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  1.  7
    Logics for Multi-Subset Spaces.Bernhard Heinemann - 2010 - Journal of Applied Non-Classical Logics 20 (3):219-240.
    We generalize Moss and Parikh's logic of knowledge, effort, and topological reasoning, in two ways. We develop both a multi-agent and a multi-method setting for it. In each of these cases, we prove a corresponding soundness and completeness theorem, and we show that the new logics are decidable. Our methods of proof rely on those for the original system. This might have been expected, since that system is conservatively extended for the given situation. Several technical details are different nevertheless here.
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  2.  32
    A Hybrid Logic for Reasoning About Knowledge and Topology.Bernhard Heinemann - 2008 - Journal of Logic, Language and Information 17 (1):19-41.
    We extend Moss and Parikh’s bi-modal system for knowledge and effort by means of hybrid logic. In this way, some additional concepts from topology related to knowledge can be captured. We prove the soundness and completeness as well as the decidability of the extended system. Special emphasis will be placed on algebras.
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  3.  4
    Topological Modal Logics Satisfying Finite Chain Conditions.Bernhard Heinemann - 1998 - Notre Dame Journal of Formal Logic 39 (3):406-421.
    We modify the semantics of topological modal logic, a language due to Moss and Parikh. This enables us to study the corresponding theory of further classes of subset spaces. In the paper we deal with spaces where every chain of opens fulfils a certain finiteness condition. We consider both a local finiteness condition relevant to points and a global one concerning the whole frame. Completeness of the appearing logical systems, which turn out to be generalizations of the well-known modal system (...)
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  4.  6
    Expressive Completeness of Modal Logic on Binary Ramified Frames.Bernhard Heinemann - 1996 - Journal of Applied Non-Classical Logics 6 (4):347-367.
    ABSTRACT We characterize those binary ramified frames for which propositional modal logic is as expressive as the corresponding first-order logic.
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  5.  5
    On Binary Computation Structures.Bernhard Heinemann - 1997 - Mathematical Logic Quarterly 43 (2):203-215.
  6.  8
    Reusing Topological Nexttime Logic.Bernhard Heinemann - 2020 - Studia Logica 108 (6):1207-1234.
    In this paper, a particular extension of the constitutive bi-modal logic for single-agent subset spaces will be provided. That system, which originally was designed for revealing the intrinsic relationship between knowledge and topology, has been developed in several directions in recent years, not least towards a comprehensive knowledge-theoretic formalism. This line is followed here to the extent that subset spaces are supplied with a finite number of functions which shall represent certain knowledge-enabling actions. Due to the corresponding functional modalities, another (...)
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  7.  25
    Using Hybrid Logic for Coping with Functions in Subset Spaces.Bernhard Heinemann - 2010 - Studia Logica 94 (1):23-45.
    We extend Moss and Parikh’s modal logic for subset spaces by adding, among other things, state-valued and set-valued functions. This is done with the aid of some basic concepts from hybrid logic. We prove the soundness and completeness of the derived logics with regard to the class of all correspondingly enriched subset spaces, and show that these logics are decidable.
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