Constraint Logic Programming (CLP) and Hereditary Harrop formulas (HH) are two well
known ways to enhance the expressivity of Horn clauses. In this paper, we present a novel
combination of these two approaches. We show how to enrich the syntax and proof theory of
HH with the help of a given constraint system, in such a way that the key property of HH as
a logic programming language (namely, the existence of uniform proofs) is preserved. We also
present a procedure for goal solving, showing its soundness and completeness for computing
answer constraints. As a consequence of this result, we obtain a new strong completeness
theorem for CLP that avoids the need to build disjunctions of computed answers, as well as
a more abstract formulation of a known completeness theorem for HH.
This paper is focused on a double extension of traditional Logic Programming which enhances it following two different approaches. On one hand, extending Horn logic to hereditary Harrop formulas (HH ), in order to improve the expressive power; on the other, incorporating constraints, in order to increase the efficiency. For this combination, called HH(C), an operational semantics exists, but no declarative semantic for it has been defined so far.One of the main features of (Constraint) Logic Programming is that the algorithmic behavior of (constraint) logic programs and its mathematical interpretations agree with each other, in the sense that the declarative meaning of a program can be interpreted operationally as a goal-oriented search for solutions. Both operational (algorithmic) and declarative (mathematical) semantics for programs are useful and widely developed in the frame of Logic Programming as well as in its extension, Constraint Logic Programming.For these reasons, HH(C) was in need of a more mathematical interpretation of programs. In this paper some fixed point semantics for HH(C) are presented. Taking as a starting point the techniques used by Miller to interpret the fragment of HH that incorporates intuitionistic implication in goals, we have formulated two novel extensions capable of dealing with the whole HH logic, including universal quantifiers, as well as with the presence of constraints. Those semantics are proved to be sound and complete w.r.t. the operational semantics of HH(C).
Current database systems supporting recursive SQL impose restrictions on queries such as linearity, and do not implement mutual recursion. In a previous work we presented the language and prototype R-SQL to overcome those drawbacks. Now we introduce a formalization and an implementation of the database system HR-SQL that, in addition to extended recursion, incorporates hypothetical reasoning in a novel way which cannot be found in any other SQL system, allowing both positive and negative assumptions. The formalization extends the fixpoint semantics of R-SQL. The implementation improves the efficiency of the previous prototype and is integrated in a commercial DBMS.
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