To:  ontologforum@xxxxxxxxxxxxxxxx 

From:  FERENC KOVACS <f.kovacs@xxxxxxxxxxxxxx> 
Date:  Sun, 6 Dec 2009 20:25:34 +0000 (GMT) 
Messageid:  <130537.19105.qm@xxxxxxxxxxxxxxxxxxxxxxxxxxx> 
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 higherorder systems but, as noted a couple of times in this forum by Pat Hayes and others, a system does not become higherorder 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 semidecidability of firstorder 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 ntuples of objects in the domain is (the extension of) an nplace relation. This is the assumption that, from a purely theoretical perspective, separates firstorder from higherorder logic. But, importantly, this assumption cannot in fact be implemented in a reasoning system, as higherorder logics are semantically incomplete: given any proposed reasoning method for a second or higherorder logic, there will be logically valid argu ments whose validity cannot it cannot demonstrated by that method. > In higherorder 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 mid1990s. As have many other higherorder 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 higherorder  are theoretically firstorder (in the sense that they are complete relative to a weaker semantics for the systems (socalled "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 firstorder theory to which standard firstorder 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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