Graph Structures for Knowledge Representation and Reasoning

Although tools exist to aid practitioners in the construction of directed graphs typified by Conceptual Graphs (CGs), it is still quite possible for them to draw the wrong model, mistakenly or otherwise. In larger or more complex CGs it is furthermore often difficult–without close inspection–to see clearly the key features of the model. This paper thereby presents a formal method, based on the exploitation of CGs as directed graphs and the application of Formal Concept Analysis (FCA). FCA elucidates key features of CGs such as pathways and dependencies, inputs and outputs, cycles, and joins. The practitioner is consequently empowered in exploring, reasoning with and validating their real-world models.

[1]  Tanya Braun,et al.  Lifted Junction Tree Algorithm , 2016, KI.

[2]  Tanya Braun,et al.  Preventing Groundings and Handling Evidence in the Lifted Junction Tree Algorithm , 2017, KI.

[3]  Prakash P. Shenoy,et al.  Probability propagation , 1990, Annals of Mathematics and Artificial Intelligence.

[4]  Kristian Kersting,et al.  Exploiting symmetries for scaling loopy belief propagation and relational training , 2013, Machine Learning.

[5]  Kristian Kersting,et al.  Scaling Lifted Probabilistic Inference and Learning Via Graph Databases , 2016, SDM.

[6]  Kristian Kersting,et al.  Counting Belief Propagation , 2009, UAI.

[7]  Jesse Davis,et al.  Lifted Variable Elimination: Decoupling the Operators from the Constraint Language , 2013, J. Artif. Intell. Res..

[8]  Guy Van den Broeck,et al.  Lifted Probabilistic Inference for Asymmetric Graphical Models , 2014, AAAI.

[9]  Pedro M. Domingos,et al.  Exploiting Logical Structure in Lifted Probabilistic Inference , 2010, StarAI@AAAI.

[10]  Prakash P. Shenoy,et al.  Axioms for probability and belief-function proagation , 1990, UAI.

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

[12]  David J. Spiegelhalter,et al.  Local computations with probabilities on graphical structures and their application to expert systems , 1990 .

[13]  Nevin Lianwen Zhang,et al.  Exploiting Contextual Independence In Probabilistic Inference , 2011, J. Artif. Intell. Res..

[14]  Adnan Darwiche,et al.  Modeling and Reasoning with Bayesian Networks , 2009 .

[15]  Guy Van den Broeck.  Lifted Inference and Learning in Statistical Relational Models , 2013 .

[16]  Pedro M. Domingos,et al.  Probabilistic theorem proving , 2011, UAI.

[17]  Adnan Darwiche,et al.  Recursive conditioning , 2001, Artif. Intell..

[18]  Nima Taghipour,et al.  Lifted Probabilistic Inference by Variable Elimination , 2013 .

[19]  Nir Friedman,et al.  Probabilistic Graphical Models - Principles and Techniques , 2009 .

[20]  Jesse Davis,et al.  First-order Decomposition Trees , 2013, NIPS.

[21]  Adnan Darwiche,et al.  Compiling Bayesian Networks Using Variable Elimination , 2007, IJCAI.

[22]  Pedro M. Domingos,et al.  Lifted First-Order Belief Propagation , 2008, AAAI.

[23]  Evelina Lamma,et al.  Lifted Variable Elimination for Probabilistic Logic Programming , 2014, Theory and Practice of Logic Programming.

[24]  David J. Hill,et al.  Lifted Inference for Relational Continuous Models , 2010, Statistical Relational Artificial Intelligence.

[25]  Luc De Raedt,et al.  Exploiting local and repeated structure in Dynamic Bayesian Networks , 2016, Artif. Intell..

[26]  Leslie Pack Kaelbling,et al.  Lifted Probabilistic Inference with Counting Formulas , 2008, AAAI.