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

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A p-adic probability logicAngelina Ilić StepićFaculty of Mathematics, BelgradeNebojša IkodinovićFaculty of Mathematics, BelgradeZoran OgnjanovićMathematical Institute of SerbianAcademy of Sciences and ArtsAleksandar PerovićFaculty of Transportation and Traffic EngineeringIn this article we present a p-adic valued probabilistic logic, denoted L Qp . The logic allows making statements suchas K r,ρ α with the intended meaning ”the probability of α belongs to the ball with the center r and the radius ρ”. Wedescribe the corresponding class of models that combine properties of the usual Kripke models and p-adic probabilities,and give sound and complete infinite axiomatic system. We prove decidability of L Qp .14
An optimised index structure for static deductional databasesbased on fuzzy or probabilistic DLsIvan ČukićMatematički fakultet, Beogradivan@math.rsThe standard indexing structures in the common database systems like B-trees and ISAMs are focussed on quick dataalteration and querying for specific records. With RDF and semantic databases, the data (knowledge) is not changedoften. In these scenarios, B-trees waste too much space, while ISAM wastes resources on keeping the structure sorted andon maintaining the overflow pages.The second feature of the common indexes that is not needed in querying RDF with SPARQL is locating one specificrecord. The result of a simple SVO query, where only one variable is known is always a list of records that contain thatfixed value.The structure presented in this paper is optimised specifically for this case, and to have as small memory footprint aspossible (one page at any time for one SVO query) that makes it suitable for deployment on the embedded systems.The additional advantage of this structure is that it provides an efficient way of keeping sorted weights for all storedsentences. This comes handy when the standard RDF inferencing methods are enriched with fuzzy or probabilisticreasoning.15
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