Exploiting lattices in a theory of space and time

Abstract

We outline an axiomatic theory expressed in a first order predicate logic formalism. The theory modifies and extends Bowman Clarke's calculus of individuals. The theory is primarily concerned with a topological description of space and time. From this theory various classification hierarchies are singled out and expressed as lattice structures. The nodes of these lattices correspond to concepts expressed in the theory as monadic predicates, but also concepts expressed using higher arity predicates. We concentrate upon that part of the theory that is used to describe space. The logical structure and interrelationship of these different lattice structures are discussed. Some attention is given to how, by singling out such structures, the theory may be effectively implemented within a resolution-based automated reasoning setting.