16

             Ackermann-Based Forgetting for
              Expressive Description Logics
                (Abstract of Invited Talk)

                                  Yizheng Zhao

                         The University of Manchester, UK
                         yizheng.zhao@manchester.ac.uk


Forgetting refers to a non-standard reasoning problem concerned with eliminat-
ing terms (i.e., concept and role names) from description logic-based ontologies
whilst preserving sufficiently many logical consequences up to the remaining
terms. On one hand, it turns out to be a very useful technique in ontology-based
information processing, as it allows users to focus on specific parts of ontologies
in order to create restricted views or decompositions for in-depth analysis or
sharing with other users; forgetting is also useful for information hiding, expla-
nation generation, logical difference computation, and ontology debugging and
repair. On the other hand, forgetting is an inherently difficult problem – it is
much harder than standard reasoning (satisfiability testing) – and very few log-
ics are known to be complete for forgetting, there has been insufficient research
on the topic and very few forgetting tools are available at present.
    This work investigates practical methods for semantic forgetting in expres-
sive description logics not considered so far. In particular, we present a practical
method for forgetting concept and role names from ontologies expressible in the
description logic ALCOIH(O, u), i.e., the basic ALC extended with nominals,
inverse roles, role inclusions, the universal role and role conjunctions, and a
practical method for forgetting role names from ontologies expressible in the de-
scription logic ALCOQH(O, u), i.e., ALCOH(O, u) additionally extended with
qualified number restrictions. Being based on non-trivial generalisations of a
monotonicity property called Ackermann’s Lemma, these methods are the first
and the only approaches so far that allow for concept and role forgetting in
description logics with nominals and that allow role forgetting in description
logics with qualified number restrictions. The methods are goal-oriented and
incremental. They always terminate and are sound in the sense that the forget-
ting solution is equivalent to the original ontology up to the interpretations of
the forgotten names, possibly with the interpretations of the newly-introduced
nominals or concept definers during the forgetting process.
    The methods are implemented in Java using the OWL API and the pro-
totypical implementation, namely, Fame, was evaluated on several corpora of
publicly accessible biomedical ontologies (in order to verify the practicality of
the methods). Despite our methods not being complete, the evaluation results
showed that Fame was successful in most test cases (i.e., forgot all concept and
role names specified in the forgetting signatures) within a very short period of
time.

Copyright c 2017 by the paper’s authors
In: P. Koopmann, S. Rudolph, R. Schmidt, C. Wernhard (eds.): SOQE 2017 – Pro-
ceedings of the Workshop on Second-Order Quantifier Elimination and Related Topics,
Dresden, Germany, December 6–8, 2017, published at http://ceur-ws.org.