From: Michael Kifer <kifer@cs.sunysb.edu>

Date: Thu, 08 Nov 2007 17:22:01 -0500

To: axel@polleres.net

Cc: "Public-Rif-Wg \(E-mail\)" <public-rif-wg@w3.org>

Message-ID: <32649.1194560521@cs.sunysb.edu>

Date: Thu, 08 Nov 2007 17:22:01 -0500

To: axel@polleres.net

Cc: "Public-Rif-Wg \(E-mail\)" <public-rif-wg@w3.org>

Message-ID: <32649.1194560521@cs.sunysb.edu>

> > Michael Kifer wrote: > > Model theory of builtin predicates is not a problem. Modes (binding > > patterns) are extra-logical. We have to decide what do about them in terms > > of our recommendation (e.g., issue an error and abort). > > Do you think the definition of binding patterns below works? What do you mean by "works"? I was talking about a model-theory. I did not find a model-theoretic definition (for binding patterns) in what you wrote below. > BTW: One thing which is non-standard in the Eiter et al. definition is > that an the extension of a predicate can be input. > > > Builtin functions present a bigger challenge. They can also have fixed > > interpretation as functions, but builtin functions are partial, so they > > require special treatment in the model theory, and I am not sure if this > > complication is worth the trouble. > > Would an extra "error" constant value solve that problem? Yes. This is what I called a "complication". Once you have this constant, you need to explain what would be the truth value of things like p(abc,error) and Not p(abc,error), where p/2 is a non-builtin predicate. This would require to introduce a multivalued logic already into BLD (since neither p(abc,error) nor Not p(abc,error) should be considered as true). I do not think we should do it. --michael > Axel > > > --michael > > > >> Evaluable predicates: > >> > >> The most general definition of external predicates (built-ins), I know > >> of (in an attempt to write down the definition of Eiter et al. [1] in a > >> RIF suitable way): > >> > >> An evaluable predicate &pred(X_1,....,X_n) is assigned with one or more > >> binding patterns, where a binding pattern is a vector {in,out}^n. > >> Intuitively, an evaluable atom provides a way for deciding the truth > >> value of an output tuple depending on the extension of a set of input > >> predicates and terms. Note that this means that evaluable predicates, > >> unlike usual definitions of built-ins in logic programming, can not only > >> take constant parameters but also (extensions of) predicates as input. > >> inputs can not only be terms, but also predicate names (in which case > >> the *extension* of the respective predicate is the input.) External > >> predicates have a fixed interpretation assigned. The distinction > >> between input and output terms is made in order to guarantee that > >> whenever all input values of one of the given binding patterns are bound > >> to concrete values, the fixed interpretation only allows a finite number > >> of bindings for the output values, which can be computed by an external > >> evaluation oracle. > >> > >> > >> 1. T. Eiter, G. Ianni, R. Schindlauer, H. Tompits. A Uniform Integration > >> of Higher-Order Rea- > >> soning and External Evaluations in Answer Set Programming. In > >> International Joint Con- > >> ference on Artificial Intelligence (IJCAI) 2005, pp. 90–96, Edinburgh, > >> UK, Aug. 2005. > >> > >> > >> -- > >> Dr. Axel Polleres > >> email: axel@polleres.net url: http://www.polleres.net/ > >> > >> > >> > >> > >> > > > > > > > -- > Dr. Axel Polleres > email: axel@polleres.net url: http://www.polleres.net/ > > > > >Received on Thursday, 8 November 2007 22:22:16 UTC

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