Elvira Pino

Institutions for logic programming

Abstract The compositionality of the semantics of logic programs with respect to (different varieties of) program union has been studied recently by a number of researchers. The approaches used can be considered quite ad hoc in the sense that they provide, from scratch, the semantic constructions needed to ensure compositionality and, in some cases, full abstraction in the given framework. In this paper, we study the application of general algebraic methods for obtaining, systematically, this kind of results. In particular, the method proposed consists in studying the adequate institution for describing the given class of logic programs and, then, in using general institution-independent results to prove compositionality and full abstraction. This is done in detail for the class of definite logic programs with respect to three kinds of composition operations: Ω-union, standard union and module composition. In addition two different institutions are considered: the standard institution of Horn clause logic and a new institution that better captures the input/output operational behaviour of logic programs. Finally, a similar solution is sketched for other classes of logic programs.

A Functorial Framework for Constraint Normal Logic Programming

The semantic constructions and results for definite programs do not extend when dealing with negation. The main problem is related to a well-known problem in the area of algebraic specification: if we fix a constraint domain as a given model, its free extension by means of a set of Horn clauses defining a set of new predicates is semicomputable. However, if the language of the extension is richer than Horn clauses its free extension (if it exists) is not necessarily semicomputable. In this paper we present a framework that allows us to deal with these problems in a novel way. This framework is based on two main ideas: a reformulation of the notion of constraint domain and a functorial presentation of our semantics. In particular, the semantics of a logic program P is defined in terms of three functors:

Semantics of Normal Logic Programs with Embedded Implications

({\mathcal {OP}}_{P} ,{\mathcal {ALG}}_{P} ,{\mathcal {LOG}}_{P})

A transformational semantics of static embedded implications of normal logic programs

that apply to constraint domains and provide the operational, the least fixpoint and the logical semantics of P, respectively. To be more concrete, the idea is that the application of

On the integration of modular heterogeneous specifications

{\mathcal {OP}}_{P}

Algebraic Methods in the Compositional Analysis of Logic Programs

to a specific constraint solver provides the operational semantics of P that uses this solver; the application of

Semantics of structured normal logic programs

{\mathcal {ALG}}_{P}

Towards a Navigational Logic for Graphical Structures

to a specific domain provides the least fixpoint of P over this domain; and, the application of

Satisfiability of Constraint Specifications on XML Documents

{\mathcal {LOG}}_{P}

A General Algebraic Framework for Studying Modular Systems

to a theory of constraints provides the logic theory associated to P. In this context, we prove that these three functors are in some sense equivalent.