### Abstract

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.

Original language | English |
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Title of host publication | 20th International Conference on Logic Programming |

Publisher | Springer |

Publication status | Published - 2004 |

### Bibliographical note

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

Other identifier: 2000714

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## Cite this

Ray, O., Broda, K., Russo, A., Demoen, B., & Lifschitz, V. (2004). Generalised Kernel Sets for Inverse Entailment. In

*20th International Conference on Logic Programming*Springer. http://www.cs.bris.ac.uk/Publications/pub_master.jsp?id=2000714