# Re: evaluable predicates, general definition

```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