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Re: [ontolog-forum] The Lindenbaum lattice and a biography of Adolf Lind

To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
Cc: cg@xxxxxxxxxxxxx, 'Pavlos Peppas' <pavlos@xxxxxxxxxx>
From: "Rich Cooper" <rich@xxxxxxxxxxxxxxxxxxxxxx>
Date: Wed, 7 Jan 2015 13:43:35 -0800
Message-id: <!&!AAAAAAAAAAAYAAAAAAAAAAb3x6NyrzVKo6ReWvn+7BjCgAAAEAAAAK9+NgPuvKdDjQDNIWP+ayYBAAAAAA==@xxxxxxxxxxxxxxxxxxxxxx>
The paper at:
http://pavlos.bma.upatras.gr/paperFs/8.pdf     (01)

doesn't respond to a link click - no site found.  neither does:     (02)

http://pavlos.bma.upatras.gr/    (03)

same symptoms.  I tried several hours apart, with the same outcome.    (04)

-Rich    (05)

Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2    (06)

-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx 
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F Sowa
Sent: Thursday, January 01, 2015 7:58 PM
To: ontolog-forum@xxxxxxxxxxxxxxxx
Cc: cg@xxxxxxxxxxxxx; Pavlos Peppas
Subject: Re: [ontolog-forum] The Lindenbaum lattice and a biography of Adolf 
Lindenbaum    (07)

On 1/1/2015 2:07 PM, David Whitten wrote:
> what are the AGM operations?  Do I know them by another name?    (08)

They're named after the three authors of the classic paper:    (09)

Alchourrón, C.E., P. Gärdenfors, and D. Makinson, 1985, “On the Logic
of Theory Change: Partial Meet Contraction and Revision Functions”,
Journal of Symbolic Logic, 50: 510–530.    (010)

The two basic operators determine walks through the lattice of theories.    (011)

  - Contraction:  Removing an axiom (or belief) from a theory.  This
    moves up the lattice to a more general theory.  This is always safe
    because it can never create an inconsistency.    (012)

  - Expansion:  Adding an axiom (or belief).  This moves down the
    lattice.  If the new axiom is inconsistent with the others, it
    causes a drop to the inconsistent theory (AKA the absurd theory)
    at the bottom of the lattice.    (013)

I prefer to add a third operator:    (014)

  - Relabeling:  Systematically renaming one or more names (of functions,
    relations, or constants) to names that are otherwise unused.  This
    jumps to a theory in another branch of the lattice that is isomorphic
    to the original.  Logicians usually ignore it because it doesn't add
    anything new, but it is very useful for metaphors and analogies.  It
    is also guaranteed to preserve consistency.    (015)

Other operations are defined in terms of these three.    (016)

  - Revision:  Replacing one or more axioms.  This is a sideways move,
    equivalent to contraction followed by expansion.    (017)

  - Consolidation.  Restoring consistency to a theory that has become
    inconsistent because of some unsafe expansion.  This process usually
    involves some contraction and/or relabeling and possibly expansion.    (018)

  - Merging.  Expanding one theory by adding all the axioms of another
    theory.  This theory is a common specialization of both theories
    that were merged.  If the starting theories were inconsistent,
    the merger drops to the absurd theory at the bottom.  In that case,
    consolidation is required.    (019)

For an intro to the axioms of belief (or theory) revision and related
issues, see http://plato.stanford.edu/entries/logic-belief-revision/    (020)

Following is a 42-page survey of the field by Pavlos Peppas.  He gives
a thorough survey with applications and 111 references:
http://pavlos.bma.upatras.gr/paperFs/8.pdf    (021)

See his web site for more recent papers about belief revision and
applications:  http://pavlos.bma.upatras.gr/    (022)


John    (023)

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