Some Probability Logics and their Applications in Computer Sciences

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Some Probability Logics and their Applications in Computer Sciences

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dc.contributor.advisor Rašković, Miodrag
dc.contributor.author Ognjanović, Zoran en_US
dc.date.accessioned 2009-12-03T12:14:52Z
dc.date.available 2009-12-03T12:14:52Z
dc.identifier.uri http://hdl.handle.net/123456789/197
dc.description.abstract The thesis consists of seven chapters and two appendixes. The Chapter 1 and the appendixes contain known notions and properties from probability logics. In Chapter 2 some propositional probability logics are introduced and their languages, models, satisfiability relations, and (in)finitary axiomatic systems are given. Object languages are countable, formulas are finite, while only proofs are allowed to be infinite. The considered languages are obtained by adding unary probabilistic operators of the form P≥s. Decidability of the logics is proved. In Chapter 3 some first order probability logics are considered while in Chapter 4 new types of probability operators are introduced. The new operators are suitable for describing events in discrete sample spaces. It is shown that they are not definable in languages of probability logics that have been used so far. A propositional and a first-order logic for reasoning about discrete linear time and finitely additive probability are given in Chapter 5. Sound and complete infinitary axiomatizations for the logics are provided as well. In Chapter 6 a probabilistic extension of modal logic is studied and it is shown that those logics are closely related, but that modal necessity is a stronger notion than probability necessity. In Chapter 7 decidability of these logics is shown by reducing the corresponding satisfiability problem to the linear programming problem. Finally, two automated theorems provers based on that idea are described. en_US
dc.description.provenance Made available in DSpace on 2009-12-03T12:14:52Z (GMT). No. of bitstreams: 1 phdZoranOgnjanovic.pdf: 1259633 bytes, checksum: bb26a60a090535d82ab7876e980f22b2 (MD5) en_US
dc.publisher Kragujevac en_US
dc.title Some Probability Logics and their Applications in Computer Sciences en_US
mf.author.birth-date 1964
mf.title.original Neke verovatnosne logike i njihove primene u računarstvu
mf.subject.area Mathematics en_US
mf.subject.keywords probability logic, uncertain reasoning, axiomatization, infinitary inference rules, completeness, decidability, linear programming, temporal logic, automated theorem proving en_US
mf.subject.subarea mathematical logic, artificial intelligence, uncertain reasoning en_US
mf.subject.msc 03B48, 03B70, 03B45, 03B44, 68T15, 68T27, 68T37
mf.contributor.committee Mijajlović, Žarko; Marković, Zoran; Banković, Dragić
mf.university.en University of Kragujevac
mf.university.faculty Faculty of sciences
mf.document.references 123
mf.document.pages 128
mf.format.resolution 300 DPI

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