A logic for reasoning about probabilities
Information and Computation - Selections from 1988 IEEE symposium on logic in computer science
Reasoning about knowledge and probability
Journal of the ACM (JACM)
Inferences in probability logic
Artificial Intelligence
Reasoning about knowledge
Some first-order probability logics
Theoretical Computer Science
Modal logic
Fuzzy logic: mathematical tools for approximate reasoning
Fuzzy logic: mathematical tools for approximate reasoning
Complete deductive systems for probability logic with application to harsanyi type spaces
Complete deductive systems for probability logic with application to harsanyi type spaces
A Complete Deductive System for Probability Logic1
Journal of Logic and Computation
Final coalgebras for functors on measurable spaces
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
Deduction Systems for Coalgebras Over Measurable Spaces
Journal of Logic and Computation
Coalgebraic logic over general measurable spaces ??? a survey
Mathematical Structures in Computer Science
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Approximating Markov processes through filtration
Theoretical Computer Science
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Probability logics have been an active topic of investigation of beliefs in type spaces in game theoretical economics. Beliefs are expressed as subjective probability measures. Savage's postulates in decision theory imply that subjective probability measures are not necessarily countably additive but finitely additive. In this paper, we formulate a probability logic Σ+ that is strongly complete with respect to this class of type spaces with finitely additive probability measures, i.e. a set of formulas is consistent in Σ+ iff it is satisfied in a finitely additive type space. Although we can characterize Σ+-theories satisfiable in the class as maximally consistent sets of formulas, we prove that any canonical model of maximally consistent sets is not universal in the class of type spaces with finitely additive measures, and, moreover, it is not a type space. At the end of this paper, we show that even a minimal use of probability indices causes the failure of compactness in probability logics.