Abstract
We propose a method for computing supported models of normal logic programs in vector spaces using gradient information. First, the program is translated into a definite program and embedded into a matrix representing the program. We introduce a loss function based on the implementation of the immediate consequence operator \(T_P\) by matrix-vector multiplication with a suitable thresholding function, and we incorporate regularization terms into the loss function to avoid undesirable results. The proposed thresholding operation is an almost everywhere differentiable alternative to the non-linear thresholding operation. We report the results of several experiments where our method shows promising performance when used with adaptive gradient update.
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Notes
- 1.
\(\gamma ^{\bot }\) is an upper bound on false values that variables can take, and \(\gamma ^{\top }\) is a lower bound on true values. \(\gamma =\frac{n}{n+1}\) where n is the length of the longest positive part in the rules, and \(\tau \) was estimated as described [2].
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This work has been supported by JSPS KAKENHI Grant No. JP21H04905.
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Takemura, A., Inoue, K. (2022). Gradient-Based Supported Model Computation in Vector Spaces. In: Gottlob, G., Inclezan, D., Maratea, M. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2022. Lecture Notes in Computer Science(), vol 13416. Springer, Cham. https://doi.org/10.1007/978-3-031-15707-3_26
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