Mathematical Foundations of Evidence Theory

Reasoning schemes in artificial intelligence (and elsewhere) use information and knowledge, but the inference my depend on assumptions which are uncertain. In this case arguments in favour of and against hypotheses can be derived. These arguments may be weighed by their likelihoods and thereby the credibility and plausibility of different possible hypotheses can be obtained. This is, in a nutshell, the idea to be explored and developed in this article.

[1]  Philippe Besnard,et al.  Evidence Theory Based on General Consequence Relations , 1995, Int. J. Found. Comput. Sci..

[2]  Johan de Kleer,et al.  An Assumption-Based TMS , 1987, Artif. Intell..

[3]  R. Wójcicki.  Theory of Logical Calculi: Basic Theory of Consequence Operations , 1988 .

[4]  Jürg Kohlas.  SUPPORT- AND PLAUSIBILITY FUNCTIONS INDUCED BY FILTER-VALUED MAPPINGS , 1993 .

[5]  P. Halmos.  Lectures on Boolean Algebras , 1963 .

[6]  Hung T. Nguyen,et al.  On Random Sets and Belief Functions , 1978, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[7]  Jürg Kohlas,et al.  Probabilistic Assumption-Based Reasoning , 1993, UAI.

[8]  Raymond Reiter,et al.  Foundations of Assumption-based Truth Maintenance Systems: Preliminary Report , 1987, AAAI.

[9]  Ryszard Wójcicki,et al.  Theory of Logical Calculi , 1988 .

[10]  Kathryn B. Laskey,et al.  Assumptions, Beliefs and Probabilities , 1989, Artif. Intell..

[11]  Jürg Kohlas.  The reliability of reasoning with unreliable arguments , 1991, Ann. Oper. Res..

[12]  Michael Clarke,et al.  Symbolic and Quantitative Approaches to Reasoning and Uncertainty , 1991, Lecture Notes in Computer Science.

[13]  Gregory M. Provan,et al.  A logic-based analysis of Dempster-Shafer theory , 1990, Int. J. Approx. Reason..

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

[15]  Jürg Kohlas.  Symbolic Evidence, Arguments, Supports and Valuation Networks , 1993, ECSQARU.

[16]  Madan M. Gupta,et al.  Conditional Logic in Expert Systems , 1991 .

[17]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[18]  J. Neveu.  Bases mathématiques du calcul des probabilités , 1966 .