Quantitative Logic Programming Revisited

Uncertainty in Logic Programming has been investigated since about 25 years, publishing papers dealing with various approaches to semantics and different applications. This paper is intended as a first step towards the investigation of uncertainty in Constraint Functional Logic Programming. We revise an early proposal, namely van Emden’s

Quantitative Logic Programming

[22], and we improve it in two ways. Firstly, we generalize van Emden’s

QLP

to a generic scheme

$QLP{\mathcal{(D)}}$

parameterized by any given

Qualification Domain

$\mathcal{D}$

, which must be a lattice satisfying certain natural axioms. We present several interesting instances for

$\mathcal{D}$

, one of which corresponds to van Emden’s

QLP

. Secondly, we generalize van Emden’s results by providing stronger ones, concerning both semantics and goal solving. We present

Qualified SLD

Resolution

over

$\mathcal{D}$

, a sound and strongly complete goal solving procedure for

$QLP{\mathcal{(D)}}$

, which is applicable to open goals and can be efficiently implemented using

CLP

technology over any constraint domain

$\mathcal C_{D}$

able to deal with qualification constraints over

$\mathcal{D}$

. We have developed a prototype implementation for van Emden’s

QLP

as an instance of

$QLP{\mathcal (D)}$

, on top of the

CFLP

system

$\mathcal{TOY}$

.