fom
Posts:
1,969
Registered:
12/4/12


Re: LOGIC & MATHEMATICS
Posted:
May 29, 2013 10:24 PM


On 5/29/2013 7:13 AM, Julio Di Egidio wrote: > > (By the way, your news: links do not work, at least not for me.) >
I almost forgot that I put these in the thread. Assuming this is to what you had been referring, I have taken the time to find the hypertext links.
======================================
> I understand certain basic relations > geometrically, > > news://news.giganews.com:119/Jr2dnbdYvtfPdlrNnZ2dnUVZ_t> dnZ2d@giganews.com >
https://groups.google.com/forum/?fromgroups#!msg/sci.logic/V41XKFS9zSU/4vcFbzXcyRMJ
the "corrected" version reflects a name change
THIS > NOT
> and I understand compositionality through an > intensional axiomatized equational theory, > > news://news.giganews.com:119/IqudndogJ8> VB1zNnZ2dnUVZ_qydnZ2d@giganews.com >
https://groups.google.com/group/sci.logic/msg/362a82b11fe77f70?dmode=source
> Truth table semantics begins with geometric > forms instantiating all possibilities for > logical equivalence, > > news://news.giganews.com:119/zsCdnW9U7v4BOlzNnZ2dnUVZ_hmdnZ2d@giganews.com
https://groups.google.com/group/sci.logic/msg/446ad325630ae309?dmode=source
the diagrams are not really readable in the web page.
There are incidence tables. The column headings are 4tuple column vectors of '' and '' delimited by columns of ''. The row labels are triples of 4tuple column vectors.
Each locus in the tables has a 'T' or 'F' positioned to be coherently matched with the column headings.
In the first table,
T >  F > 
In the second table,
T >  F > 
Fix a column heading to fix representation of Logical Equivalence (biconditional), LEQ.
Fix a row to fix truth table components.
Ordering is still an issue, it will depend on a specific representation that you may not choose. The point with the first selection is that LEQ is the initial representation that decides the form of a truth table. A truth table is needed for the semantics of a complete connective. The ordering in the next step fixes a truth table for a complete connective...
> and ends with a canonical ordering that > fixes a representation for a complete > connective, > > news://news.giganews.com:119/AuqdnYcXm8eaLVzNnZ2dnUVZ_hdnZ2d@giganews.com > > These particular constructions actually > become quite complex. Certain group theoretic > constructions reflecting the choice of > representation provide a syntactic labeling > of the free orthomodular lattice on two generators.
https://groups.google.com/group/sci.logic/msg/75ca0a179004e0e6?dmode=source
The ordering is based on an Euler trail and a palindromic symmetry for the 15 symbols different from LEQ. The center is XOR. The last three form a truth table for NOR.
To understand this emphasis on LEQ, note that Tarski wrote a paper treating LEQ as the primitive connective of "logistic". This had been important to Lesniewski's deliberations. These analyses had been secondorder. But, I am concerned with demarcations that ground a system of connectives with a classical bivalence. I am not trying to "purport" a logical system as much as I am trying to represent an analysis of it.
> My understanding of propositions is > based on a free DeMorgan algebra, > > news://news.giganews.com:119/Jr2dnbNYvtf9cFrNnZ2dnUVZ_tdnZ2d@giganews.com
https://groups.google.com/forum/?fromgroups#!msg/sci.logic/IFbunFH1vJ8/o5eUKxD2Nv0J
The "corrected" version has the name change
THIS > NOT
> and, in fact, I view DeMorgan algebra > as foundational rather than Boolean > algebra, > > news://news.giganews.com:119/Jr2dnbBYvtedcFrNnZ2dnUVZ_tdnZ2d@giganews.com >
https://groups.google.com/forum/?fromgroups#!msg/sci.logic/3nLe4eMRpgU/40irzsxhEUgJ
The "corrected" version has the name change
THIS > NOT
> The ortholattice O_6 which appears in these > constructions is fundamental to models of > logic as discerned by Pavicic and Megill in > > http://arxiv.org/pdf/quantph/9906101v3.pdf
> Although I have nothing to show for my efforts, > I have taken the issue of demarcation very > seriously. After all, what exactly is meant > by "foundational" if one is starting somewhere > in the middle?
There are other posts in this initial sequence. Look for 'fom' 02  10
https://groups.google.com/group/sci.logic/index/browse_frm/month/201212?_done=%2Fgroup%2Fsci.logic%2Fbrowse_frm%2Fmonth%2F201212%3F&
https://groups.google.com/group/sci.logic/browse_frm/month/201212?start=250&sa=N
However you come to view these posts, please try to keep in mind that it is hard to see things differently from others. And, since I received no inquiries, there is little to no explanation.

