121188697
Fuzzy logic and arithmetical hierarchy
Fuzzy logic is understood as a logic with a comparative and truth-functional notion of truth. Arithmetical complexity of sets of tautologies (identically true sentences) and satisfiable sentences (sentences true in at least one interpretation) as well of sets of provable formulas of the most important systems of fuzzy predicate logic is determined or at least estimated.
117335756
Logics of Knowing and Believing
What is the relation of intelligence (natural or artificial) to logic? This is surely a fascinating question with many aspects. We shall not discuss what intelligence is; but we shall start by saying that logic is understood as the study of consequence and of deduction as obtaining consequences from (accepted, assumed) premises (axioms). It goes without saying that intelligence has a logical aspect (among various other aspects). Intelligent systems are said to work with various sorts of knowledge; knowledge representation and processing, and even reasoning about knowledge are considered to be important topics in AI. Knowledge may be uncertain; thus one has to work with beliefs. It has turned out that logical aspects of reasoning about knowledge and beliefs are well formalized by means of some systems of modal logic called logic of knowledge and of belief respectively. An excellent survey of propositional (Boolean) logics of knowledge and belief in relation to computational complexity (with full proofs of main results) is given by Halpern (1992). Most basic facts on these logics are surveyed in Sect. 2 of this chapter. Section 3 surveys basic facts on predicate (Boolean) logics of knowledge and belief; Hughess and Cresswell (1984) contains details. The main part is Sect. 4 where we take into consideration the fact that most knowledge in AI systems (not speaking about natural intelligence) is imprecise (vague, fuzzy), which leads us to fuzzy logic.
122713833
GETTING BELIEF FUNCTIONS FROM KRIPKE MODELS
11139069
Trakhtenbrot Theorem and Fuzzy Logic
Trakhtenbrot theorem is shown to be valid for the three main fuzzy logics – Łukasiewicz, Godel and product logic.
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.
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.
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.
16117062
Analytic Renormings of C(K) Spaces
A ladder system is disposed between two spaced storage shelves. The ladder may move longitudinally along the shelves, and may also be moved laterally between the shelves. Further, the ladder may pivot about a lateral axis such that the ladder may be picked up over obstructions in an aisle between the shelves. In this way, one can quickly and easily position the ladder at any position along or between the two storage shelves for accessing items stored on the shelves. This ladder system is particularly useful in the crowded warehouse-type retail outlets which are now gaining popularity.