Extending Constructive Logic Negation with Types

Negation has traditionally been a difficult issue in Logic Programming. Most of Prolog programmers have been restricted to use just a weak negation technique, like negation as failure.Many alternative semantics were proposed for achieving constructive negation in the last 20 years, but no implementation was provided so far because of its exponential complexity and the difficulty for developing it. First effective implementations of constructive negation into standard Prolog compilers are available just recently, around 2003, provided by our previous works.In this paper we present an extension of our implementations by introducing types in programs, thus improving usability as well as efficiency in some cases of our implementations of constructive negation. This can make constructive negation an interesting approach for its use in data bases querying, web search, filtered search, ontologies querying, coding rules, business rules, etc.Thanks to the use of types, our constructive negation can provide concrete values as results, instead of constraints (as in our previous works). We provide details about the semantics and the implementation in our approaches of classical, finite constructive, and intensional negation. The paper also includes some practical examples additionally allowing for providing measurements of computational behavior.