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  1. The Modal Logic of Affine Planes is Not Finitely Axiomatisable.Ian Hodkinson & Altaf Hussain - 2008 - Journal of Symbolic Logic 73 (3):940-952.
    We consider a modal language for affine planes, with two sorts of formulas (for points and lines) and three modal boxes. To evaluate formulas, we regard an affine plane as a Kripke frame with two sorts (points and lines) and three modal accessibility relations, namely the point-line and line-point incidence relations and the parallelism relation between lines. We show that the modal logic of affine planes in this language is not finitely axiomatisable.
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  • Line-Based Affine Reasoning in Euclidean Plane.Philippe Balbiani & Tinko Tinchev - 2007 - Journal of Applied Logic 5 (3):421-434.
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  • Correspondence Between Kripke Frames and Projective Geometries.Shengyang Zhong - 2018 - Studia Logica 106 (1):167-189.
    In this paper we show that some orthogeometries, i.e. projective geometries each defined using a ternary collinearity relation and equipped with a binary orthogonality relation, which are extensively studied in mathematics and quantum theory, correspond to Kripke frames, each defined using a binary relation, satisfying a few conditions. To be precise, we will define four special kinds of Kripke frames, namely, geometric frames, irreducible geometric frames, complete geometric frames and quantum Kripke frames; and we will show that they correspond to (...)
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  • On the Axiomatizability of Some First-Order Spatio-Temporal Theories.Sándor Vályi - 2015 - Synthese 192 (7):1-17.
    Spatio-temporal logic is a variant of branching temporal logic where one of the so-called causal relations on spacetime plays the role of a time flow. Allowing only rational numbers as space and time co-ordinates, we prove that a first-order spatio-temporal theory over this flow is recursively enumerable if and only if the dimension of spacetime does not exceed 2. The situation is somewhat different compared to the case of real co-ordinates, because we establish that even dimension 2 does not permit (...)
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  • A Spatial Modal Logic with a Location Interpretation.Norihiro Kamide - 2005 - Mathematical Logic Quarterly 51 (4):331.
    A spatial modal logic is introduced as an extension of the modal logic S4 with the addition of certain spatial operators. A sound and complete Kripke semantics with a natural space interpretation is obtained for SML. The finite model property with respect to the semantics for SML and the cut-elimination theorem for a modified subsystem of SML are also presented.
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  • Logic for Physical Space: From Antiquity to Present Days.Marco Aiello, Guram Bezhanishvili, Isabelle Bloch & Valentin Goranko - 2012 - Synthese 186 (3):619-632.
    Since the early days of physics, space has called for means to represent, experiment, and reason about it. Apart from physicists, the concept of space has intrigued also philosophers, mathematicians and, more recently, computer scientists. This longstanding interest has left us with a plethora of mathematical tools developed to represent and work with space. Here we take a special look at this evolution by considering the perspective of Logic. From the initial axiomatic efforts of Euclid, we revisit the major milestones (...)
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