Probability description language P − ALCNTatjana StojanovićUniversity <strong>of</strong> Kragujevac, Faculty <strong>of</strong> Science,tanjat@kg.ac.rsDescriptive logics (DL) are commonly used languages for representing ontologies. Classical DL are a part <strong>of</strong> first-orderlogic, and as such do not alow representation <strong>of</strong> uncertainty <strong>of</strong> any kind. Some authors introduced a possibility in DL [3,7]. O<strong>the</strong>rs work with statistical probability in DL [3, 4]. Last year Lutz and Scrhöder [5] published <strong>the</strong>ir result introducingsubjective probability in descriptive language ALC and some weaker languages. They used a Halpern’s approaches forfirst-order logic [2] and <strong>the</strong>y obtained probabilistic DLs with two-dimensional semantics similar to popular combinations<strong>of</strong> 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 <strong>of</strong> 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 <strong>of</strong> that work will be to prove that this formal system is sound and complete, and <strong>the</strong>n to describe algorithmfor checking consistency <strong>of</strong> a set <strong>of</strong> formulas. For all <strong>of</strong> that we will use <strong>the</strong> same technique as used in [6] for first-orderlanguage. Since, for <strong>the</strong> 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 <strong>of</strong> First-Order Logics <strong>of</strong> 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
Pseudo-Random Number Generator Using as a Seed Distance(Movement) <strong>of</strong> a Laboratory Cultured DaphniaeDjordje DjordjevićUniversity Nise-mail: djoka@ni.ac.rsSrbislav NešićConstruction Cluster Dundjer Nise-mail: SrbaNesic@gmail.comLaboratory cultured Daphniae (Daphnia Magna) are used for a scale <strong>of</strong> experiments, in particular for water qualityassessment. Their distance (position and movement) can be used as a seed for random number generator. Such a number,using bio-seed, can be used in different simulations, especially in <strong>the</strong> chaos-based models. 11 The work presented here was in part supported by <strong>the</strong> <strong>Serbian</strong> Ministry <strong>of</strong> Education and Science (project III44006)35