NDLI: Reasoning with recursive loops under the PLP framework

Content Provider	ACM Digital Library
Author	Shen, Yi-Dong
Copyright Year	2008
Abstract	Recursive loops in a logic program present a challenging problem to the PLP (Probabilistic Logic Programming) framework. On the one hand, they loop forever so that the PLP backward-chaining inferences would never stop. On the other hand, they may generate cyclic influences, which are disallowed in Bayesian networks. Therefore, in existing PLP approaches, logic programs with recursive loops are considered to be problematic and thus are excluded. In this article, we propose a novel solution to this problem by making use of recursive loops to build a stationary dynamic Bayesian network. We introduce a new PLP formalism, called a Bayesian knowledge base. It allows recursive loops and contains logic clauses of the form $\textit{A}$ ← $A_{1},…,A_{l},$ $\textit{true},$ $\textit{Context},$ $\textit{Types},$ which naturally formulate the knowledge that the $A_{i}s$ have direct influences on $\textit{A}$ in the context $\textit{Context}$ under the type constraints $\textit{Types}.$ We use the well-founded model of a logic program to define the direct influence relation and apply SLG-resolution to compute the space of random variables together with their parental connections. This establishes a clear declarative semantics for a Bayesian knowledge base. We view a logic program with recursive loops as a special temporal model, where backward-chaining cycles of the form $\textit{A}←$ … $\textit{A}←$ … are interpreted as feedbacks. This extends existing PLP approaches, which mainly aim at (nontemporal) relational models.
Starting Page	1
Ending Page	31
Page Count	31
File Format	PDF
ISSN	15293785
e-ISSN	1557945X
DOI	10.1145/1380572.1380576
Volume Number	9
Issue Number	4
Journal	ACM Transactions on Computational Logic (TOCL)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2008-08-29
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Bayesian networks Logic programming Cyclic influences Recursive loops The well-founded model
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Logic Computational Mathematics Computer Science

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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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