APPENDIX II: Used settheoretical (and logical) Symbols

'95-Knowbot

(The english version is in this case identical with the german text)

ANHANG II: Verwendete mengentheoretische (und logische) Symbole


AUTHOR: Gerd Döben-Henisch
COAUTHOR: Joachim Hasebrook
DATE OF FIRST GENERATION: Jan 13, 1998
DATE OF LAST CHANGE: Jan 26, 1998
ADDRESS: INM - Institute for New Media, Frankfurt, Germany
EMAIL: doeb@inm.de
URL: INM
Copyright (c) Gerd Döben-Henisch
STATUS: Work in Progress
COOPERATION: Everybody is invited to share the discussions, to contribute with own ideas. The authors decide whether such contributions are accepted for incorporation in the final version.

LOGICAL SIGNS
& 'AND'
or := 'OR'
~ := 'NOT'
=> := 'IF...THEN....'
iff := 'IF AND ONLY IF'
P(x) := 'x is the ARGUMENT of the PREDICAT P' or 'x has the PROPERTY P'
(A: ) := 'UNIVERSAL QUANTIFIER'
(E: ) := 'EXISTENTIAL QUANTIFIER'

SET-THEORTICAL SIGNS
in := 'ELEMENT OF'
~in := 'NOT ELEMENT OF '
c := 'SUBSET OF'
u := 'SMALL UNION'
cut := 'SMALL CUT '
{x| A[x] } := 'SET OF x which FULLFILL EXPRESSION A'
pow(x) := 'POWERSET OF x'
dm(f) := 'DOMAIN OF RELATION/FUNCTION f'
rn(f) := 'RANGE OF RELATION/FUNCTION f'
f:X ---> Y := 'f is a MAPPING (FUNCTION) FROM DOMAIN X TO RANGE Y'
f(x) = y := 'y IS THE VALUE OF FUNCTION f AT ARGUMENT x'
FUN(x) := 'x IS A FUNCTION'
(a,b) in X x Y := 'The ORDERED PAIR (a,b) is Element of the SET PRODUCT X x Y with a from X and b from Y'
Nat := 'SET OF NATURAL NUMBERS'
x := 'SIMPLE CARTESIAN PRODUCT'
< a_1,a_2> in X x Y := 'The 2-TUPEL < a_1, a_2> IS ELEMENT OF THE CARTESIAN PRODUCT X x Y WITH a_1 from X and a_2 from Y '
TUP(x) := 'x IS AN TUPEL, i.e. FUN(x) & dm(x) c Nat'
<a_1, ..., a_n> := 'TUPEL WITH n-MANY ELEMENTS a_1, ..., a_n'
a_i := 'THE VALUE OF THE i-th ELEMENT OF THE TUPEL a'
X^n := 'N-ADIG CARTESIAN PRODUCT OF X'


INHALT