Semantical foundations of spatial logics
Oliver Lemon · 1996
We explore several "spatial" logics and investigate their credentials as logics of space or of spatial objects and relations. A semantical adequacy criterion for spatial logics is developed, according to which a logic is spatial only if consistent theories in that logic are realizable in a standard model of space. Various (so-called) spatial logics are shown not to satisfy this criterion. In effect, these observations amount to incompleteness results for classes of spatial logics, because they show that consistent sets of formulae in these logics have no models of the intended sort. In addition, we present a complete axiomatization of space; a modal logic of connected regions of the plane. 1 MOTIVATION In recent years there has been much interest in logics of space (eg: [Randell et al., 1992, Gotts et al., 1996, Asher and Vieu, 1995, Bennett, 1995]). Different research programmes have developed from work (eg: [Tarski, 1956, Whitehead, 1929, Clarke, 1981, Clarke, 1985]) on logic and m...