Epistemology of models - and their output

So when we have a model of some natural phenomena, what can we say about the results? Some amateur philosophical observations . . .

First, the model is a rational construct. It may be inspired or motivated by empirical observations of the referent it is abstracting, but the model in the end is a rational construct. That means it involves all of the limits of such constructs - such as limited view of the referent, perspective driven evaluation of possibilities, and so on.

Second, the access to results of the model involve using empirical observations of the operation of the model. So this is empiricism based on rationalism.

Or is it? What if the model is considered as a rational construct of a generative item? Still a rational construct, but designed to also create rational constructs - meaning the results of the model (which can be many things - models have many possible degrees of freedom as output.

So what does this say about the epistemology of model results? Do they represent some possible (possibly counterfactual?) version of "the original" the model is inspired by (the referent)? Not precisely. I believe they are nothing more than the rational output of a rational construct, but they are inspired by the referent. Within certain identified bounded differences, they can serve as an abstraction for study or to reveal certain behavioral phenomena - but they are not epistemologically equivalent. More thoughts later.

Tags: modeling, epistemology, philosophy

Simulation as a Symbol of Meaning

These are a couple of board captures from a recent conversation on the relationship between the Semiotic Triangle (or Triangle of Reference) and the effort of representing some referent within a simulation (by first modeling it).

If the referent is the original object, in ideal form (whatever that is - meaning that all perceptions bring prejudice, so that in a Hume-like sense we can never know the ideal form, only our perceptions of the form), then a model of that referent is a conceptualization of it (much in the way that we talk about conceptual models as the blueprint for data modeling, and that an ontological representation is the expression of a conceptualization). By going one step further, and expressing that model in a simulation that mimics the dynamic existence of the referent (albeit, in some abstracted way - such as in a computer simulation), then the simulation becomes the expressed symbol representing the referent.

This highlights two prejudices that I (and others at the VMASC research group I interact with) have, namely that the act of going from referent to simulation really encompasses two different paradigms - the modeling paradigm (where we seek to understand the referent, in terms of some theory or model), and the simulation paradigm where that model (or theory) is then given form in a method that can give it dynamic existence (life?) over time, taking some inputs as the initial state of that "life", follow the strictures of the model (theory) and progress the processes of the model over time to induce changes to the objects and relations amongst those objects.

An interesting idea, if only because it implies that a simulation is a symbol for some referent. Much as a word (in natural language) is a symbol for some referent.

This reliance on the earliest version of the semiotic triangle leaves out an important stage in the transference of meaning from one agent to another - and that is understanding (or, more formally, in the domain of M&S, the agreement of one model with another).

Regardless of the flaws, the triangle is an interesting tool in understanding what is "modeling and simulation". And it can be seen (from the diagrams following) that there is some effort at reimposing the triangle on each of the vertical arms of the original triangle - (1) going from referent to model, and (2) going from model to simulation. An interesting theory like the triangle of reference is always coming up again and again the more you consider it in additional contexts...

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Tags: semiotics, modeling, simulation, semantics, ontology

primitives of meaning - meet bundle theory

My idea of primitives of meaning to describe a conceptual entity (by identifying all of the atomic concepts that combine to make the "whole" entity) is essentially the same as bundle theory, but I was (sadly) unaware of that theory when I did my writing on the atomic-concept based ontology for modeling and simulation (2005-2006) that led to my master's theory.

For a brief introduction to Bundle Theory see this wikipedia entry.

One of the things that Included in my model of an ontology for modeled worlds, is that the components are (1) concepts, (2) entities which are a combination of a set of concepts, (3) relationships between concepts, (4) rules determining under what conditions the relationships are valid. This is a system that is vulnerable to the same complaints about compresence that bundle theory is vulnerable to. However, since my theory is to apply to a modeled world that can be expressed, I don't think that the language/reality vulnerability of bundle theory applies here. By that I mean, since the point of my ontology theory is to provide an ontology for expressing the meaning of a world that can be expressed in a human generated artifact, an artifact about which questions concerning the described world are decidable, then the number and nature of relationships between (what I call) entities and their bundled concepts is countable and finite. But I may be wrong. :)

Tags: bundle theory

Modeling paradigms for modeling the Ontological elements of a PMESII environment

In appendix C of Behavioral Modeling and Simulation: From Individuals to Societies there is a decent overview of some modeling techniques to capture PMESII factors.

