Zoran Ognjanović
Serbian Academy of Sciences and Arts
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Publication
Featured researches published by Zoran Ognjanović.
Journal of Logic and Computation | 1999
Zoran Ognjanović; Miodrag Rašković
We introduce new types of probability operators of the form QF , whereF is a recursive rational subset of [0; 1]. A formulaQF is satisfied in a probability model if the measure of the set of worlds that satisfy is in F . The new operators are suitable for describing events in discrete sample spaces. We provide sound and complete axiomatic systems for a number of probability logics augmented with the QF -operators. We show that the new operators are not definable in languages of probability logics that have been used so far. We study decidability of the presented logics. We describe a relation of ‘being more expressive’ between the new probability logics.
International Journal of Approximate Reasoning | 2010
Dragan Doder; Miodrag Rašković; Zoran Marković; Zoran Ognjanović
We introduce a method for measuring inconsistency based on the number of formulas needed for deriving a contradiction. The relationships to previously considered methods based on probability measures are discussed. Those methods are extended to conditional probability and default reasoning.
european conference on logics in artificial intelligence | 2004
Miodrag Rašković; Zoran Ognjanović; Zoran Marković
The paper presents a logic which enriches propositional calculus with three classes of probabilistic operators which are applied to propositional formulas: P ≥ s(α), CP = s(α, β) and CP ≥ s (α, β), with the intended meaning ”the probability of α is at least s”, ”the conditional probability of α given β is s”, and ”the conditional probability of α given β is at least s”, respectively. Possible-world semantics with a probability measure on sets of worlds is defined and the corresponding strong completeness theorem is proved for a rather simple set of axioms. This is achieved at the price of allowing infinitary rules of inference. One of these rules enables us to syntactically define the range of the probability function. This range is chosen to be the unit interval of a recursive nonarchimedean field, making it possible to define another probabilistic operator CP ≈ 1(α, β) with the intended meaning ”probabilities of α ∧ β and β are almost the same”. This last operator may be used to model default reasoning.
Mathematical Logic Quarterly | 2003
Zoran Marković; Zoran Ognjanović; Miodrag Rašković
We introduce a probabilistic extension of propositional intuitionistic logic. The logic allows making statements such as P≥sα, with the intended meaning “the probability of truthfulness of α is at least s”. We describe the corresponding class of models, which are Kripke models with a naturally arising notion of probability, and give a sound and complete infinitary axiomatic system. We prove that the logic is decidable.
Scientometrics | 2014
Miloš Savić; Mirjana Ivanović; Miloš Radovanović; Zoran Ognjanović; Aleksandar Pejović; Tatjana Jakšić Krüger
Digital preservation of scientific papers enables their wider accessibility, but also provides a valuable source of information that can be used in a longitudinal scientometric study. The Electronic Library of the Mathematical Institute of the Serbian Academy of Sciences and Arts (eLib) digitizes the most prominent mathematical journals printed in Serbia. In this paper, we study a co-authorship network which represents collaborations among authors who published their papers in the eLib journals in an 80 year period (from 1932 to 2011). Such study enables us to identify patterns and long-term trends in scientific collaborations that are characteristic for a community which mainly consists of Serbian (Yugoslav) mathematicians. Analysis of connected components of the network reveals a topological diversity in the network structure: the network contains a large number of components whose sizes obey a power-law, the majority of components are isolated authors or small trivial components, but there is also a small number of relatively large, non-trivial components of connected authors. Our evolutionary analysis shows that the evolution of the network can be divided into six periods that are characterized by different intensity and type of collaborative behavior among eLib authors. Analysis of author metrics shows that betweenness centrality is a better indicator of author productivity and long-term presence in the eLib journals than degree centrality. Moreover, the strength of correlation between productivity metrics and betweenness centrality increases as the network evolves suggesting that even more stronger correlation can be expected in the future.
foundations of information and knowledge systems | 2008
Aleksandar Perović; Zoran Ognjanović; Miodrag Rašković; Zoran Marković
The paper presents a sound and strongly complete axiomatization of reasoning about polynomial weight formulas. In addition, the PSPACE decision procedure for polynomial weight formulas developed by Fagin, Halpern and Megiddo works for our logic as well. The introduced formalism allows the expression of qualitative probability statements, conditional probability and Bayesian inference.
Logic Journal of The Igpl \/ Bulletin of The Igpl | 2015
Ioannis Kokkinis; Petar Maksimovic; Zoran Ognjanović; Thomas Studer
In this article, we introduce the probabilistic justification logic PJ, a logic in which we can reason about the probability of justification statements. We present its syntax and semantics, and establish a strong completeness theorem. Moreover, we investigate the relationship between PJ and the logic of uncertain justifications.
foundations of information and knowledge systems | 2010
Dragan Doder; Zoran Marković; Zoran Ognjanović; Aleksandar Perović; Miodrag Rašković
The aim of the paper is to present a sound, strongly complete and decidable probabilistic temporal logic that can model reasoning about evidence.
International Journal of Approximate Reasoning | 2014
Angelina Ilić-Stepić; Zoran Ognjanović; Nebojša Ikodinović
In this paper we present the proof-theoretical approach to p-adic valued conditional probabilistic logics. We introduce two such logics denoted by CPL Z p and CPL Q p fin . Each of these logics extends classical propositional logic with a list of binary (conditional probability) operators. Formulas are interpreted in Kripke-like models that are based on p-adic probability spaces. Axiomatic systems with infinitary rules of inference are given and proved to be sound and strongly complete. The decidability of the satisfiability problem for each logic is proved. We presented two p-adic valued conditional probabilistic logics.Formulas are interpreted in Kripke-like models.Axiomatic systems are given and proved to be sound and strongly complete.The decidability of the satisfiability problem for each logic is proved.
Journal of Logic and Computation | 2013
Dragan Doder; John Grant; Zoran Ognjanović
Spatiotemporal databases can be used to efficiently store and retrieve information about objects moving in space and time. Probabilities are added to model the case where the locations are not known with certainty. A few years ago a new formalism was introduced to represent such information in the form of atomic formulas, each of which represents the probability (in the form of an interval because even the probabilities are not known precisely) that a particular object is in a particular location at a particular time. We extend this formalism to obtain several different probabilistic logics by adding logical operators. Furthermore, we axiomatize these logics, provide corresponding semantics, prove that the axiomatizations are sound and complete, and discuss decidability issues. While we relate these logics to previous axiomatizations of probabilistic logics, this article is self-contained: no prior knowledge of probabilistic logics is assumed.