A Behavioral Comparison of Some Probabilistic Logic Models

• Published in: Probabilistic Inductive Logic Programming Vol. 4911; pp. 305 - 324
• Main Authors: Muggleton, Stephen, Chen, Jianzhong
• Format: Book Chapter
• Language: English
• Published: Germany Springer Berlin / Heidelberg 2008; Springer Berlin Heidelberg
• Series: Lecture Notes in Computer Science
• Subjects: Artificial intelligence; Bayesian Network; Computer programming / software development; Conditional Probability Table; Descriptive Attribute; Inductive Logic Programming; Logic Program; Mathematical theory of computation
• ISBN: 9783540786511; 3540786511
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-540-78652-8_12

Probabilistic Logic Models (PLMs) are efficient frameworks that combine the expressive power of first-order logic as knowledge representation and the capability to model uncertainty with probabilities. Stochastic Logic Programs (SLPs) and Statistical Relational Models (SRMs), which are considered as domain frequency approaches, and on the other hand Bayesian Logic Programs (BLPs) and Probabilistic Relational Models (PRMs) (possible worlds approaches), are promising PLMs in the categories. This paper is aimed at comparing the relative expressive power of these frameworks and developing translations between them based on a behavioral comparison of their semantics and probability computation. We identify that SLPs augmented with combining functions (namely extended SLPs) and BLPs can encode equivalent probability distributions, and we show how BLPs can define the same semantics as complete, range-restricted SLPs. We further demonstrate that BLPs (resp. SLPs) can encode the relational semantics of PRMs (resp. SRMs). Whenever applicable, we provide inter-translation algorithms, present their soundness and give worked examples.