The Minimal Ontology Principle

Philosophical Foundations of OPM-based Modelling and Simulation

James Brucato

and Dov Dori

2,3

Palermo Euro Terminal srl, Banchina Sammuzzo Porto, Palermo, Italy

Massachusetts Institute of Technology, Boston, U.S.A.

Technion, Israel Institute of Technology, Haifa, Israel

Keywords: Object Process Methodology, Software Engineering, System Engineering, Computability, Compositional

Logics.

Abstract: Traditionally, Software Engineering (SWE) and Systems Engineering (SE) were almost different disciplines

with little overlap and with a different set of approaches and concepts. Yet, both SWE and SE reflect two

sides of the same coin: both revolve around development and lifecycle support of systems. While SWE

focuses on software-intensive systems, SE has focused on systems in general. However, most systems

nowadays not only combine hardware and software, ever more intertwined and increasingly interdependent,

they also comprise humans and organizations as stakeholders. This work aims to underline the importance

of the holism as highly effective approach to both SWE and SE as it is the result of a huge and very

representative set of philosophical investigations, partially illustrated in this work, assuming that the

historical distinction between SWE and SE is becoming ever less relevant and that it is high time they be

treated as one overarching discipline provided with a minimal ontology in order to facilitate the conceptual

modelling process and improve models understandability. We propose the Object Process Methodology

(OPM), together with its holistic approach to systems modelling and simulation, as main building block of

the bridge between SWE and SE disciplines with respect the issues above.

1 INTRODUCTION

This work is intended to investigate the validity and

usefulness of the distinction between SWE and SE

with respect to the modelling and simulation

approach. Since they are considered as different

disciplines, despite the fact that they are becoming

ever more interdependent because of the highly

increasing number of systems that nowadays

combine hardware and software to succesfully meet

the stakeholders expectations and the users needs,

we claim that an effective modelling and simulation

approach shall be able to merge all the different

aspects pertaining both the disciplines. To reach this

goal it shall be provided, first, with a strong

philosophical background in order to take into

account the most wide set of historical facts, second,

it shall be domain independent in order to be highly

flexible and useful beyond the disciplines

boundaries, third, with the smallest set of symbols

composing its vocabulary and its syntax in order to

be easy to learn maximizing, in the same time, the

system models understandability and sharing.

Along and as results of their evolution, humans have

been able to invent a huge set of languages (oral,

written, iconic, sculpture, architectural, melodic,

scientific and so on) in order to create amazing

pictures of the world. Even those all the languages

are limited in their constituents (building blocks)

they provide the human kind with a source of

potentially infinite combinations, but only and only

if there is a set of rules to combine simple symbols

and/or set of symbols generating more complex

combinations of them.

We propose the OPM (Dori, 2002) as a bridge

between SWE and SE because of its strongly holistic

oriented modelling and simulation approach that

properly fulfils the requirements above.

In the same time, the minimal ontology principle

is illustrated in order to provide the OPM with a

clear definition of its assumtions.

405

Brucato J. and Dori D..

The Minimal Ontology Principle - Philosophical Foundations of OPM-based Modelling and Simulation.

DOI: 10.5220/0005140804050409

In Proceedings of the International Conference on Knowledge Engineering and Ontology Development (KEOD-2014), pages 405-409

ISBN: 978-989-758-049-9

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

2 PHILOSOPHICAL

FOUNDATIONS OF

MODELLING AND

SIMULATION

From a philosophical point of view, the systems-

software dualism can be traced back to the 1950’s

and early 1960’s when the AI (Artificial

Intelligence) was emerging as a new, unpredicted

and unpredictable discipline, historically identified

as a branch of the cognitive sciences paradigm. AI

was founded at a conference held during the summer

of 1956 at Dartmouth College in Hanover, New

Hampshire where John McCarthy, Marvin Minsky,

Nathaniel Rochester and Claude Shannon presented

a very innovative work able to merge a considerable

number of philosophical theories developed in the

early 20th century, including linguistics

investigations and epistemological approaches, and

the most advanced engineering experimental works

(McCarthy, Minsky, Rochester and Shannon, 1955).

