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Re: [ontolog-forum] Conjunction and Disjunction

To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Rich Cooper" <rich@xxxxxxxxxxxxxxxxxxxxxx>
Date: Sat, 4 Jul 2009 11:31:58 -0700
Message-id: <20090704183234.EC12A138CD5@xxxxxxxxxxxxxxxxx>

John S and John B:




RC>    1.    Paul goes to the water fountain;


 >>     2.    Wanda goes to the water fountain;


The only combination that can be derived by strict deduction

is the conjunction of #1 and #2. 


Please forgive me for dropping into metaphor, but I think this is equivalent to stating that, given a relational table of data, all rows are true.  Therefore the conjunction of all rows is also true, for that column. 


So the point is that the conjunction may be true by definition, or by construction, of the way we interpret relational tables. 


But each entry in the table (of the two S0, S1 in this case) is a sequence of symbols, lisp-like in my personal projection.  And every symbol came from some symbol producing input source.  So why not view each entry as a conjunct of the symbols in the sequence? 


Using the same reasoning I offered earlier about relational tables, I can analyze sentences as lisp lists.  Every symbol in a sequence can eval to Si := false or to a new sequence Si := f(Si).  So why not view it as a disjuncts of its symbols, any of which can be false or otherwise. 


In either case, if I want to look for a match to some third querying statement, filled with symbols, including some variables that have to be unified across a binding to S0 or to S1, I can then state a reasonable definition of EQUALITY among rows in the table.  A query row is EQUAL to any row that can be retrieved and matched against said query row after unification. 


But EQUALITY is just a constant value returned from a comparison function, which could also provide < and > or even just /= functinality.  If I can COMPARE any two rows under unification, that seems to me to be more basic to the conversion of reality to symbols than the consideration of whether to start with conjuncts or disjuncts. 


Now the Reality => FOL translation has Existence, Disjunction, Comparison and Equality.  That's an excess of riches, so to speak.  This is way more than we need, as a basis, to build the axioms and the deduction mechanisms.  What can be struck from the list?





Rich Cooper


Rich AT EnglishLogicKernel DOT com

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