Re: [ontolog-forum] new logic

[Adrian Walker <adriandwalker@xxxxxxxxx>]

Hi Paola & All,

Actually, there's another, widely used form of logic that can accurately be described as new.  New, that is, on the historical timescale for logic.

It's FOL with negation changed to SQL-style closed world negation.  It says, if something cannot be proven from the axioms and data provided, then that something is false.  So there are only two possible answers to most questions -- true or false.  

In FOL, on the other hand, a question can have no proof, and also no disproof, so the answer is a third possibility, "unknown".

The entire world economy runs on SQL-style closed world negation for its use of databases. And this kind of negation can be extended to other deductive systems, see e.g. [1,2].

Interestingly, the many distinguished authorities in the Semantic Web field nevertheless appear to take the view that FOL style open world negation is  the 'correct' one to use computationally.  This creates some complications for database-like work, not only for negation, but also for aggregations like the 'sum' or 'count' of a table of numbers.  (We can simulate closed world negation with count=0). The ongoing work on the specs and implementation practice for the SPARQL language reflects some of these complications.

One argument that is advanced for the open world approach is that inference over the Web should be monotonic, that is, as Web data accumulates new data, no previously proven deductions should vanish.   However, consider the conclusion 'b' that follows from {'b if not c', 'not c'}.  If we now add the fact {c}, there is an inconsistency {'not c', c}.  Anything at all. such as the irrelevant item 'd' can be proved from an inconsistency like this.  So it makes sense to remove 'not c' when we add 'c'.  But then the deduction 'b' vanishes.  So there is a useful sense in which open world approach  is actually non-monotonic too.

Just my 2 cents,                          -- Adrian


[1]  Backchain Iteration: Towards a Practical Inference Method that is Simple 
  Enough to be Proved Terminating, Sound and Complete. Journal of Automated Reasoning, 11:1-22

[2]  Internet Business Logic
A Wiki and SOA Endpoint for Executable Open Vocabulary English over SQL and RDF
Online at www.reengineeringllc.com    Shared use is free

On Mon, Nov 16, 2009 at 2:59 PM, Paola Di Maio <paola.dimaio@xxxxxxxxx> wrote:

I know it may deliberatelly stir up an old argument we ve had on this list

JSowa, and others, say that there is only one type of logic, FOL

I myself and others, without being able to prove just yet, say that there are different type of logic
(cant quite tell what I mean by that other than as already discussed, but I can observe it and then heard others
discussing it)

I am reading an interesting article that actually mentions 'new logic', that I though some on this list
might enjoy discussing (er... trashing?) , excerpt and link below


The new logic, the logic born of the application of the technical
sophistication of mathematical logic to the project of informal logic, has
triggered the very rapprochement that mathematical logic was not structured to
deliver or to seek. The new logic, whatever its various differences of mission
and detail, has sought for mathematically describable models of what human
agents actually do in real-life situations when they cogitated, reflected,
calculated and decided. Here was an approach that would in an essential way
take what mathematical logic would see as inert context into the theory itself,
where it would be directly engaged by the ensuing formalisms.” (Gabbay and
Woods 2001), pg. 143)

http://www.isy.vcu.edu/~mwenger/INFO790DSS-IntuitiveDecisionMaking-MRW.pdf







--
Paola Di Maio
**************************************************



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