Semantical considerations on nonmonotonic logic
Artificial Intelligence
0-1 laws and decision problems for fragments of second-order logic
Information and Computation - Selections from 1988 IEEE symposium on logic in computer science
Towards a theory of knowledge and ignorance: preliminary report
Logics and models of concurrent systems
A note on non-monotonic modal logic
Artificial Intelligence
Minimal belief and negation as failure
Artificial Intelligence
Asymptotic Conditional Probabilities: The Unary Case
SIAM Journal on Computing
Nonmonotonic Logic: Context-Dependent Reasoning
Nonmonotonic Logic: Context-Dependent Reasoning
The 0-1 law fails for frame satisfiability of propositional modal logic
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Fragments of Existential Second-Order Logic without 0-1 Laws
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
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We analyze the asymptotic conditional validity of modal formulas, i.e., the probability that a formula ψ is valid in the finite Kripke structures in which a given modal formula φ is valid, when the size of these Kripke structures grows to infinity. We characterize the formulas ψ that are almost surely valid (i.e., with probability 1) in case φ is a flat, S5- consistent formula, and show that these formulas ψ are exactly those which follow from φ according to the nonmonotonic modal logic S5G. Our results provide - for the first time - a probabilistic semantics to a well-known nonmonotonic modal logic, establishing a new bridge between nonmonotonic and probabilistic reasoning, and give a computational account of the asymptotic conditional validity problem in Kripke structures.