Philosophy

Are facts dead?

Clifford Heath — Sun, 22 Apr 2012 06:49:05 GMT

Although humorous, this article illustrates one of the challenges facing us as proponents of fact-based modeling:

Facts, 360 B.C.-A.D. 2012

While I'm not much interested in the political angles taken, there is an element of cultural truth here, I fear.

How is Philosophy important for you and your future and society in general?

Lylle123 — Mon, 31 Jan 2011 04:14:29 GMT

How is Philosophy important for you and your future and society in general? I just want to know how you think about philosophy. :]

Philosophy questions?

Gregoory — Mon, 17 Jan 2011 06:49:41 GMT

how far can you trust your sense experience according to plato?
why according to Descartes the only proof of existence is thought?
where does knowledge come orm according to John locke
can you prove the world exist out of your mind according to Berkeley

predicats and elementary facts

rolemo — Mon, 20 Oct 2008 15:22:28 GMT

what i dont understand is the fact that you can say that A exists (and create an existential fact), or you can define the property existence (or inexistence), then go on and say that A has the property existence (creating an elementary fact).

isnt it the same content declared in two different ways - once as an existential fact and once as an elementary fact?

Hilbert's Program and the Formalisation of ORM

VictorMorgante — Fri, 22 Aug 2008 08:27:24 GMT

Hi all,

At the turn of the last century and with the burgening of formal theories in mathematics, Hilbert lay down a challenge to mathematicians the world over to find solutions to the most pressing and challenging unsolved problems in mathematics.

Among those problems was proving the consistency of the formal theories, the 'toolboxes' if you will, used by mathematicians as the very basis for proofs, especially within (also burgening) proof theory.

In what became known as 'Hilbert's Program' it was evident, from the outset, that if you are going to prove the consistency of a formal theory...it needs to be proven within the precepts of the theory itself. The reason for this is that "If you prove consistency of theory A using the tools of theory B...then how can you be absolutely sure that theory B is consistent?" (Nagel & Newman, 2001, p. 24-44).

Godel has the distinction of proving the consistency of first order logic (FOL) and the incompleteness of a set of theories based on higher order logic (HOL). Within each set of proofs, he stuck to the tenet of Hilbert's program and worked within the precepts of the formal theories under analysis.

With Dr Halpin's doctoral thesis, and the formalisation of ORM, we are led to the consistency of ORM (Niam) under the tenets of the isomorphic relationship between ORM and KL (a FOL formulated within the paper). i.e. The paper 'proves' the consistency of ORM (a formal theory) under the precepts of another formal theory (KL).

So, I have a few questions. What is it about this one paper that allows it to seemingly break from the tenets of Hilbert's program? What is it about the isomorphism of ORM and KL that leads us to believe that there is absolutely no doubt that we can take the consistency of KL as proof of the consistency of ORM? Is it that we are saying (and indeed accepting) that ORM and KL are 100% isomorphic?

If ORM and KL are isomorphic, then why does the paper question the work of Leung who tried to prove the consistency of ORM using ORM (Halpin, 1989, p. '3-9')? If KL and ORM are 100% isomorphic, then if you do proofs in KL...you do proofs in ORM. Isomorphism doesn't work only one way....it works both ways.

Best regds
Victor

References (I've had requests to expand on references made in this post):

Nagel E. & Newman J. 2001, Gödel’s Proof. rev. ed. New York University Press.

Halpin T. A. 1989, A Logical Analysis of Information Systems: static aspects of the data-oriented
perspective (PHD Thesis).

Axioms of ORM

VictorMorgante — Mon, 21 Jul 2008 05:00:27 GMT

Hi all,

A question that swills around in my mind, and has done so for the last couple of months, is why we speak little about the 'axioms of ORM'.
For example (and not 'issue'), the Big Brown Book (Dr Halpin and Dr Morgan's latest ORM book "Information Modeling and Relational Databases") has no index reference for 'axiom' or 'axioms of ORM'. A quick internet search of 'axioms of ORM' returns no results of mention (in fact it returns 'no' results that I could find).

We speak of 'Axiomatic Set Theory' and we have a methodology (ORM) based on 'First Order Logic' (FOL) and yet we speak little of 'Axiomatic ORM Theory' or 'Axiomatic Conceptual Modeling'.

