Re: [ontolog-forum] Ontologies as social mediators

[FERENC KOVACS <f.kovacs@xxxxxxxxxxxxxx>]

Chris Menzel wrote:

 

On Dec 5, 2009, at 10:48 AM, doug foxvog wrote:
> Ferenc wrote:
>>
>> ... I have been trying to visualize the
>> condition where objects, properties and relations change theri character
>> and they become one of the other two as a result of mental operations.
>> ... So jsut a few examples
>> One of these operations is abstraction
>> that helps you see the properties of an object and create a list of such
>> properties.
>> Then by taking one of those properties as an OBJECT, you can go on to
>> define another set of properties.
>
> This is quite valid.  The issue of "chang[ing] their character" arises from
> the limitations of first order logic.  Computational complexity becomes
> greater when describing properties of properties and reasoning about them.

That is of course true in full higher-order systems but, as noted a
couple of times in this forum by Pat Hayes and others, a system does
not become higher-order in a sense that increases its complexity
simply in virtue of permitting reasoning about properties and
relations.  The complexity of such reasoning increases (from the
semi-decidability of first-order logic to full undecidability) only
under a very strong assumption: that every subset of the domain of an
interpretation is (the extension of) a property; more generally, that
every set of n-tuples of objects in the domain is (the extension of)
an n-place relation.  This is the assumption that, from a purely
theoretical perspective, separates first-order from higher-order
logic.  But, importantly, this assumption cannot in fact be
implemented in a reasoning system, as higher-order logics are
semantically incomplete: given any proposed reasoning method for a
second- or higher-order logic, there will be logically valid argu
ments whose validity cannot it cannot demonstrated by that method.

> In higher-order logic, one can treat relations, classes, and statements
> "relation instances", and instances of classes and make statements about
> them using relations which accept such classes.  The Cyc reasoner has been
> doing this since at least the mid-1990s.

As have many other higher-order systems (as I'm sure you know).  For
the reasons above, however, the implemented reasoning methods for
these systems -- even those whose formal semantics are fully
higher-order -- are theoretically first-order (in the sense that they
are complete relative to a weaker semantics for the systems (so-called
"general semantics", based on the work of Henkin) that abandon the
strong assumption above).  Indeed, some implementations of such
systems (the HOL System, for example) translate the entire system into
an explicit first-order theory to which standard first-order reasoning
methods can then be applied directly.

Chris Menzel

I am certainly not well educated in formal logic, but to me it appears to me that

1) semantics (semantic analyis) should not be constrained to syntax parsing for terminal symbols,

2) reasoning should not be confined to the use of syllogisms in inferences, and
3) computability of valid conclusions by processing chained data base tables should not be a problem provided that a proper GUI is available

4) without verbs as relations the representations of concepts in various networks do not make sense or offer pracical use for people who want to go from one domain to another using a common interface/template that could be provided by relations other than those in use today. You may want to zoom in and out from your 2D representations as opposed to moving in the plane. And to that end you need to be able to change scale in an orderly fashion

Ferenc.

  

 

 

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