Restricted Predicates for Hypothetical Datalog

TL;DR

This paper introduces restricted predicates in Hypothetical Datalog, enabling negative assumptions by pruning predicate semantics, and implements this concept in the DES deductive system.

Contribution

It proposes a novel concept of restricted predicates for Hypothetical Datalog, allowing negative assumptions, and provides an implementation in the DES system.

Findings

Restricted predicates enable negative assumptions in Hypothetical Datalog.

Implementation of restricted predicates in the DES system.

Enhanced expressiveness for hypothetical reasoning with negation.

Abstract

Hypothetical Datalog is based on an intuitionistic semantics rather than on a classical logic semantics, and embedded implications are allowed in rule bodies. While the usual implication (i.e., the neck of a Horn clause) stands for inferring facts, an embedded implication plays the role of assuming its premise for deriving its consequence. A former work introduced both a formal framework and a goal-oriented tabled implementation, allowing negation in rule bodies. While in that work positive assumptions for both facts and rules can occur in the premise, negative assumptions are not allowed. In this work, we cover this subject by introducing a new concept: a restricted predicate, which allows negative assumptions by pruning the usual semantics of a predicate. This new setting has been implemented in the deductive system DES.