A metalogic programming approach: language, semantics and applications

Abstract

This paper presents a logic programming language of novel conception, called Reflective Prolog, which allows declarative metaknowledge representation and metareasoning. The language is defined by augmenting pure Prolog (Horn clauses) with capabilities of self-reference and logical reflection. Self-reference is designed as a quotation device (a carefully defined naming relation) which allows the construction of metalevel terms that refer to object-level terms and atoms. Logical reflection is designed as an unquotation mechanism (a distinguished truth predicate) which relates names to what is named, thus extending the meaning of domain predicates. The reflection mechanism is embodied in an extended resolution procedure which automatically switches the context between levels. This implicit reflection relieves the programmer from having to explicitly deal with control aspects of the inference process. The declarative semantics of a Reflective Prolog definite program P is provided in terms of the least reflective Herbrand model of P, characterized by means of a suitable mapping defined over the Herbrand interpretations of P. The extended resolution is proved sound and complete with respect to the least reflective Herbrand model. By illustrating Reflective Prolog solutions to an organic set of problems, and by discussing the main differences with respect to other approaches to logic metaprogramming, we show that the proposed language deploys, within its field of action, greater expressive and inferential power than those available till now. The interpreter of the language has been fully implemented. Because of its enhanced power, logic semantics and working interpreter, Reflective Prolog is offered as a contribution toward making the declarative approach of logic programming applicable to the development of increasingly sophisticated knowledge-based systems.

Reflection principles in computational logic

“…In this and the following sections, we present a formalization of the proposed concept of reflection which should constitute a simple way of understanding reflective programs as well as a description of how reflection allows one to uniformly treat different application areas. The applications of reflection that we have previously studied (and reported in detail elsewhere [20,24,25]) are instances of the new formalization. Thus we are able to present them as case studies and show how RCL can constitute a uniform framework for several problem domains.…”

“…Formulae of the metalevel express some kind of syntactic or semantic properties of object formulae (as outlined in the simple examples above), and thus express some kind of metaknowledge, that can be used in deduction in various ways, thus performing metareasoning. The reader may refer to [2,3,24] for a discussion about possible uses of metaknowledge and metareasoning.…”

“…Therefore, in Reflective Prolog, language and metalanguage are amalgamated in a non-conservative extension, though avoiding semantic problems. Reflective Prolog has been proposed as an enhanced knowledge-representation language [24].…”

Elio Lanzarone: a life for science

“…The main joint achievement by Elio and Stefania has been the definition of Reflective Prolog [11,14,16]. The objective of this approach was that of developing a more expressive and powerful logic programming language, while preserving the essential features of logic programming: Horn clause syntax, model-theoretic semantics, resolution via unification as procedural semantics, correctness and completeness properties.…”

Annotated RDF

“…This is much like the case of metalogics where each logical sentence has a "name" and metalevel statements use the name as a first class object in formulas. Reflection principles are used to tie a sentence and its name together [Costantini and Lanzarone 1994]. To date, there is no single mechanism for integrating RDF and metalevel statements about RDF in a practically usable and theoretically clean framework.…”