Mathematical Models for Handling Partial Knowledge in Artificial Intelligence

Knowledge acquisition is one of the most important aspects influencing the quality of methods used in artificial intelligence and the reliability of expert systems. The various issues dealt with in this volume concern many different approaches to the handling of partial knowledge and to the ensuing methods for reasoning and decision making under uncertainty, as applied to problems in artificial intelligence. The volume is composed of the invited and contributed papers presented at the Workshop on Mathematical Models for Handling Partial Knowledge in Artificial Intelligence, held at the Ettore Majorana Center for Scientific Culture of Erice (Sicily, Italy) on June 19-25, 1994, in the framework of the International School of Mathematics "G.Stampacchia". It includes also a transcription of the roundtable held during the workshop to promote discussions on fundamental issues, since in the choice of invited speakers we have tried to maintain a balance between the various schools of knowl­ edge and uncertainty modeling. Choquet expected utility models are discussed in the paper by Alain Chateauneuf: they allow the separation of perception of uncertainty or risk from the valuation of outcomes, and can be of help in decision mak­ ing. Petr Hajek shows that reasoning in fuzzy logic may be put on a strict logical (formal) basis, so contributing to our understanding of what fuzzy logic is and what one is doing when applying fuzzy reasoning.

Invited Papers.- Ellsberg Paradox Intuition and Choquet Expected Utility.- Fuzzy Logic as Logic.- Mathematical Foundations of Evidence Theory.- Semantics for Uncertain Inference Based on Statistical Knowledge.- Prospects and Problems in Applying the Fundamental Theorem of Prevision as an Expert System: An Example of Learning about Parole Decisions.- Coherent Prevision as a Linear Functional without an Underlying Measure Space: The Purely Arithmetic Structure of Logical Relations among Conditional Quantities.- Revision Rules for Convex Sets of Probabilities.- Some Mathematical Tools for Decision Making under Partial Knowledge.- From Bayesian Networks to Causal Networks.- Contributed Papers.- Generalized Concept of Atoms for Conditional Events.- Checking the Coherence of Conditional Probabilities in Expert Systems: Remarks and Algorithms.- A Hyperstructure of Conditional Events for Artificial Intelligence.- Possibilistic Logic and Plausible Inference.- Probability Logic as a Fuzzy Logic.- Algorithms for Precise and Imprecise Conditional Probability Assessments.- A Valuation-Based Architecture for Assumption-Based Reasoning.- Computing Symbolic Support Functions by Classical Theorem-Proving Techniques.- Inconsistent Knowledge Integration in a Probabilistic Model.- Conditional and Comparative Probabilities in Artificial Intelligence.- Roundtable.- Panel Discussion.- List of Participants to the Workshop.