...information.

This specification is normally given in terms of a set theoretic semantics. As we shall see later, just because valid inferences are precisely characterised, this does not necessarily mean that it is possible to construct an algorithm which will determine whether any inference is valid.

...reflexivity

Everything is connected to itself.

...follows:

For this definition to work properly we actually need some further axioms governing . In particular, existential axioms are needed to fix certain properties of the domain of spatial regions.

...exists.

This may seem odd, since only a limited number of different kinds of inference can be made at any stage in a proof. However, in general one cannot know in advance how many inference steps will be needed to prove some conclusion; so, if we fail to prove a formulae after a certain number of steps, we never know whether it is not a consequence or whether it is a consequence but requires more inference steps to be proved.

...programs.

It is worth noting that the architecture which I shall propose is markedly different to that assumed in the software paradigm known as logic programming (this paradigm is exemplified by the language Prolog --- although some would say that Prolog is far removed from the ideal of a `pure' logic programming language).

A G Cohn
Wed Nov 1 13:20:53 GMT 1995