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  1. Uncertain Inference.Henry E. Kyburg Jr & Choh Man Teng - 2001 - Cambridge University Press.
    Coping with uncertainty is a necessary part of ordinary life and is crucial to an understanding of how the mind works. For example, it is a vital element in developing artificial intelligence that will not be undermined by its own rigidities. There have been many approaches to the problem of uncertain inference, ranging from probability to inductive logic to nonmonotonic logic. Thisbook seeks to provide a clear exposition of these approaches within a unified framework. The principal market for the book (...)
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  • (1 other version)Proof systems for probabilistic uncertain reasoning.J. Paris & A. Vencovska - 1998 - Journal of Symbolic Logic 63 (3):1007-1039.
    The paper describes and proves completeness theorems for a series of proof systems formalizing common sense reasoning about uncertain knowledge in the case where this consists of sets of linear constraints on a probability function.
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  • Probabilistic logic.Nils J. Nilsson - 1986 - Artificial Intelligence 28 (1):71-87.
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  • (1 other version)What does a conditional knowledge base entail?Daniel Lehmann & Menachem Magidor - 1992 - Artificial Intelligence 55 (1):1-60.
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  • Some considerations on the logics PFD A logic combining modality and probability.Wiebe van der Hoeck - 1997 - Journal of Applied Non-Classical Logics 7 (3):287-307.
    ABSTRACT We investigate a logic PFD, as introduced in [FA]. In our notation, this logic is enriched with operators P> r(r € [0,1]) where the intended meaning of P> r φ is “the probability of φ (at a given world) is strictly greater than r”. We also adopt the semantics of [FA]: a class of “F-restricted probabilistic kripkean models”. We give a completeness proof that essentially differs from that in [FA]: our “peremptory lemma” (a lemma in PFD rather than about (...)
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  • A completeness proof for adapted probability logic.H. Jerome Keisler - 1986 - Annals of Pure and Applied Logic 31:61-70.
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  • Hyperfinite models of adapted probability logic.H. Jerome Keisler - 1986 - Annals of Pure and Applied Logic 31:71-86.
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  • A probabilistic extension of intuitionistic logic.Z. Ognjanovic & Z. Markovic - 2003 - Mathematical Logic Quarterly 49 (4):415.
    We introduce a probabilistic extension of propositional intuitionistic logic. The logic allows making statements such as P≥sα, with the intended meaning “the probability of truthfulness of α is at least s”. We describe the corresponding class of models, which are Kripke models with a naturally arising notion of probability, and give a sound and complete infinitary axiomatic system. We prove that the logic is decidable.
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