As we have 'Well formed theorems of FOL', why isn't it that we say 'Well formed theorems of ORM'?

Indeed, we speak of 'models' and 'diagrams', but their interpretation in FOL are 'theorems' and yet we rarely say 'theorems of ORM'. I'm not sure that I've heard anyone say "that's a 'well formed' ORM model". I can hear someone saying it...but it might be just 'me' remembering 'me' saying it.

Why is this?

I know that for my money, when i hear 'axiomatic' I instantly envisage a rock solid methodology, visions of 'soundness', visions of 'foundations' from which to build solutions based on tried, tested and (ultimately) 'trusted'...axioms. Concepts of 'completeness' and 'consistency' immediately spring to mind (not withstanding the limits of these, and that Halpin/Morgan do speak of 'consistency' within the BBB).

I'm curious what people think of this. Indeed, there may be a good reason 'why' we would rarely use those terms. If there is, i'd certainly like to hear the reasons.

And on the contrary and counter side...if there is no particular reason why we wouldn't use these terms, let this be the start and sounding board for healthy promotion/discussion of all the good reasons why it is a good idea to start promoting ORM that way.

Personally, I feel that it is almost as if there is an undercurrent that says "Oh, the general populous wouldn't understand those terms". I believe they would. I also believe it would be a 'coming out' for ORM and sign of great maturity that the community is resolved to speak of conceptual design in the language of the mathematical basis on which it is derived and designed.

If you have any thoughts on this, would like promote the concept, or have a good reason why it would not be a good idea, please join in this discussion. I am resolved to say nothing more on the matter. Personally, I'll accept whatever you have to say.

Best regards

Victor

ORM for Data Warehouses and Data Marts - Useful?

Tom Kregel — Mon, 30 Jun 2008 16:48:05 GMT

I am an experienced data modeler in both the OLTP and OLAP worlds. I have found ORM very useful in OLTP. I am wondering what people feel is the usefulness of ORM to design a data warehouse or a data mart. I am thinking that ORM is more likely to be useful in the warehousing portions since these models are often 3^rd normal form or close to it. Marts with dimensions, facts, stars and snowflakes I have doubts about. I see some usefulness in the strict business rule statements in ORM style “Fact” definitions. Could ORM add certain type of objects to make it more useful in this domain?

ORM for a WFF?

JParrish — Fri, 06 Jun 2008 15:29:45 GMT

I wasn't sure which forum would be best to post this in.

I am teaching myself about formal logic.. with the catalyst being that I am creating a "Rule Engine" of sorts.. I want to approach defining a "rule" as a well formed formula.. hoping to create a relational schema to store those definitions. So I was wondering does anyone know of any ORM already done to represent the notions of truth-functions? I'm still getting some of the concepts clear in my mind so I didn't want to jump right in and create a model.. although it probably would be a good exercise.Thanks!

SOL as isomorphic interpretation of theories in a FOL

VictorMorgante — Sat, 31 May 2008 10:19:50 GMT

Hi there,

I believe OF is as good a place as any if I want to find logicians.

Does anyone know how well known it is that theorems of 'Second Order Logic' may be expressed/interpreted as isomorphic interpretations of theorems expressed in First Order Logic.

i.e. Is there good documentary evidence that although Godel's incompleteness theorems apply to SOLs/Higher order Logics, that isomorphism doesn't just stop there. i.e In that Godel Numbers are few within the countless stream of natural numbers, there are (sound) isomophic interpretations within the countless streams of (symbols expressed as) theorems of First Order Logic that (in their interpretation) are theorems of a SOL, and so the best (or worst, take your pick) that may be said of FOL is that it may 'consistently model an inconsistent model'.

How well known is that? If you know, and know any good papers that point that out, can you let me know.

Or is it as simple as understanding that 'any' UOD may be modelled in a FOL, and within an inconsistent theory (as a UoD), you can prove anything.
i.e. it's so trivial, that nobody writes about it.

I don't mind if this is a dumb question. I would just like to hear what others have to say.

