A declarative semantics for CLP with qualification and proximity

Abstract

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 report we propose a new scheme SQ-CLP 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.

On the Incorporation of Interval-Valued Fuzzy Sets into the Bousi-Prolog System: Declarative Semantics, Implementation and Applications

“…Proximity-based Logic Programming is a framework that provides us with the capability of enriching semantically classical logic programming languages by using Proximity Equations (PEs). A limitation of this approach is that PEs are mostly defined for a specific domain [6,23], being the designer who manually fixes the values of these equations. This fact makes harder to use PLP systems in real applications.…”

A Transformation-based implementation for CLP with qualification and proximity

“…Examples include three basic qualification domains that are stable, namely the qualification domain B of classical boolean values, the qualification domain U of uncertainty values and the qualification domain W of weight values. Moreover, Theorem 2.1 of Rodríguez-Artalejo and Romero-Díaz (2010b) shows that the ordinary cartesian product D 1 × D 2 of two qualification domains is again a qualification domain, while the strict cartesian product D 1 ⊗ D 2 of two stable qualification domains is a stable qualification domain.…”

Dedekind–MacNeille completion and Cartesian product of multi-adjoint lattices

“…In order to illustrate these ideas, let us consider now the so-called domain of weight values W used in the Qualified Logic Programming (QLP) framework of [3,[28][29][30], whose elements are intended to represent proof costs (as we will explain in Section 5), measured as the weighted depth of proof trees. In essence, W can be seen as lattice (N ∪ {∞}, ≥), where ≥ is the reverse of the usual numerical ordering (with ∞ ≥ d for any d ∈ N) and thus, the bottom element is ∞ and the top element is 0.…”