From: Axel Polleres <axel.polleres@deri.org>

Date: Thu, 08 Nov 2007 22:00:12 +0000

Message-ID: <473386EC.30705@deri.org>

To: Michael Kifer <kifer@cs.sunysb.edu>, "Public-Rif-Wg (E-mail)" <public-rif-wg@w3.org>

Date: Thu, 08 Nov 2007 22:00:12 +0000

Message-ID: <473386EC.30705@deri.org>

To: Michael Kifer <kifer@cs.sunysb.edu>, "Public-Rif-Wg (E-mail)" <public-rif-wg@w3.org>

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? 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? 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 22:00:29 UTC

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