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Logics with the Qualitative Probability Operator

Zoran Ognjanović, Aleksandar Perović & Miodrag Rašković

Logic Journal of the IGPL 16 (2):105-120 (2008)

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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.details 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 (...) Download Export citation Bookmark 13 citations
On qualitative axiomatizations for probability theory.Louis Narens - 1980 - Journal of Philosophical Logic 9 (2):143 - 151.details In the literature, there are many axiomatizations of qualitative probability. They all suffer certain defects: either they are too nonspecific and allow nonunique quantitative interpretations or are overspecific and rule out cases with unique quantitative interpretations. In this paper, it is shown that the class of qualitative probability structures with nonunique quantitative interpretations is not first order axiomatizable and that the class of qualitative probability structures with a unique quantitative interpretation is not a finite, first order extension of the theory (...) Download Export citation Bookmark 4 citations

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