{log}: A language for programming in logic with finite sets

An extended logic programming language is presented, that embodies the fundamental form of set designation based on the (nesting) element insertion operator. The kind of sets to be handled is characterized both by adaptation of a suitable Herbrand universe and via axioms. Predicates is an element of and = designating set membership and equality are included in the base language, along with their negative counterparts is not an element of and not equal. A unification algorithm that can cope with set terms is developed and proved correct and terminating. It is proved that by incorporating this new algorithm into SLD resolution and providing suitable treatment of is an element of, not equal, and is not an element of as constraints, one obtains a correct management of the distinguished set predicates. Restricted universal quantifiers are shown to be programmable directly in the extended language and thus are added to the language as a convenient syntactic extension. A similar solution is shown to be applicable to intensional set-formers, provided either a built-in set collection mechanism-or some form of negation in goals and clause bodies is made available.