NDLI: Approximating the Semantics of Logic Programs by Recurrent Neural Networks

Content Provider	Springer Nature Link
Author	Hölldobler, Steffen Kalinke, Yvonne Störr, Hans Peter
Copyright Year	1999
Abstract	In [1] we have shown how to construct a 3-layered recurrent neural network that computes the fixed point of the meaning function TP of a given propositional logic program P, which corresponds to the computation of the semantics of P. In this article we consider the first order case. We define a notion of approximation for interpretations and prove that there exists a 3-layered feed forward neural network that approximates the calculation of TP for a given first order acyclic logic program P with an injective level mapping arbitrarily well. Extending the feed forward network by recurrent connections we obtain a recurrent neural network whose iteration approximates the fixed point of TP. This result is proven by taking advantage of the fact that for acyclic logic programs the function TP is a contraction mapping on a complete metric space defined by the interpretations of the program. Mapping this space to the metric space R with Euclidean distance, a real valued function fP can be defined which corresponds to TP and is continuous as well as a contraction. Consequently it can be approximated by an appropriately chosen class of feed forward neural networks.
Starting Page	45
Ending Page	58
Page Count	14
File Format	PDF
ISSN	0924669X
Journal	Applied Intelligence
Volume Number	11
Issue Number	1
e-ISSN	15737497
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	1999-01-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Artificial Intelligence (incl. Robotics) Mechanical Engineering Manufacturing, Machines, Tools
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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