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 formulasψthat 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 fromΦaccording to the nonmonotonic modal logic S5{sub}G. 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.
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机译:转换术语± Sup> [n i Sub>] f(+/-) min sup>的条件最小化结构的逻辑动态过程的方法Sub> AND ± Sup> [m i Sub>] f(+/-) min Sub>在功能添加结构中± Sup> f < Sub> 1 Sub>(Σ RU Sub>) min Sub>,不带纹波f 1 Sub>(± Sup>←←)和循环ΔtΣ Sub>→5∙f(&)-和5个条件逻辑函数f(&)-,并通过三元数系统的算术公理同时转换术语参数的过程f RU Sub>(+ 1,0,-1)及其实现其的功能结构(俄罗斯逻辑版本)