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Re: [RIF] A Modest Proposal: Work Out Some Concrete Examples; Example-1: CHANGE-BABY-IF-WET rule

From: Michael Kifer <kifer@cs.sunysb.edu>
Date: Fri, 27 Jan 2006 18:07:22 -0500
To: "Ginsberg, Allen" <AGINSBERG@imc.mitre.org>
Cc: public-rif-wg@w3.org
Message-Id: <20060127230722.7434E20731E@kiferdesk.lmc.cs.sunysb.edu>


>  
> Hi Michael, Thanks for your response. For now I just want to respond to
> your statement that first-order logic is ill-suited to analyze the
> meaning of production rules. I want to stress that first-order logic,
> in this instance, is just a vehicle for expressing an analysis.   The
> analysis could be done in natural language, but I find using logical
> notation to be helpful in expressing things and also as a step towards
> a more formal analysis.

Hi Allen,
Yes, I understand what you are trying to do.
What I meant was that you are not really using first-order logic, but
first-order logic interspersed with English. That may still be formal, but
not a logic. 

Of course, there were arguments here that the semantics doesn't need to be
model-theoretic and be based on a logic. So, the above is just my personal
point of view.

> 
> Let me restate what it is that I think needs to done, and let me do
> that by means of another example.
> 
> Let's consider the necessity operator in modal logic, let us denote it
> "N".   "Np" (p is necessarily true) means, according to a kripkean
> semantics that p is true on all possible worlds.  To be clear about
> what that means, we can quantify over possible worlds and explicate the
> meaning of Np as 
> 	(forall x)(PW(x) -> T(p,x))  
> 
> i.e., if x is a Possible World [Pw(x)] then p is True in x T(p,x].
> 
> We should, of course, go on to provide first-order axioms that express
> our interpretation of PW(x) etc. 
> 
> Clearly if I want to use modal operators in practice, some form of
> modal logic is a cleaner way to do that.
> 
> BUT, if I want to EXPLAIN to someone what these operators MEAN then I
> need to tell them the story about possible worlds and truth in a
> possible world, etc.  The full story would involve explicating
> kripke-structures and accessibility relations and so on.  
> 
> My feeling is that if one wanted to express the semantics of
> modal-logic in a formal fashion, then using first-order logic is a good
> way to do that.
> 
> In the same way, if I want to explain to someone what a production
> system is, then I need to tell them the story about Working Memory,
> facts being in working memory, facts being added or deleted from
> working memory, etc.  That is what my analysis was trying to do and
> that is what I think the RIF should enable.    My feeling is that using
> first-order logic is a good way to express those semantics.

In some cases -- yes. But even when a new logic can be encoded
in first-order logic, the encoding is not always useful and a direct
semantics is much preferred. That is, encoding in first-order is not always
a good way to express semantics.

In particular, I think that the semantics of production systems should be
defined at a level higher than the working memory business. This seems too
close to an implementation.

> 
> I don't know much about the particulars of Flora-2 or transaction
> logic, but it sounds to me that the semantics of that logic could
> equally be explicated in first-order logic.  In other words, to
> understand the meaning of the Flora-2 version of change-baby-if-wet
> requires quantifying over states and probably actions.  The semantics
> of states and actions needs to be explicated. 

In this particular case, I don't think an encoding in standard first-order
logic is possible. At least, I don't know how.

> Using first-order logic to do these sorts of analyses is good because
> it forces one to say exactly what types of things one is postulating as
> basic entitles and so forth.

As you may have guessed from the above, I agree only partially, but
disagree in general.


