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>

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 UTC

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