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  1.  71
    Negation in the Context of Gaggle Theory.J. Michael Dunn & Chunlai Zhou - 2005 - Studia Logica 80 (2-3):235-264.
    We study an application of gaggle theory to unary negative modal operators. First we treat negation as impossibility and get a minimal logic system Ki that has a perp semantics. Dunn 's kite of different negations can be dealt with in the extensions of this basic logic Ki. Next we treat negation as “unnecessity” and use a characteristic semantics for different negations in a kite which is dual to Dunn 's original one. Ku is the minimal logic that has a (...)
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  2. Belief Functions on Distributive Lattices.Chunlai Zhou - 2013 - Artificial Intelligence 201 (C):1-31.
  3.  68
    Probability Logic of Finitely Additive Beliefs.Chunlai Zhou - 2010 - Journal of Logic, Language and Information 19 (3):247-282.
    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 (...)
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  4.  10
    Properties of Intuitionistic Provability and Preservativity Logics.Rosalie Iemhoff, Dick de Jongh & Chunlai Zhou - 2005 - Logic Journal of the IGPL 13 (6):615-636.
    We study the modal properties of intuitionistic modal logics that belong to the provability logic or the preservativity logic of Heyting Arithmetic. We describe the □-fragment of some preservativity logics and we present fixed point theorems for the logics iL and iPL, and show that they imply the Beth property. These results imply that the fixed point theorem and the Beth property hold for both the provability and preservativity logic of Heyting Arithmetic. We present a frame correspondence result for the (...)
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