Symbolic Possibilistic Logic: Completeness and Inference Methods

This paper studies the extension of possibilistic logic to the case when weights attached to formulas are symbolic and stand for variables that lie in a totally ordered scale, and only partial knowledge is available on the relative strength of these weights. A proof of the soundness and the completeness of this logic according to the relative certainty semantics in the sense of necessity measures is provided. Based on this result, two syntactic inference methods are presented. The first one calculates the necessity degree of a possibilistic formula using the notion of minimal inconsistent sub-base. A second method is proposed that takes inspiration from the concept of ATMS. Notions introduced in that area, such as nogoods and labels, are used to calculate the necessity degree of a possibilistic formula. A comparison of the two methods is provided, as well as a comparison with the original version of symbolic possibilistic logic.

[1]  Karem A. Sakallah,et al.  On Finding All Minimally Unsatisfiable Subformulas , 2005, SAT.

[2]  Johan de Kleer,et al.  A General Labeling Algorithm for Assumption-Based Truth Maintenance , 1988, AAAI.

[3]  Joseph Y. Halpern.  Defining Relative Likelihood in Partially-Ordered Preferential Structures , 1996, UAI.

[4]  Odile Papini,et al.  A possibilistic handling of partially ordered information , 2003, UAI.

[5]  Pierre Marquis,et al.  Consequence Finding Algorithms , 2000 .

[6]  D Dubois,et al.  Belief structures, possibility theory and decomposable confidence measures on finite sets , 1986 .

[7]  Nicholas Rescher,et al.  Plausible reasoning , 1976 .

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

[9]  J. Dekleer.  An assumption-based TMS , 1986 .

[10]  Odile Papini,et al.  Reasoning with partially ordered information in a possibilistic logic framework , 2004, Fuzzy Sets Syst..

[11]  Didier Dubois,et al.  Possibilistic logic : a retrospective and prospective view , 2003 .

[12]  Henri Prade,et al.  Encoding formulas with partially constrained weights in a possibilistic-like many-sorted propositional logic , 2005, IJCAI.

[13]  Philippe Smets,et al.  Quantified Representation of Uncertainty and Imprecision , 1998 .

[14]  Kevin McAreavey,et al.  Computational approaches to finding and measuring inconsistency in arbitrary knowledge bases , 2014, Int. J. Approx. Reason..

[15]  Lhouari Nourine,et al.  About Keys of Formal Context and Conformal Hypergraph , 2008, ICFCA.

[16]  Didier Dubois,et al.  Timed possibilistic logic , 1991, Fundam. Informaticae.

[17]  Didier Dubois,et al.  Dealing with Multi-Source Information in Possibilistic Logic , 1992, ECAI.

[18]  Didier Dubois,et al.  Possibility Theory: Qualitative and Quantitative Aspects , 1998 .

[19]  Didier Dubois,et al.  Ordinal and Probabilistic Representations of Acceptance , 2004, J. Artif. Intell. Res..

[20]  Raymond Reiter,et al.  A Theory of Diagnosis from First Principles , 1986, Artif. Intell..

[21]  David Lewis.  Counterfactuals and Comparative Possibility , 1973 .

[22]  Didier Dubois,et al.  Conditional Preference Nets and Possibilistic Logic , 2013, ECSQARU.

[23]  Didier Dubois,et al.  Handling Uncertainty, Context, Vague Predicates, and Partial Inconsistency in Possibilistic Logic , 1991, Fuzzy Logic and Fuzzy Control.

[24]  Didier Dubois,et al.  Possibilistic Logic - An Overview , 2014, Computational Logic.

[25]  Steven Schockaert,et al.  Generalized possibilistic logic: Foundations and applications to qualitative reasoning about uncertainty , 2017, Artif. Intell..

[26]  Didier Dubois,et al.  Nonmonotonic Reasoning, Conditional Objects and Possibility Theory , 1997, Artif. Intell..

[27]  H. Prade,et al.  Possibilistic logic , 1994 .

[28]  Rafael Peñaloza,et al.  Context-dependent views to axioms and consequences of Semantic Web ontologies , 2012, J. Web Semant..

[29]  Didier Dubois,et al.  Inconsistency Management and Prioritized Syntax-Based Entailment , 1993, IJCAI.