Authors: Rašković, Miodrag 
Ognjanović, Zoran 
Marković, Zoran 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: A logic with conditional probabilities
Journal: Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science)
Volume: 3229
First page: 226
Last page: 238
Conference: European Workshop on Logics in Artificial Intelligence, JELIA 2004
Issue Date: 1-Jan-2004
Rank: M22
ISBN: 978-3-540-30227-8
ISSN: 0302-9743
DOI: 10.1007/978-3-540-30227-8_21
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 a is at least s", "the conditional probability of α given β is s", and "the conditional probability of a 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 a A α and β are almost the same". This last operator may be used to model default reasoning.
Keywords: Probability | Conditional probability | Formal logic | Mathematical models | Probability functions
Publisher: Springer Link

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