These approaches/techniques include:
Concept Maps
Concept Graphs
Social Networks
Casual Graphs
Systems Dynamics Model
Neural Networks
Situation Theory

The link above gives a nice reference to particular appendix, or the book is available for browsing here:





Tags:

More on Topology

A few more decent references on topology representing a couple of decades worth of text books on the subject (1961, 1970, 1980).

First this is from 1961 -


Here is one from 1970 -


And finally, from 1980 -


Tags: topology

System Topology

I rely on System Topology in the same that a network engineer for an information network would refer to a Network Topology. Only I am referring to the interconnected processes, and their relations amongst each other (as captured in the IDEF series of diagrams, or more recently, by Sowa's claim that a system is much more appropriately looked at as an interconnected graph of processes, rather than a group of data/object states, that only use process as a connective tissue).

A nice little definition (from Wolfram Mathworld) -

Topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. Tearing, however, is not allowed. A circle is topologically equivalent to an ellipse (into which it can be deformed by stretching) and a sphere is equivalent to an ellipsoid. Similarly, the set of all possible positions of the hour hand of a clock is topologically equivalent to a circle (i.e., a one-dimensional closed curve with no intersections that can be embedded in two-dimensional space), the set of all possible positions of the hour and minute hands taken together is topologically equivalent to the surface of a torus (i.e., a two-dimensional a surface that can be embedded in three-dimensional space), and the set of all possible positions of the hour, minute, and second hands taken together are topologically equivalent to a three-dimensional object.

My intention is to use the term system topology to refer to the overall graph of interconnected processes within a system, which I submit is potentially dynamic and can be potentially changed as much as the value or nature of objects affected by those processes.

A decent book (compliments of Google Books, once again) introducing the mathematics of topology . . .




Tags: system topology

Data Modeling - the quest for a good definition of Conceptual Model

Some promising results are herein:



Also Interesting:

• Data Modeling 101
  
• Introduction to Data Modeling
  
• Wikipedia entry (some decent links)
  

Tags: data modeling

Dimensions of Processes (1) - Time and Temporal Placement

The first dimension I am exploring, concerning a methodical decomposition of process, is the dimension of time and temporal placement of the process within its universe of occurrence.

First, on spatial reasoning, there is an informal introduction to the whole concept on wikipedia, of which the salient point (for automata) is:

Spatial-temporal reasoning is also studied in computer science. It aims at describing the common-sense background knowledge on which our human perspective on the physical reality is based. Methodologically, qualitative constraint calculi restrict the vocabulary of rich mathematical theories dealing with temporal or spatial entities such that specific aspects of these theories can be treated within decidable fragments with simple qualitative (non-metric) languages. Contrary to mathematical or physical theories about space and time, qualitative constraint calculi allow for rather inexpensive reasoning about entities located in space and time. For this reason, the limited expressiveness of qualitative representation formalism calculi is a benefit if such reasoning tasks need to be integrated in applications. For example, some of these calculi may be implemented for handling spatial GIS queries efficiently and some may be used for navigating, and communicating with, a mobile robot.

Much ink has been spilt on this topic in the artificial intelligence community - on temporal relationships and temporal reasoning. In beginning my review in this area, I will take the Elsevier handbook on Temporal Reasoning as my root node, and begin exploring the research of the PhDs whose work is featured there.

First the three editors

• Michael Fisher
  
• Dov Gabbay
  
• Lluis Vila
  

Next the contributing authors

• Jérôme Euzenat
  
• Angelo Montanari
  
• Peter Jonsson
  
• Manolis Koubarakis
  
• Alfonso E. Gerevini
  
• Mark Reynolds
  
• Clare Dixon
  
• Marc Denecker
  
• Alessandro Artale
  
• Enrico Franconi
  
• Chitta Baral
  
• Michael Gelfond
  
• Jan Chromicki
  
• David Toman
  
• Michael Wooldridge
  
• Maria Fox
  
• Derek Long
  
• Elpida Keravnou-Papailiou
  
• Yuval Shahar
  
• Benjamin Kuipers
  

Side Topics:

Qualitative Spatial Reasoning using Constraint Calculi by Renz and Nebel

Guido Governatori very interesting series of publications on related topics

Approximate Qualitative Temporal Reasoning by Thomas Bittner

Tags: time, temporal reasoning, processes