Abs t rac t : This paper presents a review of d i f f e r e n t approximate reasoning techniques which have been proposed for dea l ing w i t h uncer ta in or imprecise knowledge ,espec i a l ly in expert systems based on product i o n ru le methodology. Theore t i ca l approaches such as Bayesian i n fe rence ,Sha fe r ' s b e l i e f theory or Zadeh's p o s s i b i l i t y theory as wel l as ...

The paper shows t h a t t he s t a t e of a r t i n a r t i f i c i a l i n t e l l i g e n c e r e q u i r e s development of a s e m i o t i c system theory wh i ch shou ld p l a y i n t h i s f i e l d t he same r o l e t h a t was p l ayed by f o r m a l systems a t i t s i n i t i a l s t a g e s . Basic problems of s e m i o t i c model and systems t heo ry are d i scussed . I l l u s t r...

We discuss recent work of Chambers, Dotterrer, Ferry, Manin, and Weinberger, which resolved a fundamental question in quantitative topology: if f : Sm → Sn is a contractible map with Lipschitz constant L, what can we say about the Lipschitz constant of a null-homotopy of f? In the mid-90s, Gromov wrote an article on quantitative topology [G], raising a number of interesting questions. We will f...

The contribution of the fourth generation quarks to the rare Bs → l+l− and Bs → l+l−γ decays are studied. Constraints on the extended Cabibbo–Kobayashi–Maskawa matrix elements |VtbV ∗ ts| and |Vt′bV ∗ t′s| are obtained from the existing experimental result for the branching ratio of the B → Xsγ decay. The branching ratios of the above–mentioned decays, as well as the photon spectrum in the Bs →...