Haifa, Israel ∗Corresponding author. url: https://www.cs.man.ac.uk/~schmidt/ (R. A. Schmidt) orcid:

Advances and Challenges in the Development and Application of Forgetting Tools (Abstract)

Renate A. Schmidt

0 0 Department of Computer Science, The University of Manchester , Oxford Road, Manchester M13 9PL , United Kingdom

2022

000 0 0002

Forgetting is a content extraction method for formal knowledge bases. Because knowledge not only consists of what is explicitly stated in the knowledge base but also of what can be inferred, knowledge extraction is a challenging problem. Forgetting attempts to create a compact and faithful representation of the stored knowledge over a user-specified signature by performining inferences on the symbols not in this signature. The result is a restricted view of the knowledge base that is equivalent to the original knowledge base without using any of the specified forgetting symbols and can be used as a stand-alone knowledge base. Forgetting views are often easier to navigate, analyse and query. We can also use forgetting to transform a logical theory or a formula into a uniform interpolant. It is useful for equivalent reduction of second-order formulae to formulae in first-order logic and provides a method to automate modal correspondence theory. Another application of forgetting is abductive reasoning, which is useful for ontology formation and ontology repair. Yet another application is logical difference computation between two ontologies. In this presentation I gave an overview of our work on the development and application of forgetting methods for description and modal logics. After an introduction to the idea of forgetting and two forms of forgetting (deductive and semantic forgetting), I discussed current advances and challenges in automating and applying forgetting. A selection of references: [3, 4, 6, 8, 7, 12, 13, 11, 2, 5, 1, 9, 10].

[4]

Goranko , U. Hustadt,

R. A.

Schmidt , and

Vakarelov . SCAN is complete for all Sahlqvist formulae . In R. Berghammer,

Möller , and G. Struth, editors, Relational and Kleene-Algebraic Methods in Computer Science (RelMiCS 7) , volume 3051 of Lecture Notes in Computer Science, pages 149 - 162 . Springer, 2004 .

[5]

Koopmann ,

Del-Pinto ,

Tourret , and

R. A.

Schmidt . Signature-based abduction for expressive description logics . In D. Calvanese, E. Erdem, and M. Thielscher, editors, Proceedings of the 17th International Conference on Principles of Knowledge Representation and Reasoning (KR 2020 ), pages 592 - 602 . AI Press, 2020 .

[6]

Koopmann and

R. A.

Schmidt . Forgetting concept and role symbols in ALCH-ontologies . In K. McMillan , A. Middeldorp , and A . Voronkov, editors, Logic for Programming , Artificial Intelligence, and Reasoning (LPAR 2013 ), volume 8312 of Lecture Notes in Computer Science, pages 552 - 567 . Springer, 2013 .

[7]

Koopmann and

R. A.

Schmidt. LETHE : A saturation-based tool for non-classical reasoning . In M. Dumontier,

Glimm ,

Goncalves ,

Horridge ,

Jiménez-Ruiz ,

Matentzoglu ,

Parsia , G. Stamou, and G. Stoilos, editors, Proceedings of the 4th International Workshop on OWL Reasoner Evaluation (ORE-2015) , volume CEUR-WS/Vol-1387 of CEUR Workshop Proceedings. CEUR-WS.org , 2015 .

[8]

Koopmann and

R. A.

Schmidt . Uniform interpolation and forgetting for ALC ontologies with aboxes . In B. Bonet and S . Koenig, editors, Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence (AAAI-2015) , pages 175 - 181 . AAAI Press, 2015 .

[9]

Sakr and

R. A.

Schmidt . Semantic forgetting in expressive description logics . In B. Konev and G. Reger, editors, Frontiers of Combining Systems (FroCoS 2021 ), volume 12941 of Lecture Notes in Computer Science, pages 118 - 136 . Springer, 2021 .

[10]

Sakr and

R. A.

Schmidt . Fine-grained forgetting for the description logic ALC . In O. Arieli,

Homola ,

J. C.

Jung , and M.-L. Mugnier, editors, Proceedings of the 35th International Workshop on Description Logics (DL 2022 ), volume 3263 of CEUR Workshop Proceedings. CEUR-WS.org , 2022 .

[11]

Zhao ,

Alghamdi ,

R. A.

Schmidt ,

Feng ,

Stoilos ,

Juric , and

Khodadadi . Tracking logical difference in large-scale ontologies: A forgetting-based approach . In P. Van Hentenryck and Z.-H . Zhou, editors, Proceedings of the Thirty-Third AAAI Conference on Artificial Intelligence (AAAI-2019) , pages 3116 - 3124 . AAAI Press, 2019 .

[12]

Zhao and

R. A.

Schmidt . Forgetting concept and role symbols in ALCOIHµ +(∇, ⊓)- ontologies . In S. Kambhampati, editor, Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence (IJCAI'16) , pages 1345 - 1352 . AAAI Press/IJCAI, 2016 .

[13]

Zhao and

R. A.

Schmidt . On concept forgetting in description logics with qualified number restrictions . In J. Lang, editor, Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence (IJCAI'18) , pages 1984 - 1990 . AAAI Press/IJCAI, 2018 .