@INPROCEEDINGS{DelPintoSchmidt19b,
AUTHOR = {Del-Pinto, W. and Schmidt, R. A.},
YEAR = {2019},
TITLE = {Extending Forgetting-Based Abduction Using Nominals},
EDITOR = {Herzig, A. and Popescu, A.},
BOOKTITLE = {Proceedings of the 12th International Symposium on Frontiers of Combining Systems (FroCoS 2019)},
SERIES = {Lecture Notes in Artificial Intelligence},
VOLUME = {11715},
PUBLISHER = {Springer},
PAGES = {185--202},
URL = {http://www.cs.man.ac.uk/~schmidt/publications/DelPintoSchmidt19b.html},
ABSTRACT = {Abductive reasoning produces hypotheses to explain new observations 
with respect to some background knowledge. This paper focuses on 
ABox abduction in ontologies, where knowledge is expressed in 
description logics and both the observations and hypotheses are 
ground statements. The input is expressed in the description logic 
$\mathcal{ALC}$ and  the observation can contain any set of 
$\mathcal{ALC}$ concept or role assertions. The proposed approach 
uses forgetting to produce hypotheses in the form of a disjunctive 
set of axioms, where each disjunct is an independent explanation 
for the observation and the overall hypothesis is semantically 
minimal, i.e., makes the least assumptions required. Previous work 
on forgetting-based abduction is combined with the semantic 
forgetting method of the system FAME. The hypotheses produced are 
expressed in an extension of $\mathcal{ALC}$ which uses nominals, 
role inverses and fixpoints: $\mathcal{ALCOI}\mu(\nabla)$. This 
combination overcomes the inability of the existing forgetting-based 
approach to allow role assertions in observations and hypotheses, 
and enables the computation of other previously unreachable 
hypotheses. An experimental evaluation is performed using a prototype 
implementation of the method on a corpus of real world ontologies.},
}