	--michael  

> 
> Allen
>  
> 
> -----Original Message-----
> From: Michael Kifer [mailto:kifer@cs.sunysb.edu] 
> Sent: Thursday, January 26, 2006 10:14 PM
> To: Ginsberg, Allen
> Cc: public-rif-wg@w3.org
> Subject: Re: [RIF] A Modest Proposal: Work Out Some Concrete Examples;
> Example-1: CHANGE-BABY-IF-WET rule 
> 
> 
> You are trying to use first-order logic to analyze what this logic is
> ill-suited to do. It is a production rule whose semantics is best and
> described in Transaction Logic
> http://www.w3.org/2005/rules/wg/wiki/Transaction_Logic.
> For instance, in
> FLORA-2, which supports much of Transaction Logic, this Jess rule would
> look like this:
> 
> changeBabyIfWet(?Baby) :-
> 	wet(?Baby),
> 	changeBaby(?Baby),
> 	delete{wet(?Baby)}.
> 
> change(?Baby) can also be defined via a rule as deleting the old diaper
> and
> inserting a new one where appropriate. The exact definition depends on
> how
> exactly you represent diapers and the fact that a particular diaper is
> on a
> particular baby.
> 
> In Transaction Logic, the above changeBabyIfWet(?Baby) would be a
> state-changing action. It is defined as a sequence of queries and other
> actions. In our case, it is defined as a query (wet(?Baby)) followed by
> an
> action (changeBaby(?Baby)), which changes the underlying state by
> replacing
> the old diaper with a new one, and then deleting the fact that the
> specified baby is wet. 
> 
> 
> 	--michael  
> 
> 
> "Ginsberg, Allen" <AGINSBERG@imc.mitre.org> writes:
> > 
> > Dear RIF-WGers,
> > 
> > It seems to me that one way of clarifying what the RIF is and what it
> > can or should enable is to work on some concrete examples.
> > 
> > So here is a contribution to that effort:
> > 
> > Consider the following rule definition (taken from the book "Jess in
> > Action" by Ernest Friedman-Hill, p. 98)
> > (For those not familiar with this syntax I have provided comments.)
> > 
> > (defrule change-baby-if-wet 
> > 	 // bind the working memory element that satisfied the pattern
> to the variable ?wet
> > 	?wet <- (baby-is-wet) 
> > 	=>
> > 	(change-baby)
> > 	// remove the element bound to the variable ?wet from the
> working memory
> > 	(retract ?wet)  
> > )
> > 
> > 
> > Here are some questions: 
> > 
> > 1) From a theoretical point of view, is there a single optimal or
> > correct analysis of the "semantics" of this rule?
> >    Or is it possible that more than one reasonable analysis can be
> > given?  If so, must these analyses be equivalent?
> > 
> >    To flesh this out a bit, here are two possible analyses
> > 
> > 	(A) the meaning of this rule can be represented in classical
> > propositional logic as follows:
> > 
> > 		(P & Q) -> (R & S)
> > 
> > 	where 
> > 		P = "The variable ?wet is bound to an element in
> > working memory"
> > 		Q = "The fact [baby-is-wet] is in working memory"
> > 		R = "The fact [baby-is-changed] is in working memory"
> > 		S = "The element bound to variable ?wet is not in the
> > working memory"
> > 
> >      OR  (B) using first-order logic we might try something like
> > 
> > 	  (ForAll x)(Forall y) (Forall t) 
> > 		[ InWM(y,t) & y = fact("baby-is-wet") & Bound(x, y) ->
> > (Exists z) (z = fact("change-baby")) & InWM(z,t+1) & ~InWM(y,t+1) ]
> > 
> > 	Where 
> > 		InWM(x,t) = "x is in Working Memory at time t"
> > 		fact(<string>) is a function that returns the fact
> > associated with <string>
> >             Bound(x,y) = "x is bound to y"
> > 
> > To me, analysis (B) captures more of what is going on then analysis
> > (A). However, both analysis represent the meaning of the original
> rule
> > in terms of a formal language that has well-defined semantics itself.
> > Neither analysis is complete because they do not explicate the
> > predicates or terms involved in their representations of the rule
> > meaning, but that could be done.  In particular, there is a discrete
> > time-model involved regarding Working Memory that needs to fleshed
> out.
> > 
> > 2) Assuming an analysis like (B) is more in line with our
> understanding
> > and expectation concerning the RIF, how should it be done in the RIF?
> 
> > 
> >    Rather than answering that question I would state some criteria on
> > any proposed answer (relative to this concrete example for now):
> > 	
> > 	1) It should be clear that the RIF representation of the
> > change-baby-if-wet-rule can be generated by a general algorithm
> > 
> > 	2) It should be clear that the resulting representation can be
> > used to generate an equivalent change-baby-if-wet rule in systems
> that
> > belong
> > 		to the same family as CLIPS/JESS, for example, JRULES. 
> > 	
> > 	3) For systems in a different family (having a different
> > meta-model) such as a prolog-based system, the RIF should make it
> > possible to transform
> >          the original RIF representation of the meaning of the
> > change-baby-if-wet rule into a RIF-representation of the meaning of
> > that rule in the for
> >           systems in the other family.
> > 
> > 
> > NEXT STEPS for example-1:  
> > 
> >     1) Find equivalent rules for change-baby-if-wet rule in other
> > systems in the same family
> >     2) Find equivalent rules for change-baby-if-wet rule in other
> > systems in different families
> >     3) for each of the families on step (2), figure out reasonable
> > possible representations of the meaning of the change-baby-if-wet
> rule
> > in terms
> >          of a language or model that has well-known semantics.
> > 
> > _______________________________________________________________
> > 
> > Dr. Allen Ginsberg        The MITRE Corporation, Information
> Semantics 
> > aginsberg@mitre.org       Center for Innovative Computing &
> Informatics
> > 
> > Voice: 703-983-1604       7515 Colshire Drive, M/S H305 
> > Fax:   703-983-1379       McLean, VA 22102-7508, USA 
> > 
> > 
> > 
> 
> 
> 
> 
Received on Friday, 27 January 2006 23:07:33 GMT

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