Just as a heads up. I'm not looking to debate this. So for those who don't accept Godel...i'm not in that camp to start with, and i'm not jumping ship.
I'm just interested in what other people 'think' about it. I'll accept whatever you have to say (as your opinion)...

On the Universe of Discourse

Brian Nalewajek — Mon, 12 May 2008 18:42:11 GMT

One term of acknowledged importance in Object Role Modeling is that of Universe of Discourse (UofD), also know as domain of discourse, or more simply, domain. However, within the community of Information Systems designers, architects and practitioners (and perhaps within the subset of fact-based modelers as well), several interpretations of the term are possible. The purpose of this thread is to discuss those interpretations.

As a preface to the discussion, there is the reference to the term as a type; and there are references to instances of that type. In other words, the term Universe of Discourse is the model for a limitless number of subject or domain specific Universes of Discourse, each such universe the concern of one domain. Unless someone suggests a better way to designate the distinction, we can use "TUD" for "Term Universe of Discourse" and "a Universe of Discourse" ("a UofD") to designate any instance of that type, and "the Universe of discourse" ("the UofD") to indicate a specific instance.

TUD Term Universe of Discourse (type)
a UofD (any instance of the type)
the UofD (specific instance of the type)

How should TUD be defined? Several definitions are available and in use; which one best serves the fact-based modeling community? A key component of any definition concerns what types of things are considered part of a UofD. Certainly, a UofD will contain words, phrases, terms and other designators - as it is a universe of discourse. But should it also contain things that go beyond what might be called "the molecular level of discussion" to include concepts, relationships, facts and rules?

Given the important consequences of the choice of definition, there are likely well established schools of thought on the subject - and so "accepted" definitions for each school. For this discussion, let's not take recourse to authority, and pronounce one interpretation as correct, but rather discuss the implications of the various definitions, and see how they effect the way we do fact-based modeling. If we find that there are several different paths that lead to the same place, even that would be remarkable.

For a point of departure, the definition for TUD that I've been using is: the totality of objects, terms, concepts and facts, the identification, definition, veracity and application of which is assumed within the subject domain. That's actually a definition I cobbled together, using parts of other definitions I felt appropriate. How does that compare to your working definition, and what consequences do you expect from any difference?

BRN..

What are the origins of ORM?

Ken Evans — Mon, 12 May 2008 08:33:53 GMT

The roots of logic and deductive reasoning are to be found in the writings of Aristotle (384 BC - 322 BC) in a collection known as "The Organon". Aristotle's ideas formed the basis of logical thought until the 19^th Century when writers such as De Morgan (1847), Boole (1854), Cantor (1874) and Frege (1884) introduced new ideas into mathematics and logic.

As part of the research for my dissertation, I compiled the following table. My aim is to provide the beginnings of a navigation path back through history to better understand the foundations of ORM. I don't claim that the table is complete; it is just the result of what I have learned during my limited period of research.

Please feel free to suggest amendments or additions.

Ken

Author	Contribution
Aristotle circa 340 BC	Syllogisms
De Morgan (1848)	Universe of Discourse
Boole (1854)	Boolean Logic
Cantor (1874)	Set Theory (naïve)
Dedekind (1874)	The "Dedekind Cut" irrational numbers vs rational numbers Met Cantor in Interlaken in 1874
Frege(1884)	Axiomatic predicate logic
Russell (1901)	Type theory (avoids paradoxes in naive set theory)
Hilbert (1900)	23 unsolved fundamental mathematical questions
Zermelo (1904)	The well-ordering theorem of sets
Fraenkel (1922)	Improved Zermelo's axiom system
Skolem (1922)	Improved Zermelo's axiom system
Zermelo-Fraenkel axioms(1930)	Avoid paradoxes in naive set theory
Gödel (1931)	Incompleteness theorem
Tarski (1931) Tarski (1933)	First-order theory of real numbers Theory of truth for formalized languages
Codd (1970)	The relational model
Kripke (1972)	Truth & the nature of identity
Senko et al (1973)	Data structures and accessing in data base systems
Abrial (1974)	Data structures
Falkenberg (1976)	Concepts for modeling information
Nijssen (1977)	On the gross architecture for the next generation of database management systems.
Halpin (1989)	PhD Thesis on formalising object-role modeling