Syntactic Requirements for Well-defined Hybrid Probabilistic Logic Programs

Abstract

Hybrid probabilistic logic programs can represent several scenarios thanks to the expressivity of Logic Programming extended with facts representing discrete and continuous distributions. The semantics for this type of programs is crucial since it ensures that a probability can be assigned to every query. Here, following one recent semantics proposal, we illustrate a concrete syntax, and we analyse the syntactic requirements needed to preserve the well-definedness.

Explanations as Programs in Probabilistic Logic Programming

“…In this work, we assume that the Herbrand universe is finite (and coincides with the domain C of constants) and, thus, the set of ground instances of each probabilistic fact is finite. 4 Given a program P, we let G(P) denote the set of its ground probabilistic facts (after grounding nonground probabilistic and intensional facts, if any). An atomic choice determines whether a ground probabilistic fact is chosen or not.…”

“…In practice, range-restrictedness is often required for ensuring that all probabilistic facts become eventually ground in an SLD derivation, where a program is range-restricted if all variables in the head of a clause also appear in some atom of the body [28]. Moreover, one can still allow some probabilistic facts with nonground arguments (which are not range-restricted) as long as they are called with a ground term in these arguments; see [4,Theorem 1]. A similar condition is required in ProbLog, where a program containing a probabilistic fact of the form 0.6::p(X) is only acceptable if the query bounds variable X, e.g., p(a).…”