Qualitative probabilistic inference under varied entropy levels

In previous work, we studied four well known systems of qualitative probabilistic inference, and presented data from computer simulations in an attempt to illustrate the performance of the systems. These simulations evaluated the four systems in terms of their tendency to license inference to accurate and informative conclusions, given incomplete information about a randomly selected probability distribution. In our earlier work, the procedure used in generating the unknown probability distribution (representing the true stochastic state of the world) tended to yield probability distributions with moderately high entropy levels. In the present article, we present data charting the performance of the four systems when reasoning in environments of various entropy levels. The results illustrate variations in the performance of the respective reasoning systems that derive from the entropy of the environment, and allow for a more inclusive assessment of the reliability and robustness of the four systems.

[1]  Jeff B. Paris,et al.  O IS NOT ENOUGH , 2009, The Review of Symbolic Logic.

[2]  P. Suppes.  Probabilistic Inference and the Concept of Total Evidence , 1969 .

[3]  Donald E. Knuth,et al.  The art of computer programming, volume 3: (2nd ed.) sorting and searching , 1998 .

[4]  Paul D. Thorn,et al.  REWARD VERSUS RISK IN UNCERTAIN INFERENCE: THEOREMS AND SIMULATIONS , 2012, The Review of Symbolic Logic.

[5]  Van Fraassen,et al.  Laws and symmetry , 1989 .

[6]  E. W. Adams,et al.  The logic of conditionals , 1975 .

[7]  Gerhard Schurz,et al.  Probabilistic Semantics for Delgrande's Conditional Logic and a Counterexample to His Default Logic , 1998, Artif. Intell..

[8]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[9]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems , 1988 .

[10]  James Hawthorne,et al.  The Quantitative/Qualitative Watershed for Rules of Uncertain Inference , 2007, Stud Logica.

[11]  Donald E. Knuth,et al.  The art of computer programming. Vol.2: Seminumerical algorithms , 1981 .

[12]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[13]  Krister Segerberg.  Notes on conditional logic , 1989, Stud Logica.

[14]  Edwin T. Jaynes,et al.  Prior Probabilities , 1968, Encyclopedia of Machine Learning.

[15]  Judea Pearl,et al.  System Z: a Natural Ordering of Defaults with Tractable Applications to Nonmonotonic Reasoning^ , 1990 .

[16]  Judea Pearl,et al.  Qualitative Probabilities for Default Reasoning, Belief Revision, and Causal Modeling , 1996, Artif. Intell..

[17]  Paul D. Thorn,et al.  A Utility Based Evaluation of Logico-probabilistic Systems , 2014, Stud Logica.

[18]  Daniel Lehmann,et al.  What does a Conditional Knowledge Base Entail? , 1989, Artif. Intell..

[19]  Gerhard Schurz,et al.  Probabilistic Default Logic Based on Irrelevance and Relevance Assumptions , 1997, ECSQARU-FAPR.

[20]  Gerhard Schurz,et al.  Non-Monotonic Reasoning from an Evolution-Theoretic Perspective: Ontic, Logical and Cognitive Foundations , 2005, Synthese.

[21]  James Hawthorne,et al.  On the logic of nonmonotonic conditionals and conditional probabilities , 1996, J. Philos. Log..

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