Since the Dartmouth conference, the

international scientific community interest toward

the AI rapidly increased and the most part of further

investigations proofed the presence of an

epistemological lack of effectiveness specially with

respect to the human knowledge representation area.

This, in turn, led the scientific community to explore

the possibility of finding a common terrain where

would be possible a productive confrontation

between different disciplines, methodologies and

approaches in order to establish a new common

paradigm serving as scientific and academic

theoretical bridge, the Cognitive Science paradigm.

Recently it has been defined as a contemporary,

empirically, based effort to answer long-standing

epistemological questions – particularly those

concerned with the nature of knowledge, its

components, its development, and its deployment

(Gardner, 1986).

It is relevant that there was a close constant

overlap between the results and the assumptions of

most of those theories similar to a chain reaction

even those they were developed in different times

and places, sometime very distant one from each

other, and that it has been demonstrated that all of

them were founded assuming the validity of the

Frege’s Principle, (Frege, 1893), known as Principle

of Compositionality, that states the meaning of a

complex expression is determined by the meanings

of its constituent expressions and the rules used to

combine them (Brucato, 2003).

Early Cognitive Science scopes and assumptions,

including for first the Frege’s Principle of

Compositionality we assume as its main

epistemological pillar, they continue to play a

central role in many contemporary disciplines like

SWE and SE modelling and simulation. More

specifically, they are the philosophical foundations

of OPM-based modelling and simulation holistic

approach to SWE and SE we identify with but not

limit to:

 Wittgenstein's Tractatus logico-philosophicus

(1921). It contains the distinction between the

World, and the Language (s) used to describe

(give a picture of) it. This is the main

assumption of the well known Picture Theory

of the Meaning Wittgenstein developed to state

that the language is a picture of the world and it

is obtained combining the language building

blocks (the signs, later called symbols) into

propositions according to the predetermined set

of syntactic rules specifically pertaining to the

adopted language. He often used to compare

the process of composing a syntactically

correct proposition to the work of an architect

who designs and constructs a new building. If

something has been designed wrongly, the

building will not be able to be used for the

intended purposes, hence it will be basically

useless, with respect to the language, if the

syntactic rules are not properly followed the

proposition will be non-sensed and, in some

cases, it will also be not understandable;

 Hierarchy of Languages (Russell, B., 1905).

Here Bertrand Russell illustrated the necessity

to adopt a higher level language to completely

and consistently describe a lower level

language. This theory has been formalized as

Type Theory;

 The Mathematical Theory of Communication

developed by Shannon and Weaver (Shannon,

1938). The communication is assumed to be

the result of the information transmitting

process. Using a physical channel, a

predetermined quantity of information the

sender previously compressed through a code

he shares with the receiver, is possible to

reproduce at one point (the destination) either

exactly or approximately a message selected at

another point (the source);

 The ballistic researches of Von Neumann

(1945) led him to the definition of a stable

machine structure, known as Von Neumann

Architecture, which served as the basis of all

the modern calculators and computational

machines;

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 Alan Turing’s definition of Computability

(Turing, 1936), a reformulation of Gödel’s

Undecidable Problem and inspired by

Newman investigations onto the decidability

of mathematical propositions.

3 PHILOSOPHICAL OUTCOMES

OPM is different from other modelling languages

not only because it allows to go beyond what

Wittgenstein called the limit of the Language,

consisting of the impossibility to completely

describe the World, it also subsumes most of the

theories involved in the foundations of the Cognitive

Science paradigm.

In addition, OPM provides stakeholders with

both the iconic, graphical, view of the systems and

its equivalent textual description. The two reinforce

one each other recursively through the dual-channel

processing, as they cater to the visual and verbal

cognitive processing channels (Mayer, 2005; Dori,

2008).

OPM also takes into account both the structure

and the behavior of systems in order to provide a

comprehensive vision of the building blocks that

compose a system together with the processes

involved and requested to perform the tasks it has

been designed for.

