7323684
Combining Functions for Certainty Degrees in Consulting Systems
Abstract Consulting systems are rule-based systems of Artificial Intelligence working with propositions that may be uncertain, i.e. may have a truth-value different from “true” and “false”. The work of a consulting system consists, roughly, in propagation of uncertain knowledge throughout the net of rules according to some combining functions. It is shown that the notion of an ordered Abelian group is central for the definition of these combining functions. Various particular groups, both Archimedean and non-Archimedean, are considered for use in consulting systems. Practical experiments with them are also described.
44650386
Fuzzy Logic and Arithmetical Hierarchy, II
A very simple many-valued predicate calculus is presented; a completeness theorem is proved and the arithmetical complexity of some notions concerning provability is determined.
120841015
SYSTEMS OF CONDITIONAL BELIEFS IN DEMPSTER-SHAFER THEORY AND EXPERT SYSTEMS
Various notions of soundness for systems of conditional beliefs are introduced and interrelated (the term “belief” being used in the sense of Dempster-Shafer theory). An application to the analysis of the use of Dempster-Shafer theory in classical (rule-based, MYCIN-like) expert systems is sketched. Some open problems are formulated.
61701554
Metamathematics of Fuzzy Logic
Preface. 1. Preliminaries. 2. Many-Valued Propositional Calculi. 3. Lukasiewicz Propositional Logic. 4. Product Logic, Godel Logic. 5. Many-Valued Predicate Logics. 6. Complexity and Undecidability. 7. On Approximate Inference. 8. Generalized Quantifiers and Modalities. 9. Miscellanea. 10. Historical Remarks. References. Index.
122713833
GETTING BELIEF FUNCTIONS FROM KRIPKE MODELS
205092353
A simple dynamic logic
Abstract A system of dynamic predicate logic is presented. It allows nonstandard modelling of time, which makes recursive axiomatization possible, and is essentially one-sorted (the same elements code data and time), which makes the system reasonably simple and transparent. The system is subjected to usual mathematical considerations; in particular, it is shown to be equivalent to the three-sorted system due to Andreka, Nemeti and Sain (1982). A conservation result for the latter system is obtained as a by-product.
18639151
Polynomial algebras on classical banach spaces
For the classical Banach spacesX = ℓp,C(K) we identify alln such that every polynomial of degreen + 1 onX is uniformly approximable on the unit ball by elements of the algebra generated by all polynomials of degree up ton onX.
15243737
Dual renormings of Banach spaces
We prove that a Banach space admitting an equivalent WUR norm is an Asplund space. Some related dual renormings are also presented.