The CHR-based Implementation of the SCIFF Abductive System

Abstract

Abduction is a form of inference that supports hypothetical reasoning and has been applied to a number of domains, such as diagnosis, planning, protocol verification. Abductive Logic Programming (ALP) is the integration of abduction in logic programming. Usually, the operational semantics of an ALP language is defined as a proof procedure.The first implementations of ALP proof-procedures were based on the meta-interpretation technique, which is flexible but limits the use of the built-in predicates of logic programming systems. Another, more recent, approach exploits theoretical results on the similarity between abducibles and constraints. With this approach, which bears the advantage of an easy integration with built-in predicates and constraints, Constraint Handling Rules has been the language of choice for the implementation of abductive proof procedures. The first CHR-based implementation mapped integrity constraints directly to CHR rules, which is an efficient solution, but prevents defined predicates from being in the body of integrity constraints and does not allow a sound treatment of negation by default.In this paper, we describe the CHR-based implementation of the SCIFF abductive proof-procedure, which follows a different approach. The SCIFF implementation maps integrity constraints to CHR constraints, and the transitions of the proof-procedure to CHR rules, making it possible to treat default negation, while retaining the other advantages of CHR-based implementations of ALP proofprocedures.

Constraint Handling Rules - What Else?

“…Its application FLUXPLAYER [109] won the General Game Playing competition at the AAAI conference in 2006. SCIFF is a framework to specify and verify interaction in open agent societies [13,15]. The SCIFF language is equipped with a semantics based on abductive logic programming.…”

Peirce: an Algorithm for Abductive Reasoning Operating with a Quaternary Reasoning Framework

“…The theory set T and the fact set F satisfy condition (1), whereas a theory T 1 = { r → w, s → w, w } has F as its logical consequence; therefore T 1 and F do not satisfy condition (1). Let H = { r, s, r ∧ s, r ∧ w, w } be a set of candidate hypotheses.…”

“…The conditions in abductive reasoning are motivated by several factors which are linked to context (information associated to space), circumstances (information associated with time), intention (manifestation of the will to reach some wanted conclusions), belief or faith (information that is accepted on principle) etc. Examples of specific conditions used in abductive reasoning are as follows: (1) In abductive reasoning used for medical diagnoses, regional context may allow one to specify a set of diseases that are common or uncommon for a given region; (2) In abductive reasoning used for anthropological studies, the specification of possible agents that might have been responsible for the death of a hominid based on the knowledge that the hominid lived 4 million years ago (circumstance); (3) In abductive reasoning for judicial decisions, possible conditions may be specified with the intent of acquitting (or condemning) a defendant; and (4) In abductive reasoning for religious or metaphysical beliefs, the faith or belief that there is life after death can be declared as a condition upon which reasoning are made.…”

“…Let A = { a 1 , a 2 , a 3 , ..., a n } and B = { b 1 , b 2 , b 3 , ..., b m } be two finite and non-empty sets of PL sentences. Then, A ⊨ B if and only if the interpretations in which a 1 ∧ a 2 ∧ a 3 ∧... ∧ a n is true, b 1…”

“…The condition (1) prevents that the theory set T alone has as logical consequence the facts set F. Hypotheses satisfying condition (2) are called candidate hypotheses, and they can explain the single fact denoted by F. Candidate hypotheses satisfying condition (3) are called consistent hypotheses. Conversely, candidate hypotheses that do not satisfy condition (3) are called inconsistent hypotheses and should be discarded.…”