A Declarative Semantics for CLP with Qualification and Proximity

Uncertainty in Logic Programming has been investigated during the last decades, dealing with various extensions of the classical LP paradigm and different applications. Existing proposals rely on different approaches, such as clause annotations based on uncertain truth values, qualification values as a generalization of uncertain truth values, and unification based on proximity relations. On the other hand, the CLP scheme has established itself as a powerful extension of LP that supports efficient computation over specialized domains while keeping a clean declarative semantics. In this paper we propose a new scheme SQCLP designed as an extension of CLP that supports qualification values and proximity relations. We show that several previous proposals can be viewed as particular cases of the new scheme, obtained by partial instantiation. We present a declarative semantics for SQCLP that is based on observables, providing fixpoint and proof-theoretical characterizations of least program models as well as an implementation-independent notion of goal solutions.

💡 Research Summary

The paper introduces SQCLP, a novel extension of the Constraint Logic Programming (CLP) paradigm that integrates two orthogonal notions of uncertainty: qualification values and proximity relations. Qualification values generalize traditional truth‑value annotations by allowing each atom to carry a value drawn from an arbitrary lattice (the Q‑domain) equipped with a partial order and a binary combination operator ⊗. This structure can model diverse metrics such as confidence, cost, or time, and supports the simultaneous handling of several criteria. Proximity relations replace the classical syntactic equality used in unification with a semantic similarity function 𝜃: Σ × Σ →