Logic for physical space: From antiquity to present days

Marco Aiello, Guram Bezhanishvili, Isabelle Bloch, Valentin Goranko

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    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 in the logical representation of space and investigate current trends. In doing so, we do not only consider classical logic, but we indulge ourselves with modal logics. These present themselves naturally by providing simple axiomatizations of different geometries, topologies, space-time causality, and vector spaces.
    Original languageEnglish
    JournalSynthese
    Volume186
    Issue number3
    Pages (from-to)619-632
    ISSN0039-7857
    DOIs
    Publication statusPublished - 2012

    Keywords

    • Modal logic
    • Geometry
    • Topology
    • Mathematical morphology

    Cite this

    Aiello, M., Bezhanishvili, G., Bloch, I., & Goranko, V. (2012). Logic for physical space: From antiquity to present days. Synthese, 186(3), 619-632. https://doi.org/10.1007/s11229-011-9913-9