Uncertainty Management in Logic Programming: Simple and Effective Top-Down Query Answering

Abstract

Abstract. We present a simple, yet general top-down query answering procedure for logic programs managing uncertainty. The main features are: (i) the certainty values are taken from a certainty lattice; (ii) computable functions may appear in the rule bodies to manipulate certainties; and (iii) we solve the problem by a reduction to an equational systems, for which we device a top-down procedure.

Fuzzy Description Logic Programs

“…Therefore, the minimal model of P coincides with the least fixed-point of Φ P , which can be computed in the usual way by iterating Φ P over I ⊥ . 39,40 Example 2. 23 In Ref.…”

“…Finally, we can rely on a theorem prover for fuzzy LPs only either using a usual bottom-up computation or a top-down computation for logic programs. 23,24,39,40 Of course, one has to be sure that both computations, for the fuzzy DL component and for the fuzzy LP component, are supported. With respect to the logic presented in this paper, we need the reasoning algorithm described in Ref.…”

Approximate well-founded semantics, query answering and generalized normal logic programs over lattices

“…From a computational point of view, the analysis is as in [126,127,129]. Given L = L × L, k , let h(L) be the height of the truth-value set L, i.e.…”

“…Now, observe that the truth of any ground instance of predicate symbol p i is increasing in the k order as p i enters in the A list (step 6), except it enters due to step 7, which may happen one time only. Hence, as for [126,127,129] Proof For each n-ary predicate p consider the unique rule p(x) ← ϕ(x, y) in P. Therefore, for each tuple of constants c, there is an unique rule…”

“…This always requires the computation of a whole model, even if not all the atom's truth is required to determine the answer. some work presenting top-down procedures are [18,60,68,127,140]), but in very few of them non-monotonic negation is considered [126,129], as already pointed out.…”