Abstract
An important task in logic, given a formula and a knowledge base which represents what an agent knows of the current state of the world, is to be able to guess the truth value of the formula. Logic reasoners are designed to perform inferences, that is, to decide whether a formula is a logical consequence of the knowledge base, which is stronger than that and can be intractable in some cases. In addition, under the open-world assumption, it may turn out impossible to infer a formula or its negation. In many practical situations, however, when an agent has to make a decision, it is acceptable to resort to heuristic methods to determine the probable veracity or falsehood of a formula, even in the absence of a guarantee of correctness, to avoid blocking the decision-making process and move forward. This is why we propose a method to train a classification model based on available knowledge in order to be able of accurately guessing whether an arbitrary, unseen formula is true or false. Our method exploits a kernel representation of logical formulas based on a model-theoretic measure of semantic similarity. The results of experiments show that the proposed method is highly effective and accurate.
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Notes
- 1.
Dagstuhl Seminar 22291, July 17–22, 2022.
- 2.
Two formulas may be said to be totally unrelated if knowing the truth value of one does not give any information about the truth value of the other.
- 3.
All the code and data used for the experiments described in this paper can be found in the following repository: https://github.com/ali-ballout/Learning-to-Classify-Logical-Formulas-based-on-their-Semantic-Similarity.
- 4.
The dataset for universe \(\varOmega _{12}\) has 272 false formulas and 227 true ones (1 missing because it was a duplicate), for universe \(\varOmega _{20}\) 278 false and 222 true, and for universe \(\varOmega _{30}\) 300 false and 200 true; of course, these figures vary (between training and test set) for every fold obtained from these datasets.
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Acknowledgments
This work has been partially supported by the French government, through the 3IA Côte d’Azur “Investments in the Future” project managed by the National Research Agency (ANR) with the reference number ANR-19-P3IA-0002, as well as through the ANR CROQUIS (Collecte, représentation, complétion, fusion et interrogation de données de réseaux d’eau urbains hétérogènes et incertaines) project, grant ANR-21-CE23-0004 of the French National Research Agency (ANR).
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Ballout, A., da Costa Pereira, C., Tettamanzi, A.G.B. (2023). Learning to Classify Logical Formulas Based on Their Semantic Similarity. In: Aydoğan, R., Criado, N., Lang, J., Sanchez-Anguix, V., Serramia, M. (eds) PRIMA 2022: Principles and Practice of Multi-Agent Systems. PRIMA 2022. Lecture Notes in Computer Science(), vol 13753. Springer, Cham. https://doi.org/10.1007/978-3-031-21203-1_22
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