Re: evaluable predicates, general definition

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).

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.


	--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/
> 
> 
> 
> 
>

Received on Thursday, 8 November 2007 21:39:09 UTC