From: pat hayes (phayes@ai.uwf.edu)
Date: 06/03/03
Hi Harold, a few questions about your selector notation. We have been thinking along similar lines for SCL, hence the details. If the answers are published somewhere just point me at that. >Hi Sandro, > >> > In the example, the individual constant "5.0 percent" can be >>analyzed as the >> > cterm percent[5.0], and the constant "2003/04" can be analyzed as either a >> > positional cterm interval["2003","2004"] or again as an >>object-oriented cterm >> > interval[start->"2003";end->"2004"]. Note that square brackets >>are preferable >> > for cterms to clearly set them off from the parenthesized atoms. >> >> cterms are construction functor expressions? This syntax is new to >> me; where does it come from? Does it have detractors? > >Yes, originally 'complex terms' are exactly what Prolog calls >'structures'. The >distinction between (round) parentheses for active calls and [square] brackets >for passive structures was introduced in Relfun -- cf. >http://www.relfun.org/ or >http://www.cs.unb.ca/~boley/cs6905/cs6905FLP.pdf -- and can be seen >as an obvious >generalization of Prolog's list notation via a polyadic tup >constructor, so that >[e1,...,eM] is definable as tup[e1,...,eM]. SCL follows KIF in allowing polyadicity explicitly, so we can define tup axiomatically, so this is also natural for us. > >Later, in Object-Oriented RuleML, we have permitted 'complex terms' to *also* >contain unordered roles with their fillers, or -- as in F-Logic -- to *only* >contain such frame-like 'slots'. In that sense, this is a merger of Prolog and >F-Logic. > >Well, a 'detractor' -- which sounds better as the antonym for >'constructor' than >'destructor' does -- in a unification-based language such as Prolog, >Relfun, or >F-Logic can be represented by a local unification and variable >dereferencing for >the selected part of the complex data structure (BTW, John McCarthy >in his work >on abstract syntax used 'selector' as the antonym for 'constructor'). First question, how does one unify a term which selects a subexpression which isn't present? Does the unifier have to supply a suitable binding, or does the unification fail? Eg consider unifying interval[StartDate, EndDate] with a single variable ?x >So we can access the start date of interval["2003","2004"] by unifying it with >interval[StartDate,EndDate] and dereferencing StartDate to "2003". >Similarly, we >can access the end date of interval[start->"2003";end->"2004"] via unification >with interval[start->StartDate;end->EndDate] and dereferencing >EndDate to "2004". When is dereferencing performed? (Only during unification?) What is the difference between dereferencing and binding? The above first example looks like a normal unification if we read 'StartDate' as a variable; what does it mean to dereference a variable? Does interval[start->A; end->B] unify with interval[A,B] ? How about interval[start->?x; end->B] unified with interval[A,B] ? Does that bind ?x to A ; if so, what is the common instance? What happens if we put the variable on the other side: interval[start->A; end->B] unify with interval[?x,B] ? Does this bind ?x simply to B or to something that indicates the 'end' role? What is the common instance? (More generally, how is instantiation defined over Cterms? ) Does f[a->A] unify with f[a->A, b->B] ? (The reason for asking this is that in one interpretation, any 'missing' roles should be interpreted as existentials, eg that would be appropriate for case-grammar or event description logics, and then this kind of unification would be appropriate.) Can I write a variable in a role position, eg: f[?x->A] unify with f[a->A] ?? >But instead of / in addition to this, we can introduce a 'universal' >selector sel, >parameterized by either a positive integer or a role name. > >sel[1](interval["2003","2004"]) would return "2003". >sel[end](interval[start->"2003";end->"2004"]) would return "2004". What about sel[1](interval[start->"2003";end->"2004"]) ? Is that "2003" or undefined? Final question: what is the point of all of this? Why bother writing sel[1](interval["2003","2004"]) when you could just write "2003" ? Is the following meaningful?: sel[1](?x)= "2003" when ?x bound to interval["2003","2004"] ? It seems to me that if this works then you ought to be able to use this to mimic higher-order unifications. Has that been tried? Pat -- --------------------------------------------------------------------- IHMC (850)434 8903 or (650)494 3973 home 40 South Alcaniz St. (850)202 4416 office Pensacola (850)202 4440 fax FL 32501 (850)291 0667 cell phayes@ai.uwf.edu http://www.coginst.uwf.edu/~phayes s.pam@ai.uwf.edu for spam
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