  Contact algebra is one of the main tools in the region-based theory of space.
It is an extension of Boolean algebra with a relation called contact. The
elements of the Boolean algebra are considered as formal representations of
physical bodies. The contact relation is used also to define some other
important mereotopological relations like non-tangential inclusion, dual
contact, external contact. Most of these definitions are given by means of the
operation of Boolean complementation. There are, however, some problems related
to the motivation of this operation. In order to avoid these problems we
propose a generalization of the notion of contact algebra by dropping the
operation of complement. In this paper we consider as non-definable primitives
the relations of contact, nontangential inclusion and dual contact. Part I of
the paper is devoted to a suitable axiomatization called extended distributive
contact lattice (EDCL) by means of universal first-order axioms true in all
contact algebras. EDCL may be considered also as an algebraic tool for certain
subarea of mereotopology, called in this paper distributive mereotopology. The
main result of Part I of the paper is a representation theorem, stating that
each EDCL can be embedded into a contact algebra, showing in this way that the
presented axiomatization preserves the meaning of mereotopological relations
without considering Boolean complementation. Part II of the paper is devoted to
topological representation theory of EDCL, transferring into the distributive
case important results from the topological representation theory of contact
algebras. It is shown that under minor additional assumptions on distributive
lattices as extensionality of the definable relations of overlap or underlap
one can preserve the good topological interpretations of regions as regular
closed or regular open sets in topological space.
