Reflection principles in computational logic

Abstract

We introduce the concept of reflection principle as a knowledge representation paradigm in a computational logic setting. Reflection principles are expressed as certain kinds of logic schemata intended to capture the basic properties of the domain knowledge to be modelled. Reflection is then used to instantiate these schemata to answer specific queries about the domain. This differs from other approaches to reflection mainly in the following three ways. First, it uses logical instead of procedural reflection. Second, it aims at a cognitively adequate declarative representation of various forms of knowledge and reasoning, as opposed to reflection as a means for controlling computation or deduction. Third, it facilitates the building of a complex theory by allowing a simpler theory to be enhanced by a compact metatheory, contrary to the construction of metatheories that are only conservative extensions of the basic theory. A computational logic system for embedding reflection principles, called RCL (for Reflective Computational Logic), is presented in full detail. The system is an extension of Horn clause resolution-based logic, and is devised in a way that makes important features of reflection parametric as much as possible, so that they can be tailored according to specific needs of different application domains. Declarative and procedural semantics of the logic are described and correctness and completeness of reflection as logical inference are proved. Examples of reflection principles for three different application areas are shown. Relationship with a variety of distinct sources within the literature on relevant topics is discussed.

A Praxical Solution of the Symbol Grounding Problem

“…Such an architecture is well-documented in (Barklund et al, 2000;Brazier et al, 1999;Cointe, 1999) and the interested reader may wish to consult those works for a more in-depth description.…”

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

“…The articles Barklund et al (1995a), Barklund et al (1995b), and Barklund et al (2000) generalize Reflective Prolog (Costantini and Lanzarone 1989;1994) into a metalanguage similar in spirit to LF (Harper et al 1993), Elf (Pfenning 1991), and Twelf (Pfenning and Schürmann 1999) which offers a sublanguage for expressing various kinds of naming relations (or encodings), primitives for handling naming relations, and a metalanguage of Horn clauses for expressing object-level inference rules. The article Barklund et al (1995a) considers eight previously proposed naming relations (or encodings) that are compositional in the sense that the name of a compound expression is built from its components' names.…”

“…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).…”

Elio Lanzarone: a life for science

“…Reflective Prolog principles were generalized, and finally evolved into the RCL (Reflective Computational Logic) logical framework [4,5,7]-this was joint work with Jonas Barklund, at the time Supervisor of Pierangelo's PhD thesis at the University of Uppsala, Sweden. In fact, the implicit reflection of Reflective Prolog has a semantic counterpart [11] in adding to the given theory a set of new axioms called reflection axioms, according to axiom schemata called reflection principles.…”