All these widely appreciated OPM features

impressively allow to model its own theoretical

foundations as well with all the positive effects this

can have in particular with respect to SWE and SE

as OPM represents a unique and highly effective

meta-modelling and simulation domain independent

holistic approach.

Following are the Shannon’s schematic diagram

of a general communications system (Figure 1) and

its OPM system model version according to the

Shannon and Weaver Mathematical Theory of

Communication.

Figure 1: Schematic diagram of a general communications

system according to Shannon definition.

Figure 2: OPD of Shannon’s Mathematical Theory of

Communication and related OPL.

4 THE MINIMAL ONTOLOGY

PRINCIPLE DEFINITION

A parallel development on a smaller scale has

happened within both SWE and SE with the

realization that models should serve as foundational

architecting and design artifacts. For SWE this

happened in the early 1990s, when the object-

oriented (OO) idea grew out of being a paradigm

underlying OO programming languages to the

realization that prior to coding, the program, or the

software system, should be modelled. Initially there

was the “war of languages” with over 30 different

notations and ideas trying to prevail. Then, in 1997

UML was adopted under the auspices of OMG with

9 different diagram types, which grew to 13 with the

transition to UML 2.0 in 2005. The first author's

proposal at an OMG Technical Meeting in Florida in

2000 to extend UML from the software domain to

the general systems domain was dismissed with no

consideration whatsoever, only to be resurrected six

years later with the birth of SysML. SysML was

developed and adopted in 2007 in response to OMG

UML for Systems Engineering RFP. Like UML 1.x,

it had 9 diagram types, but not quite the same set.

Some were removed from UML 2, some modified

and a couple added. Why 9 diagram type (or views,

or viewpoints)? Why 13? Why not more? Isn’t it the

case that more is better? If so, why not adopt

DODAF 2.0 from 2009? It has 51 Viewpoints

(BTW, up from 26 in DODAF 1.x from 2003)!

This trend of "diagram creep" – adding more

diagram types to a language – just adds

complicatedness to an already complicated world of

conceptual modeling languages. AS a reaction, in

order to put a stop to this trend, we offer the

following Minimal Ontology principle: If a system

can be specified at the same level of accuracy and

detail by two languages of different sizes, then the

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language with the smaller size is preferred over the

one with the larger size.

This principle does not only make perfect sense,

it is also in line with the long accepted Ockham’s

Razor (Ockham, 1495) – a principle attributed to the

14th century logician and Franciscan friar William

of Ockham, England. The principle states that

"Entities should not be multiplied unnecessarily."

Or, in one of its original Latin forms: "Pluralitas non

est ponenda sine necessitate." The most useful

statement of the principle for scientists is "when you

have two competing theories that make exactly the

same predictions, the simpler one is the better."

Ockham’s Razor inspired also the Minimum

Description Length (MDL) Principle (Rissanen,

1978), a method for inductive inference that

provides a generic solution to the model selection

problem, i.e., how does one decide among

competing explanations of data given limited

observations. MDL is based on the insight that any

regularity in a given set of data can be used to

compress the data by describe it with fewer symbols

than the number of symbols needed to describe the

original data. In a similar vein, any symbol system

(i.e., a language) that can describe a given system

using fewer symbols (a smaller language) is more

succinct and therefore preferable over a larger

language (a language with more symbols), as using

the smaller language exerts a smaller amount of

cognitive load on the human modeler. Alleviating

the cognitive load off the human modeler is highly

desirable because the modeler must cope with the

inherent complexities of man-made systems to be

built (systems engineering) or natural systems to be

investigated (science), so anything that we can do to

help by providing a simpler language is of

tremendous value.

A second principle that caters to the same

objective of facilitating the conceptual modeling

process and making the model more accessible and

comprehensible is the dual channel processing

(Mayer, 2005; Dori, 2008): A model that can be

presented bi-modally in both graphic and text is

preferred over a model that can be presented in only

one of the modalities.

