A probabilistic approach to default reasoning

A logic is defined which in addition to propositional calculus contains several types of probabilistic operators which are applied only to propositional formulas. For every s ∈ S, where S is the unit interval of a recursive nonarchimedean field, an unary operator P≥s(α) and binary operators 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) are introduced. Since S is a non-archimedean field, we can also introduce a binary operator CP≈1(α, β) with the intended meaning ”probabilities of α ∧ β and β are infinitely close”. Possible-world semantics with a probability measure on an algebra of subsets of the set of all possible worlds is provided. A simple set of axioms is given but some of the rules of inference are infinitary. As a result we can prove the strong completeness theorem fo...

• Type: Conference
• Year: 2004
• Where: NMR
• Authors: Miodrag Raskovic, Zoran Ognjanovic, Zoran Markovic
• Keywords: Artificial Intelligence, Binary Operator, Conditional Probability, Default Consequence Relation, NMR 2004