A Software System for the Computation, Visualization, and Comparison of Conditional Structures for Relational Probabilistic Knowledge Bases

Combining logic with probabilities is a core idea to uncertain reasoning. Recently, approaches to probabilistic conditional logics based on first-order languages have been proposed that employ the principle of maximum entropy (ME), e.g. the logic FO-PCL. In order to simplify the ME model computation, FO-PCL knowledge bases can be transformed so that they become parametrically uniform. On the other hand, conditional structures have been proposed as a structural tool for investigating properties of conditional knowledge bases. In this paper, we present a software system for the computation, visualization, and comparison of conditional structures for relational probabilistic knowledge bases as they evolve in the transformation process that achieves parametric uniformity.

[1]  Gai CarSO A Logic for Reasoning about Probabilities * , 2004 .

[2]  Marc Finthammer,et al.  An integrated development environment for probabilistic relational reasoning , 2012, Log. J. IGPL.

[3]  Jens Fisseler,et al.  First-order probabilistic conditional logic and maximum entropy , 2012, Log. J. IGPL.

[4]  Dan Roth,et al.  Lifted First-Order Probabilistic Inference , 2005, IJCAI.

[5]  David Poole,et al.  First-order probabilistic inference , 2003, IJCAI.

[6]  Gabriele Kern-Isberner,et al.  Novel Semantical Approaches to Relational Probabilistic Conditionals , 2010, KR.

[7]  Donald Geman,et al.  Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images , 1984 .

[8]  Gabriele Kern-Isberner,et al.  Characterizing the Principle of Minimum Cross-Entropy Within a Conditional-Logical Framework , 1998, Artif. Intell..

[9]  J. Paris The Uncertain Reasoner's Companion: A Mathematical Perspective , 1994 .

[10]  Christoph Beierle,et al.  Relational Probabilistic Conditionals and Their Instantiations under Maximum Entropy Semantics for First-Order Knowledge Bases , 2015, Entropy.

[11]  Christoph Beierle,et al.  Achieving parametric uniformity for knowledge bases in a relational probabilistic conditional logic with maximum entropy semantics , 2013, Annals of Mathematics and Artificial Intelligence.

[12]  Nils J. Nilsson,et al.  Probabilistic Logic * , 2022 .

[13]  Gabriele Kern-Isberner,et al.  Conditionals in Nonmonotonic Reasoning and Belief Revision , 2001, Lecture Notes in Computer Science.

[14]  Christoph Beierle,et al.  Using Equivalences of Worlds for Aggregation Semantics of Relational Conditionals , 2012, KI.

[15]  Christoph Beierle,et al.  How to Exploit Parametric Uniformity for Maximum Entropy Reasoning in a Relational Probabilistic Logic , 2012, JELIA.

[16]  Joseph Y. Halpern Reasoning about uncertainty , 2003 .

[17]  Gabriele Kern-Isberner,et al.  A Ranking Semantics for First-Order Conditionals , 2012, ECAI.

[18]  Ronald Fagin,et al.  Reasoning about knowledge and probability , 1988, JACM.

[19]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[20]  Thomas Lukasiewicz,et al.  Combining probabilistic logic programming with the power of maximum entropy , 2004, Artif. Intell..