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

Date: Thu, 7 Jul 2005 20:53:39 -0400

Message-ID: <17101.52883.401574.826635@DVM-Powerbook.local>

To: www-rdf-rules@w3.org

Date: Thu, 7 Jul 2005 20:53:39 -0400

Message-ID: <17101.52883.401574.826635@DVM-Powerbook.local>

To: www-rdf-rules@w3.org

> [Ian Horrocks] > > I hope we are not talking about "meaning" in any higher sense - I am > but a humble computer scientist, and know little of this meaning of > which you speak! ... I've encountered this attitude before, about how "mere mortals" are incapable of talking about any semantics except "hard nosed" semantics of data structures. It's an odd attitude to take for people working on the semantic web. > All I am talking about is a formal "language" that, > given a theory (set of statements), specifies the set of models that > are admitted by the theory. The specification typically also defines > entailment in terms of models, i.e., a statement is entailed by a > theory iff it is true in every model admitted by the theory. It's the meaning of the word "admit" here that is the crux of the issue. Let's look at a concrete example. Suppose one has a temporal logic, whose semantics are spelled out by specifying (e.g.) what relationships among situations and timelines make (eventually P) true. Even the most humble computer scientist can understand such specifications (for which I'll use the letter M.) Now let's suppose that a nonmonotonic reasoning scheme is superimposed on the temporal-logic system (or included from the beginning). The consequence relation for this system takes the form we're discussing, namely, "Q follows from S if and only if Q is true in all P-models of S," where a P-model of S is a model satisfying some extra requirement. My claim is that this inference framework doesn't change the meanings of (eventually P) in any way. Look at it from a complementary viewpoint: Suppose, as often happens, that the P-models are exactly that subset in which a certain extra set of statements S' are true. So an equivalent way of specifying the nonmonotonic inference scheme is: "Q follows from S if and only if Q is true in all models of S U S'(S)." (It's necessary in general that S' depends on S.) Is it somehow supposed to be the case that adding a few extra statements changes the meaning of S? Isn't the meaning determined by M in spite of the way the nonmonotonic inference scheme is set up? Here's simpler case. Consider a simple first-order theory with equality, and focus on the definition of 'forall'. Now suppose someone wants to add the Unique Names Assumption. You can do it by restricting attention to models in which the function that maps constants to objects is injective. Or you can do it by adding a bunch of inequalities. Neither one changes the meaning of 'forall' in the slightest. > [...] > Two languages can interoperate if, given the same theory, they admit > the same models (and perhaps under other circumstances, e.g. if, as has > been suggested w.r.t. DLP, we restrict our means of examining models so > that we are unable to distinguish some differences in models). Think of it this way: "admit" is ambiguous. A theory T admits_1 model D if D is the in the set of models allowed by the intended meaning of T T admits_2 model D if T admits_1 D and no conclusion ruled out by the intended inference machinery is true in D (If the inference machinery is deductive, then admits_1 and admits_2 are the same; otherwise, they aren't.) I simply disagree with your statement "Two languages can interoperate if...they admit the same models..." if you insist on admits_2. It seems like an extremely strong requirement on interoperation that two modules must agree on inference mechanisms in order to interoperate. > [...] > According to my simple view of formal languages, if the semantic > specification of the formal language restricts all models to have > property P, ... The word "restricts" is ambiguous the same way "admits" is. -- DrewReceived on Friday, 8 July 2005 00:52:36 GMT

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