Modal logics of succession for 2-dimensional integral spacetime

Journal of Philosophical Logic 30 (1):1-25 (2001)
We consider the problem of axiomatizing various natural "successor" logics for 2-dimensional integral spacetime. We provide axiomatizations in monomodal and multimodal languages, and prove completeness theorems. We also establish that the irreflexive successor logic in the "standard" modal language (i.e. the language containing □ and ◊) is not finitely axiomatizable
Keywords modal logic  multi-dimensional modal logic  spacetime
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DOI 10.1023/A:1017502425876
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Sara L. Uckelman & Joel Uckelman (2007). Modal and Temporal Logics for Abstract Space–Time Structures. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (3):673-681.

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