A formal definition and a sound implementation of analogical reasoning in logic programming

Abstract

A formal model of analogy is introduced in the logic programming setting, and an analogical reasoning program (called DIANA, i.e. Declarative Inference by ANAlogy) is developed in accordance with precise procedural and declarative semantics. Given the source and target domains of analogy as two logic programsPs andPt, together with a specificationS of the analogical correspondence between predicate symbols, atoms involving these symbols are analogically derived fromP=Ps ∪Pt givenS, which are not derivable fromPs orPt orPs ∪Pt alone. In this paper, the requirements of the analogical process are first stated. The declarative semantics of analogy is then given, by defining the least analogical model ofP as an extension of the classical semantics of Horn clauses. A procedural semantics is also described, in terms of an extension of SLD resolution. Both semantics rely on implicit analogical axioms defining the kind of analogical reasoning envisaged. The implementation of DIANA has been done in Reflective Prolog, a metalogic programming language previously developed by the first two authors. It is shown that analogical axioms can be viewed as an instance of reflection axioms used in Reflective Prolog. By exploiting this feature, the implementation of DIANA is argued to be sound w.r.t. the defined semantics. Examples of analogical reasoning in DIANA are also described. By comparison with the AI literature on analogy, it is claimed that this is the first approach which gives a declarative semantics to analogical reasoning, thanks to the possibility of carrying over in this field the basic logic programming concepts.