Download The Alternative Mathematical Model of Linguistic Semantics by Vilém Novák (auth.) PDF

By Vilém Novák (auth.)

In competition to the classical set conception of typical language, Novák's hugely unique monograph bargains a thought according to substitute and fuzzy units. This new technique is firmly grounded in semantics and pragmatics, and bills for the vagueness inherent in usual language-filling a wide hole in our present wisdom. the speculation will foster fruitful debate between researchers in linguistics and synthetic intellegence.

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Extra resources for The Alternative Mathematical Model of Linguistic Semantics and Pragmatics

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We have already introduced the class of finite natural numbers IFN representing the horizon. This horizon, however, is a phenomenon accompanying our view of the world. In our case, this is the view of the universe V of sets. The horizon is not steady and when sharpening the view, it can be moved farther out. When we do this, then the original class IFN disappears and there appears a new class IFN* representing the class of finite natural numbers under the sharpened view. This class can also be obtained when we only imagine the new sharpened view.

Similarly, we can define the class of rational numbers o = {~; x, Y E 7L & y o} =1= and two subclasses of it, namely 0+ = {x E 0; x ~ O} and 0- = {x E 0; x The class of finite rational numbers is IFO = {~; x, Y E 1F7L & y o} =1= where 1F7L is the class of finite integers. An important relation is that of infinite nearness x == Y iff yl < -n1 Ix - < O}. == on O. We put for every n E IF~ Hence, two rational numbers are infinitely near if their distance lies over the horizon represented by the class {lin; n E IF~}.

A) X ~ Fig (X). (b) X ~ Y =? Fig(Xh~ Fig(Y). (c) Fig(X) is a figure. (d) If X is a figure, then X = Fig (X). 37. Let X be a figure. Then the following statements are equivalent: 37 The Alternative Set Theory (a) (3u)(X = Fig(u)). (b) X is a -rr-class. (c) X is revealed. 38. (a) X is a figure. (b) If Fig (X) = Fig(y), then X = Y. (c) If X is a revealed class, then X = Fig (X). 39. Every class X contains a countable ;:-net Y which is dense in X. Proof. Let {un; n E IF~} be a sequence of sets such that every un is a maximal Rn-net on X.

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