John,
ABD logic is actually an axiomatization of the map and type (object)
constructions of topos theory in a first order two sorted language. The
sorts are map and type. There is one difference from standard FOL practice.
The first order operations are partial, but have definedness conditions
expressed in the logic. There are of course FOL systems that admit this. For
example, composition of maps is a first order function symbol, but is
defined only when the appropriate domains and ranges match for the maps
being composed. (01)
What one is doing is not denying FOL its proper place in the sun, but simply
using FOL with definedness conditions for operations and predicates, and
with a specific ontology, based on topos theory, which has been proven to be
sufficient to do a lot of mathematics and science in. This topos ontology
approach enables a lot of statements that are higher order in some
formalisms to be first order. (02)
Henson (03)
-----Original Message-----
From: John F Sowa
Sent: Sunday, October 06, 2013 7:38 AM
To: '[ontolog-forum] '
Cc: Henson Graves
Subject: Giving SysML a formal semantics (04)
There was some discussion about SysML on another forum, and
Peter Yim suggested that it be moved to Ontolog Forum. (05)
My note below summarizes the original messages by Christoph Lange
and Leo Obrst. (06)
John
-------- Original Message --------
Subject: Re: [ontoiop-wg] Possibly related work on giving SysML a formal
semantics
From: John F Sowa (07)
CL
> Graves, H., Bijan, Y., Using formal methods with SysML in aerospace
> design and engineering, Annals of Mathematics and Artificial Intelligence,
> Springer 2011
>
>
>http://www.omgwiki.org/MBSE/lib/exe/fetch.php?media=mbse:10.1007_s10472-011-9267-5.pdf
>
> They conclude with the sentence that …
>
>> A formal semantics along the lines of ABD logic should be part of the
>> formal
>> specification of SysML. (08)
Leo
> Henson Graves has been a recent contributor to various Ontology Summits,
> and is currently involved in the Ontolog mini-series on Ontology, Rules,
> Logic Programming for Reasoning and Applications.
>
> So we could ask Henson about its status. (09)
The question I would ask: "Why ABD logic instead of Common Logic?" (010)
Following is a specification of SysML that uses fUML, which is
specified in terms of Common Logic: (011)
xUML-SysML-Project-Report.PDF
Executable UML/SysML Semantics Project Report (Final), November 2008 (012)
This report is the first hit on Google when you type: xuml sysml fuml (013)
John (014)
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