The cognitive-physiological basis for this

principle is that the human mind is geared to accept

both visual-pictorial-graphic signals and audio-

verbal-written signals. Popularly, this is often

referred to as the left brain/right brain functions.

Indeed the left hemisphere is dominant in language,

processing what one hears and handling most of the

duties of speaking. The right hemisphere is mainly

in charge of spatial abilities, face recognition,

comprehending visual imagery and making sense of

what we see. Thus catering to “both sides of the

brain” through language and pictures is more likely

to get the message—in our case the conceptual

model—across.

If we accept these two principles, then we need

to find the minimal universal ontology—the

ontology that is necessary and sufficient to model

the universe and systems in it. We start by first

asserting that any thing in the universe either exists

or happens. We proceed with a series of questions

and answers:

Q1: What are the things that exist in the

universe?

A1: Objects exist or might exist.

Q2: What are the things that happen in the

universe?

A2: Processes happen or might happen. But

processes cannot happen in vacuum! So:

Q3: What are the things to which processes

happen?

A3: Processes happen to objects.

Q4: What do processes do to objects?

A4: Processes transform objects.

Q5: What does it mean for a process to transform

an object?

A5: Transforming of an object by a process

means:

 creating (generating) an object

 destroying (consuming) an object

 affecting an object.

Q6: What does it mean for a process to affect an

object?

A6: A process affects an object by changing its

state. Hence, objects must be stateful, i.e., they must

have states.

Q7: What are the main aspects that define any

existing system?

A7: A system can be defined with respect to two

major aspects: structure and behavior. Structure is

the static aspect; it relates to the question what is the

system made of?

From the structural aspect, a System is a finite

set of components and their time-invariant

interconnections. Behavior is the dynamic aspect; it

relates to the question how does the system change

over time?

Q8: What additional aspect pertains to man-made

systems?

A8: Function – the utilitarian, subjective aspect:

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why is the system built? for whom? who benefits

from operating it? What is the context of its use?

If we accept these answers, then we are ready to

prove the following theorem:

The Object-Process Theorem

Stateful objects, processes, and relations among

them constitute a necessary and sufficient universal

ontology.

The following is a complementary statement:

The Object-Process Corollary

Using stateful objects, processes, and relations

among them, one can model systems in any domain

and at any level of complexity.

Proof: Part 1 - necessity

Stateful objects and processes are necessary to

specify the two system aspects:

Specifying the structural, static system aspect

requires stateful objects and relations among them.

Specifying the procedural, dynamic system

aspect requires processes and relations between

them and the objects they transform.

Proof: Part 2 - sufficiency

Stateful objects and processes are sufficient to

specify any thing in any system:

Anything that exists can be specified in terms of

stateful objects and relations among them.

Anything that happens to an object can be

specified in terms of processes and relations between

them and the object they transform.

5 CONCLUSIONS

Having determined and proved the Object-Process

Theorem, according to the minimal ontology

principle, the optimal conceptual modeling language

must have just two types of concepts - stateful

objects and processes - along with relations among

them. Indeed, this is the theoretical foundation of

OPM. It is in the process of becoming ISO 19450

Standard - Publicly Available Specification, a freely

available ISO document that defines the syntax and

semantics of OPM (ISO, 2014). The document

length is around 140 pages, compared with 1400

pages of the current OMG UML 2.2 Standard plus

272 pages of SysML that builds on the UML

Standard documentation.

With respect to the current regrettable chasm

between SWE and SE, we should do everything in

our power to unify these two seemingly disparate

disciplines, because both handle two complementary

views that each contemporary system features: the

physical view (the focus of SE) and the informatical-

cybernetic view (the focus of SWE). To marry SE

with SWE we need a simple common language that

both domains will speak freely. Catering to both

physical and informatical things (objects and

processes). OPM can serve as an ideal bridge

between the two.

ACKNOWLEDGEMENTS

This work was supported by EU FP7 VISIONAIR

Project 262044 and Gordon Center for Systems

Engineering at Technion.

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