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Entropy 2015, 17(2), 852-865; doi:10.3390/e17020852

Relational Probabilistic Conditionals and Their Instantiations under Maximum Entropy Semantics for First-Order Knowledge Bases

1
Faculty of Mathematics and Computer Science, University of Hagen, 58084 Hagen, Germany
2
Department of Computer Science, University of Technology Dortmund, 44227 Dortmund, Germany
*
Author to whom correspondence should be addressed.
Received: 26 December 2014 / Revised: 29 January 2015 / Accepted: 9 February 2015 / Published: 13 February 2015
(This article belongs to the Special Issue Maximum Entropy Applied to Inductive Logic and Reasoning)
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Abstract

For conditional probabilistic knowledge bases with conditionals based on propositional logic, the principle of maximum entropy (ME) is well-established, determining a unique model inductively completing the explicitly given knowledge. On the other hand, there is no general agreement on how to extend the ME principle to relational conditionals containing free variables. In this paper, we focus on two approaches to ME semantics that have been developed for first-order knowledge bases: aggregating semantics and a grounding semantics. Since they use different variants of conditionals, we define the logic PCI, which covers both approaches as special cases and provides a framework where the effects of both approaches can be studied in detail. While the ME models under PCI-grounding and PCI-aggregating semantics are different in general, we point out that parametric uniformity of a knowledge base ensures that both semantics coincide. Using some concrete knowledge bases, we illustrate the differences and common features of both approaches, looking in particular at the ground instances of the given conditionals. View Full-Text
Keywords: conditional logic; probabilistic logic; maximum entropy; relational conditional; first-order knowledge base; instantiation restriction; grounding semantics; aggregating semantics; parametric uniformity; maximum entropy model conditional logic; probabilistic logic; maximum entropy; relational conditional; first-order knowledge base; instantiation restriction; grounding semantics; aggregating semantics; parametric uniformity; maximum entropy model
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Beierle, C.; Finthammer, M.; Kern-Isberner, G. Relational Probabilistic Conditionals and Their Instantiations under Maximum Entropy Semantics for First-Order Knowledge Bases. Entropy 2015, 17, 852-865.

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