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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: Sat, 3 Jan 2015 10:06:39 -0800
Message-id: <!&!AAAAAAAAAAAYAAAAAAAAAAb3x6NyrzVKo6ReWvn+7BjCgAAAEAAAAPCUy7v/o9JDlBAMKIDOdWoBAAAAAA==@xxxxxxxxxxxxxxxxxxxxxx>

This is another one:

 

A +′ p, the (non-closing) expansion of A by p is the set A{p}.

 

The symbol +’ is the least elegant symbol, where everyone else uses * for closure, + for no closure.  Or is this a trick philosophers are fond of?.

 

 

Sincerely,

Rich Cooper

EnglishLogicKernel.com

Rich AT EnglishLogicKernel DOT com

9 4 9 \ 5 2 5 - 5 7 1 2

From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Rich Cooper
Sent: Saturday, January 03, 2015 9:02 AM
To: '[ontolog-forum] '
Cc: cg@xxxxxxxxxxxxx; 'Pavlos Peppas'
Subject: Re: [ontolog-forum] The Lindenbaum lattice and a biography of Adolf Lindenbaum

 

John,

 

In the Plato paper on belief systems, it is written:

 

Abe has the basic beliefs p and q, whereas Bob has the basic beliefs p and pq. Thus, their beliefs (on the belief set level) with respect to p and q are the same.

 

The symbol ““ looks like “is equivalent to”, but it is very messily nonstandard where the usual “=” should be, or even the three hyphen equivalence symbol usually read as “defined as”.  But am I missing something symbolic in that interpretation?  Why would the author generate idiosyncratic symbology to explain something as normal as equivalence, if that is really what he meant by it. 

 

But it’s a good paper anyway. 

 

-Rich

 

Sincerely,

Rich Cooper

EnglishLogicKernel.com

Rich AT EnglishLogicKernel DOT com

9 4 9 \ 5 2 5 - 5 7 1 2

From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Rich Cooper
Sent: Friday, January 02, 2015 10:41 AM
To: '[ontolog-forum] '
Cc: cg@xxxxxxxxxxxxx; 'Pavlos Peppas'
Subject: Re: [ontolog-forum] The Lindenbaum lattice and a biography of Adolf Lindenbaum

 

Thanks John, I'm still reading the Plato paper, but when I finish it, I will read those two links as well. 

 

But for now, you wrote:

 

According to Dunn's semantics for modal logic (which I recommend),

that two-way distinction can be used to define the modal operators.

Any statement implied by the laws (or by the T-Box) is defined to

be necessarily true.  Any statement that is consistent with the

laws (or T-Box) is defined to be possible.

 

You didn’t mention “any statement that is inconsistent with the laws is …” or otherwise dispose of that remaining case.  To look for inconsistencies within a system could be a useful capability.  Could you complete the sentence please?

 

-Rich

 

Sincerely,

Rich Cooper

EnglishLogicKernel.com

Rich AT EnglishLogicKernel DOT com

9 4 9 \ 5 2 5 - 5 7 1 2

 

-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F Sowa
Sent: Friday, January 02, 2015 9:54 AM
To: ontolog-forum@xxxxxxxxxxxxxxxx
Cc: cg@xxxxxxxxxxxxx; Pavlos Peppas
Subject: Re: [ontolog-forum] The Lindenbaum lattice and a biography of Adolf Lindenbaum

 

On 1/2/2015 11:13 AM, Rich Cooper wrote:

> That belief revision article is confusing when talking about

> “epistemic value” as a measure of “entrenchment”.

 

Any document that uses the word 'epistemic' is likely to be confusing.

That comment is not a slur on the people who use the word 'epistemic'.

It's just an observation that nobody has ever been able to state a

precise definition of the words 'knowledge' and 'belief' that is

consistent with the way ordinary people use those words.

 

However, the word 'entrenchment' as used in discussions of belief

or theory revision can be defined precisely.  It just means that

you can specify a partial ordering of certain statements.

 

The simplest ordering assumes two kinds of statements.  For example,

they may be called laws and facts.  The laws are more "entrenched"

than the facts.  When you're revising a theory, you would preserve

the laws and revise the facts.

 

Another pair of terms is T-Box (terminology) vs. A-Box (assertions).

The T-Box (AKA ontology) is more entrenched than the A-Box, and

any revisions should be made to the A-Box rather than the T-Box.

 

According to Dunn's semantics for modal logic (which I recommend),

that two-way distinction can be used to define the modal operators.

Any statement implied by the laws (or by the T-Box) is defined to

be necessarily true.  Any statement that is consistent with the

laws (or T-Box) is defined to be possible.

 

In the following articles, I generalized Dunn's semantics to allow

a partial ordering of the laws by degree of entrenchment:

 

    http://www.jfsowa.com/pubs/laws.htm

    Laws, facts, and contexts

 

    http://www.jfsowa.com/pubs/worlds.pdf

    Worlds, models, and descriptions

 

For example, the most entrenched laws would be "logically true"

(i.e., valid or true in all models).  Next would be physically

true according to known laws of physics.  Next would be the laws

of various authorities, such as the Bible, the US Constitution,

your mommy, etc. -- ordered according to your personal concerns.

 

The meanings of the words 'necessary' or 'must' depend on which

laws are being considered in the current context.

 

Summary:  The reasons why I prefer Dunn's semantics and Lindenbaum

lattices are (a) they're consistent with the confusing publications

philosophers produce, (b) they're compatible with the implementations

used in AI, and (c) they're much, much easier to explain to students

and ordinary human beings.

 

John

 

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