Abbreviating First Order Logic With Identity and Membership
in [Logic]
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From: zuhair on 1 May 2010 08:48 > > Now as see how this system greatly abbreviates the formulae: > > Example: > > t .x yt;,<> w .k uw,<> u is a wiener ordered pair > i .s.r isru > i subset k > j .p.q jpqu 0eq > j=x; > > yw > > 56 characters. > > is the abbreviattion for: > > for all t Exist x for all y ( y e t <-> for all w ( Exist k for all u > ( u e w <-> > (u is a wiener ordered pair & > for all i Exist sr (iesereu -> i subset k)& > for all j Exist pq ((jepeqeu & 0eq) -> j=x))) > -> yew)). > > 95 characters. > > with only 4 controllers instead of 14 brackets. > > 39 character difference,and the formula is reduced to almost 60% of > its size, which is a significant reduction, that is besides the > formula is much clearer > and much more neat. > > Zuhair Sorry I couple spacing and controller techniques here, if we rely only on the controller technique well have: t .x yt;;,<> w .k uw;;<> u is a wiener ordered pair i .s.r isru > i subset k; j .p.q jpqu 0eq, > j=x;, > yw 9 controllers instead of 14 brackets. Zuhair
From: Frederick Williams on 1 May 2010 09:00 zuhair wrote: > > Abbreviating FOL with identity and membership FOL(=,e) Who cares? First order logic cannot characterize any infinite system, it is only of interest to limp-wristed nancy boys. -- I can't go on, I'll go on.
From: Tim Little on 2 May 2010 01:46
On 2010-05-01, zuhair <zaljohar(a)gmail.com> wrote: > t .x yt;;,<> w .k uw;;<> u is a wiener ordered pair This gives the impression of a scribble made by mentally ill patients. - Tim |