This paper provides a theoretical insight for the integration of logical constraints into a learning process. In particular it is proved that a fragment of the Łukasiewicz logic yields a set of convex constraints. The fragment is enough expressive to in- clude many formulas of interest such as Horn clauses. Using the isomorphism of Łukasiewicz formulas and McNaughton functions, logical constraints are mapped to a set of linear constraints once the predicates are grounded on a given sam- ple set. In this framework, it is shown how a collective clas- sification scheme can be formulated as a quadratic program- ming problem, but the presented theory can be exploited in general to embed logical constraints into a learning process. The proposed approach is evaluated on a classification task to show how the use of the logical rules can be effective to improve the accuracy of a trained classifier.

Giannini, F., Diligenti, M., Gori, M., Maggini, M. (2018). Characterization of the Convex Lukasiewicz Fragment for Learning from Constraints. In 32nd AAAI Conference on Artificial Intelligence, AAAI 2018 (pp.3015-3020). Palo Alto, CA : ASSOC ADVANCEMENT ARTIFICIAL INTELLIGENCE.

Characterization of the Convex Lukasiewicz Fragment for Learning from Constraints

Giannini, Francesco;Diligenti, Michelangelo;Gori, Marco;Maggini, Marco
2018-01-01

Abstract

This paper provides a theoretical insight for the integration of logical constraints into a learning process. In particular it is proved that a fragment of the Łukasiewicz logic yields a set of convex constraints. The fragment is enough expressive to in- clude many formulas of interest such as Horn clauses. Using the isomorphism of Łukasiewicz formulas and McNaughton functions, logical constraints are mapped to a set of linear constraints once the predicates are grounded on a given sam- ple set. In this framework, it is shown how a collective clas- sification scheme can be formulated as a quadratic program- ming problem, but the presented theory can be exploited in general to embed logical constraints into a learning process. The proposed approach is evaluated on a classification task to show how the use of the logical rules can be effective to improve the accuracy of a trained classifier.
2018
978-157735800-8
Giannini, F., Diligenti, M., Gori, M., Maggini, M. (2018). Characterization of the Convex Lukasiewicz Fragment for Learning from Constraints. In 32nd AAAI Conference on Artificial Intelligence, AAAI 2018 (pp.3015-3020). Palo Alto, CA : ASSOC ADVANCEMENT ARTIFICIAL INTELLIGENCE.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1034774