By Aldo Bressan
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Additional info for General Interpreted Modal Calculus
Such a translation is interesting, I think, first be- see fn. : and!. respectively. 1' ••• ML into an extensional language that may usefully be identified tural) theorem relating the intensional designatum of every wff D. ~ into ELv+l. :u for!. = v+ 1 and let us call it the case variable. In connection with our definition of equivalent QIs [Def. 1] we here formally define in ELv+l the matrix W =!. 'T ). The following set [Def. ~-see (8); that - 56 Aldo Bressan "I' ... J. J. J. J. f [Def. • , t1) (so that they are also distinct from the case variable K); -n and that x.
Yi:::> /\~x. ] ~ i"l!. - - i"l!. [Defs. 9]. ] ~ i"1 - ! ':u-cf. N11. We want to remarkthat if in everyone of two distinct *Q. 7. ~~D (V"I' II" ~-ary attribute K is in- troduced-see fn. ) [Deis. 8]. Here the extensionalization E~) of the [Def. 4]. ':u) ~E("I' ••• '''n) En (v,,, I) By Dei. :. I' ••. n); and that "i is the first variable of DEF. 3. E UQ "D En" E 1 cepts of extensional collection and intensional collection formed DEF. 6. - separated; formally: duce the concept of extensionalization of attributes and the con- DEF.
Provided for variable of type !. ) Al where! ; otherwise K· Jllly 1 the element ~ of o~ fulfilling one variable of type!. llo' y(V [see (11)], we have is the only object of type !. ~) such that des ,(A ) = Jlllv 1 1. for-Y' = [see (if)]. 1) to <2:S) do. = ~(Al' ••• , An)' where (36)1,3 hold. - ~(A1' rules. Therefore we write a = desj/fJ\v(A). The rules below cortranslation rules (N16( 59 A General Interpreted Modal Calculus (N16( 2 or not. the matrix ~(A1' ••• , 1. or K according to whether-cf.
General Interpreted Modal Calculus by Aldo Bressan