Generalised Kernel Sets for Inverse Entailment

Oliver Ray, Krysia Broda, Alessandra Russo, Bart Demoen, Vladimir Lifschitz

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

3 Citations (Scopus)


The task of inverting logical entailment is of central importance to the disciplines of Abductive and Inductive Logic Programming (ALP & ILP). Bottom Generalisation (BG) is a widely applied approach for Inverse Entailment (IE), but is limited to deriving single clauses from a hypothesis space restricted by Plotkin’s notion of C-derivation. Moreover, known practical applications of BG are confined to Horn clause logic. Recently, a hybrid ALP-ILP proof procedure, called HAIL, was shown to generalise existing BG techniques by deriving multiple clauses in response to a single example, and constructing hypotheses outside the semantics of BG. The HAIL proof procedure is based on a new semantics, called Kernel Set Subsumption (KSS), which was shown to be a sound generalisation of BG. But so far KSS is defined only for Horn clauses. This paper extends the semantics of KSS from Horn clause logic to general clausal logic, where it is shown to remain a sound extension of BG. A generalisation of the C-derivation, called a K*-derivation, is introduced and shown to provide a sound and complete characterisation of KSS. Finally, the K*-derivation is used to provide a systematic comparison of existing proof procedures based on IE.
Translated title of the contributionGeneralised Kernel Sets for Inverse Entailment
Original languageEnglish
Title of host publication20th International Conference on Logic Programming
Publication statusPublished - 2004

Bibliographical note

Other page information: 165-179
Conference Proceedings/Title of Journal: 20th International Conference on Logic Programming
Other identifier: 2000714


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