An Implementation of the IFF Procedure in DALI

Abductive Logic Programming (ALP) [11] [12] has found broad application as a powerful tool for hypothetical reasoning with incomplete knowledge, as it combines: abduction, that operates by labeling some pieces of information as abducibles, i.e. as possible hypotheses which can be assumed to hold, provided that they are consistent with the given knowledge base; and logic programming, enriched with integrity constraints to further restrict the range of possible hypotheses. In recent years, a variety of proof procedures for ALP have been proposed. A very important one is the IFF procedure of Fung and Kowalski [8]. Among the other proposals, the ACLP procedure [13] integrates abductive reasoning with constraint solving. Some recent procedures are explicitly aimed at improving the IFF. The CIFF [7] procedure is aimed at providing increasing generality on the kind of constraints that can be expressed, also in view of the definition of logical agents and multi-agent systems. On the same line, in the SCIFF procedure [1] abducibles represent hypotheses about agent behaviour; SCIFF deals with the concept of fulfillment, i.e., the correspondence of abduced atoms with events (that a logical agent has perceived) recorded in a history. All these procedures are sound, but have problems with completeness, which is not achieved for the general case. In this paper, we present a novel implementation of the IFF proof procedure. The approach of this paper is indebted to [6], that proposes some abstract argumentationbased proof procedures for assumption-based reasoning (of which abduction is an instance) building on the stable model semantics of [9]. We overcome completeness problems and obtain a correct and complete implementation by adopting a completely different novel approach. Rather that re-implementing the procedure in fact, we translate an ALP program into other formalisms, of which we exploit the inference engines. In particular, our proposal relies upon: Answer Set Programming (ASP), which is a new logic programming paradigm [14] the Answer Set (or equivalently Stable Model) semantics [9]; and the new logic programming language DALI [3] [16], which provides special proactive features, so that one can specify conditions that are to be automatically checked. Precisely, a given ALP program is (automatically) translated into: (i) an ASP program, that generates a superset of the abductive explanations (that are the expected results of the ALP program) and (ii) a DALI program that rules out incorrect solutions. Due to the proactive features of DALI, there is no need of defining a meta-interpreter: rather, the different conditions of each IFF rule are checked concurrently (and, potentially, in parallel) by means of the special DALI mechanism of internal events.