From owner-cse663-fa08-list@LISTSERV.BUFFALO.EDU  Mon Sep  1 20:14:15 2008
Date:         Mon, 1 Sep 2008 20:14:06 -0400
From: "William J. Rapaport" <rapaport@cse.Buffalo.EDU>
Subject: 663: Three Basic KR Notions
To: CSE663-FA08-LIST@LISTSERV.BUFFALO.EDU

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Subject: Three Basic KR Notions
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So that we don't get too far behind this early in the semester, I want
to finish a few things that I started on Friday via the Listserv.

Three Basic KR Notions:

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1.  "A knows (or believes, or wishes, or judges, or hopes, etc.)
     that P (or how to do alpha, or who x is, etc.)"

Here, "A" is a cognitive agent, possibly computational.

The cognitive act of knowing or believing or ... is sometimes called a
"propositional attitude" when the "object" of the cognitive act,
i.e., what is known or believed or ..., is a proposition "P".

	In this case, the proposition is usually expressed by a
	declarative sentence.

	"Proposition" is a technical term of philosophical logic,
	with no universally agreed-upon meaning.  Some people consider
	a proposition to be the meaning of the sentence that expresses
	it.  Others define a proposition to be whatever is the object
	of a belief.  Still others consider a proposition to be the
	"bearer" of truth value, i.e., that which can be either true
	or false (as opposed to: (1) "things", expressed by noun phrases;
	(2) actions (expressed by verb phrases); or (3) properties 
	(expressed by adjectives).

If what is known is how to do an action "alpha", then the cognitive act
is called "procedural knowledge".  (And, of course, computer science can
be considered the study of procedures.)


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2.  "R represents W for A"
	(or: "A uses R to represent W")
	(or: "A represents W as (or: by) R")

Here, "A" is the cognitive agent.
      "R" is a representation.
      "W" is the thing represented:  it could be a fact, or a belief,
            	                     or an existent, or a non-existent,
                                     or a truth, or a falsehood

There are several "manners" of representation:
- linguistic, pictorial, etc.

There are different "guises", i.e., *ways* of thinking about W:
- the same person can be represented under the guises "George W. Bush"
  or "President of the US" or "Commander in Chief of the US Armed
  Forces"	

- the same astromical body can be represented under the guise
  "the morning star" or the guise "the evening star" 

- the same number can be represented under the guises "2+2" or "4".

For more on all of this, see:

Hirst, Graeme (1991), "Existence Assumptions in Knowledge
Representation", Artificial Intelligence 49: 199-242.
                                
 
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3.  Sense vs. Reference

Some logicians recognize at least two kinds of representational
relations:  sense and reference.  This theory was originated by Gottlob
Frege, a turn of the last century German mathematician and philosopher.

Briefly:  
	Every expression of a language has a "sense" ("Sinn" in German)
        Some senses also have a "referent" ("Bedeutung" in German;
		there are other English translations: reference, denotation)
	A referent is an existing entity in the world (typically).
	A sense is the way in which the expression picks out its referent.
		(For "way", think "algorithm for computing".)
	Not all expressions have referents:  e.g., "unicorn" doesn't.
	But humans and other cognitive agents, such as computers, have
	to think about and compute with such "non-existents".

For more on this, see Hirst 1991 and:
"SNePS and Knowledge, Belief, & Intensionality"
http://www.cse.buffalo.edu/~rapaport/snepsintensionalitypapers.html