From: Drew McDermott <drew.mcdermott@yale.edu>

Date: Mon, 5 Feb 2001 13:52:17 -0500 (EST)

Message-Id: <200102051852.NAA04807@mr3.its.yale.edu>

To: connolly@w3.org

CC: drew.mcdermott@yale.edu, www-rdf-logic@w3.org

Date: Mon, 5 Feb 2001 13:52:17 -0500 (EST)

Message-Id: <200102051852.NAA04807@mr3.its.yale.edu>

To: connolly@w3.org

CC: drew.mcdermott@yale.edu, www-rdf-logic@w3.org

> > Should the language have types? I think the answer is a strong Yes, > but many AI languages have used sets instead. The difference is that > types behave more like a syntactic restriction on variables and > predicates, whereas sets are objects in the domain. er... the PCC/PCA work http://www.w3.org/DesignIssues/Logic#PCA shows that stuff I want to do can be done with typed lambda calcluclus. I'm guessing, but I suppose that's sorta what you mean by types. I have no idea whether the same stuff can be done without types. Folks have been asking about model-theoretic semantics for RDF; when considered as a cut-down FOPC, that's easy enough to do in terms of regular old ZF-set theory and such. I went looking for model-theoretic semantics for typed lambda calculus and found hairballs. Is that what you mean by sets? i.e. sets in the model theory? Or sets ala RDF Classes? There are two alternative lines of descent from Russell and Whitehead: set theory and type theory. The former avoids paradoxes by careful axioms, the latter by requiring that all formulas are well-typed. Set theory uses less machinery, but the resulting mathematical economy is of little relevance to us (in my opinion). By set I mean "RDF class," i.e., a collection of objects referred to by terms in the theory. (The model theory has its own requirements.) > > Should the language have functions? They are often very handy. In > PDDL, for instance, we have recently added functions that denote > fluents, so that volume_in(tank3) might denote the time-varying amount of > fluid in tank3. PDDL? pointer? My web page: http://www.cs.yale.edu/~dvm, follow link to "Planning Domain Definition Language." (It's currently being revised by the committee organizing the 2002 planning competition.) > Some of the participants in a the discussion assume that > intensionality = quotation. It's true that quotation is one way to > implement intensionality, but it's not the only way. The other is > just to use possible-world semantics. pointer? Hughes and Cresswell, Intro. to Modal Logic Robert Moore's 1995 Logic and Representation, which I haven't read, but appears to contain a recent update of his classic Ph. D. thesis from the 70s on possible-world semantics for belief and action. Ernie Davis's book on knowledge representation may talk about possible worlds. I'm pretty sure it goes into the quotation idea in some detail. (His student Leora Morgenstern wrote a thesis on the subject.) The key idea behind possible worlds is to analyze believes(a, p) as "In all possible worlds consistent with what agent a believes, p is true." It may seem as if we have to quote p to make it into a term, but we don't. We just treat it as denoting a function from possible worlds to truth values. In fact, all propositions are such functions. So "believes" is a function from (agents, prop) -> prop where prop = worlds -> truth-values and believes(a, p) is true in world W if in all worlds W' "accessible to W" such that W' is consistent with what a believes, p is true in W'. We need to toss in an accessibility relation so that we can control the quantification. So we can say things like believes(Fred, believes(Mary, faithful(Fred))) The accessibility relation, and the property "consistent with what a believes" are just given. (The usual semantic move.) These entities must be constrained by various axioms, such as believes(a, p) -> believes(a, believes(a, p)) which is true if the accessibility relation is transitive. > I don't understand the power of "triples." Doesn't XML already have > "triples"? If I say > > <foo u="x"> > <baz v="y"/> > </foo> > > isn't there a triple x-baz-y? The nodes in that triple aren't URIs. > What's the big deal? Well... triples look like an important primitive when your (my) background is in the Web, where links have two ends and a type. The subject-verb-object thing seems to be an important primitive in human communication (cf Chomsky). RFC822 header fields have the same property/value structure, with an implicit subject. Likewise library catalog cards. OOP programming uses object.prop = value all the time. Triples are an idiom that show up all over the place, in my experience. They look like a pretty important and useful modelling primitive. I think the object/property/value will continue to be an important idiom for communication with users, whether or not it continues to be The Ultimate Primitive in a universal language for the web. Ah, from this remark and those made by others, I begin to understand a bit what the appeal of triples is. > Let me repeat the problem: If RDF is just a mechanism for describing > the syntax of some other language, then it's irrelevant. Not totally; you have to have some syntax to put in email and to put into and out of tools. There's a certain investment in software and wetware in RDF. Maybe not indispensable, but not irrelevant either. I guess my objection goes like this: I've got nothing against binary relations. If there were a good reason, I would even go along with eliminating everything *but* binary relations. But everyone acknowledges that we need something else (quantifiers, types, statements about statements, etc.), so we must be able to put something else around the binary relations. Here's where we run into trouble. Using binary relations to *describe* something else does *not* succeed in wrapping that something else around the binary relations. It just shifts us to talking about a completely different language, or, more often, *not* talking about it. [Jonathan Borden:] I view RDF as simply a mechanism to represent directed graphs whose nodes and arcs are labelled with URIs -- no more -- no less. As a language naked RDF is capable of describing such labelled directed graphs. On top of that, the presumption is that one can layer logical statements. The first point is not quite true; the second is obscure. If the purpose is to represent graphs on URIs, then the question becomes whether the contents of a KR system is essentially a graph, or essentially a set of sentences. Through the ages (or at least the last forty years), people have been attracted to the graph idea, but sooner or later they give up on it. The development of Cyc is a classic example. It started off as a semantic network, but eventually switched to being a variant of predicate calculus. You can still have graphs, for indexing or algorithmic purposes, but they're not the primary notation. The reason is that it's just too clumsy to do semantics on a graph. If you insist that we really do need to represent graphs (say, to encode knowledge about a telephone switching network), then you might want to consider RDF as a graph-description sublanguage of our target language. But you still have to give up the idea that the truth value of a subgraph is independent of its context. If I describe Friedrich's beliefs about the French telephone system, I do not thereby describe the French telephone system. I don't know what is meant by "layering logical statements" on RDF, unless it means describing another language in RDF, which, as I said above, is not very productive. -- Drew McDermott P.S. I'm about to disappear for a while for a medical reason, not because I've run out of things to say!Received on Monday, 5 February 2001 13:52:20 UTC

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