On the declarative and procedural semantics of definite metalogic programs

Abstract

We present a declarative and procedural semantics for an amalgamation of object language and metalanguage. We define the class of definite metalogic programs, based on a definite clause language, a binary demonstration predicate, and a naming scheme with both primitive and structured names. The declarative semantics is an extension of the semantics of logic programs dealing with multiple theories and names. The procedural semantics uses a resolution rule and a meta-level to object-level reflection rule.

In Praise of Impredicativity: A Contribution to the Formalization of Meta-Programming

“…If the encoding is efficiently invertible, then adjustments to the deduction methods suffice to implement a language that handles meta-programs by relying on naming relations. metaProlog (Bowen 1985;Bowen and Weinberg 1985), MOL (Eshghi 1986), the language proposed by Barklund in the article Barklund (1989), Reflective Prolog (Costantini and Lanzarone 1989;1994), R-Prolog * (Sugano 1989;, and the language proposed by Higgins in the article Higgins (1996) have efficiently invertible naming relations. 'LOG (Cervesato and Rossi 1992) and Gödel (Hill and Lloyd 1994) do not have invertible naming relations.…”

“…The article van Harmelen (1992) argues that naming relations can encode, together with an object formula, pragmatic and semantic information resulting in a more efficient (meta-language) version of the original formula. Naming relations have indeed been defined for achieving such "compilations" what explains their large number and, as a consequence, the large number of formalizations of meta-programming in first-order logic: metaProlog (Bowen 1985;Bowen and Weinberg 1985), MOL (Eshghi 1986), the language proposed by Barklund in the article Barklund (1989), Reflective Prolog (Costantini and Lanzarone 1989;Costantini and Lanzarone 1994), R-Prolog * (Sugano 1989;Sugano 1990), 'LOG (spoken "quotelog") (Cervesato and Rossi 1992), Gödel (Hill and Lloyd 1994), the language proposed by Higgins in the article Higgins (1996), and the generalization of Reflective Prolog proposed in the article Barklund et al (2000).…”

“…Higgins has proposed in the article Higgins (1996) a language relying on two naming relations similar to those of 'LOG associating with every syntactic object a first-order "primitive name" and a first-order "structured name": "We have names of symbols, terms, clauses, and sets of clauses." The procedural semantics of Higgins' language is "a resolution rule and a meta-level to object-level reflection rule."…”

Reflection principles in computational logic

“…Considering in particular the application of the general framework presented in this paper to the field of metalogic languages, Reflective Prolog (Section 6.1) has been compared to the other main approaches in [24]. A more recent approach, not considered there, is that of [39], which is very similar to [24] about the treatment of naming and unification, except for providing multiple theories, and names for theories. Theories are able to exchange formulae that they can prove, by means of a distinguished binary predicate demo, appearing explicitly in the body of clauses, and having the name of a theory as the first argument, and the name of a formula as the second argument.…”