Volume 7: January - December 1997

Issue 1: 1997

Abstract


Modal logics for incidence geometries

  • Modal logics for incidence geometries
  • P. Balbiani, LF. Del Cerro1, T. Tinchev3 and D. Vakarelov3 1Institut de recherche en informatique de Toulouse, Universite Paul Sabatier, 118 route de Narbonne, F-31062 Toulouse Cedex, France, 2Laboratoire d'informatique de Paris-Nord, Institut Galilee, Universite Paris-Nord, Avenue Jean-Baptiste Clement, F-93430 Villetaneuse, France and 3Department of Mathematical Logic with Laboratory for Applied Logic, Faculty of Mathematics and Informatics, Sofia University, Boul. James Boucher 5, 1126 Sofia, Bulgaria

    ABSTRACT

    Incidence geometry is based on two-sorted structures consisting of 'point' and 'lines' together with an intersort binary relation called incidence. We introduce an equivalent one-sorted geometrical structure, called incidence frame, which is suitable for modal considerations. Incidence frames constitute the semantical basis of MIG, the modal logic of incidence geometry. A completeness theorem for MIG is proved: a modal formula is a theorem of MIG if and only if it is valid in all incidence frames. Extensions to projective and affine geometries are also considered.

    Keywords: incidence geometry, modal logic, irreflexivity, rule.

    Pages: 59 - 78

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