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Darko Sarenac [5]D. Sarenac [4]
  1. Johan van Benthem & Darko Sarenac, The Geometry of Knowledge.
    The most widely used attractive logical account of knowledge uses standard epistemic models, i.e., graphs whose edges are indistinguishability relations for agents. In this paper, we discuss more general topological models for a multi-agent epistemic language, whose main uses so far have been in reasoning about space. We show that this more geometrical perspective affords greater powers of distinction in the study of common knowledge, defining new collective agents, and merging information for groups of agents.
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  2. J. Van Benthem, G. Bezhanishvili, B. Ten Cate & D. Sarenac (forthcoming). Modal Logics for Products of Topologies. Studia Logica. To Appear.
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  3. J. Van Benthem, G. Bezhanishvili, B. Ten Cate & D. Sarenac (2006). Multimodal Logics of Products of Topologies. Studia Logica 84 (3):369 - 392.
    We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion ${\bf S4}\oplus {\bf S4}$ . We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies. We prove that both of these logics are complete for the product of rational numbers ${\Bbb Q}\times {\Bbb Q}$ (...)
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  4. J. van Benthem, G. Bezhanishvili, B. ten Cate & D. Sarenac (2006). Multimo Dal Logics of Products of Topologies. Studia Logica 84 (3).
    We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion S4 ⊕ S4. We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies.We prove that both of these logics are complete for the product of rational numbers ℚ × ℚ with the appropriate topologies.
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  5. J. van Benthem, G. Bezhanishvili, B. ten Cate & D. Sarenac (2006). Mr2290114 (2007i: 03026) 03b45. Studia Logica 84 (3):369-392.
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  6. Johan van Benthem, Guram Bezhanishvili, Balder Ten Cate & Darko Sarenac (2006). Modal Logics for Product Topologies. Studia Logica 84 (3):375-99.
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  7. Johan van Benthem, Guram Bezhanishvili, Balder ten Cate & Darko Sarenac (2006). Multimo Dal Logics of Products of Topologies. Studia Logica 84 (3):369-392.
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  8. G. E. Mints & Darko Sarenac (2003). Completeness of Indexed Ε-Calculus. Archive for Mathematical Logic 42 (7):617-625.
    Epsilon terms indexed by contexts were used by K. von Heusinger to represent definite and indefinite noun phrases as well as some other constructs of natural language. We provide a language and a complete first order system allowing to formalize basic aspects of this representation. The main axiom says that for any finite collection S 1,…,S k of distinct definable sets and elements a 1,…,a k of these sets there exists a choice function assigning a i to S i for (...)
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