6] Z. Ognjanović, M. Rašković, Some first-order probability logics, Theoretical Computer Science, 247(1-2) (2000), 191-212.[7] G. Qi, J. Z. Pan, Q. Ji, Extending Description Logics with Uncertainty Reasoning in Possibilistic Logic, ECSQARU(2007), 828–839.34