The four dimensions of artifacts

1
The four dimensions of artifacts

• Pawel Garbacz
• Catholic University of Lublin
• Poland

2
The four dimensions of artifacts

• PURPOSE
• DESIGN KNOWLEDGE

3
The four dimensions of artifactsOutline of the
project

• Methodology
• Tools
• Theory
• Evaluation
• Comparison
• Artifacts and relative identity
• Functional parts vs. mereological parts
• The minimal mereology for the functional parthood
  and some its extensions

4
The four dimensions of artifactsCautions

• Beware! I will speak about types not tokens.
• Forget about temporal properties of artifacts!

5
The four dimensions of artifactsTools

• (Elements of) the classical theory of consequence
  operation
• An ontology of situations and objects
• A first-order language L sufficiently rich for
  speaking about artifacts

6
The four dimensions of artifactsInnocent
ambiguity
7
Kinds of artifacts

• Human-orientated artifacts

• Artifact-orientated artifacts

8
Purpose

• Pawel Garbacz copies his paper The four
  dimensions of artifacts.

9
Purpose

• USER ???
• AUTHOR ??
• COMMUNITY !

• Pawel Garbacz copies his paper The four
  dimensions of artifacts.

10
Purpose

• Pawel Garbacz scans a book.
• Pawel Garbacz scans a book.

11
Purpose

• (3.1) If x is a purpose of an artifact y for a
  user z, then z knows what it would be for x to
  obtain.
• (3.2) For every artefact x, there is a user y
  such that Purpose(x, y)??.

12
Design

• If both Smith and Brown wish to achieve the same
  purpose y and because of
• these wishes Smith produces an artifact x1 and
  Brown produces an artifact x2,
• then if Smith resorts to the design of x1 and
  Brown does not resort to the design
• of x2, then it is more probable that x1 makes it
  easier for Smith to achieve y than
• that x2 makes it easier for Brown to achieve y.
  If both probabilities happen to be
• equal, then Smiths producing x1 is likely to be
  more economical in terms of
• time, energy, materials, etc., than Browns
  producing x2.

13
Design
14
Design

• (3.3) For every artifact x, there exists an
  abstract structure which determines the
  artifactual nature of x.
• This structure is a join semi-lattice ltX, ?gt of
  situations.
• A poset ltX, ?gt is a join semi-lattice if for
  every x, y?X, their join x?y exists and
• belongs to X.

15
Design or designs?
16
Design

• (3.4) ltX, ?gt is a design of x with respect to a
  design ltY, ?gt of y iff X?Y.
• (3.5) A design ltX, ?gt is less specific than a
  design ltY, ?gt iff X?Y and X?Y.
• (3.6) If join semi-lattices ltX1, ?gt and ltX2, ?gt
  are designs of an artifact x, then either X1?X2
  or X2?X1.
• (3.8) If designi(x1)designj(x2), then
  Purpose(x1, y)Purpose(x2, y).

17
Knowledge

• (3.9) For every artifact x, Knowledge(x)??.
• (3.10) C(Knowledge(x))Knowledge(x).
• (3.11) CK(x)(X) C(X?Knowledge(x)).
• (3.12) C(Knowledge(x))?L.
• (3.13) CK(x)(Purpose(x, y))?L.
• (3.14) If designi(x1)designj(x2), then
  Knowledge(x1)Knowledge(x2).
• (3.15) CK(x)(Purpose(x, y)?designi(x))?L.

18
Use
Press the power shot button in intervals of at
least 5 seconds!
Pawel Garbacz presses the power shot button in
intervals of at least 5 seconds.
The situation that Pawel Garbacz presses the
power shot button in intervals of at least 5
seconds
19
Use

• An artifact x,
• its user,
• and other artifacts and natural objects
• OCCUR
• in xs philosophical instructions of use.
  

20
Use
USER ??? AUTHOR ?? COMMUNITY !
Pawel Garbacz presses the green
button.
21
Use

• (3.16) If designi(x1)designj(x2), then Use(x1,
  y)Use(x2, y).
• (3.17) Purpose(x, y)?CK(x)(designi(x)?Use(x, y)).
• (3.18) CK(x)(designj(x)?Use(x, y))?L.

22
Dimensions of artifacts

• (3.31) Artifact ltPurpose, design, Knowledge,
  Usegt.

Set of sets of situations
Chain of semilattices of situations
Set of sentences closed under C
Set of sets of situations
23
Dimensions of artifacts

• (3.31) Artifact ltPurpose, design, Knowledge,
  Usegt.

What is an artifact?
How to speak about artifacts?
An artifact-token represented by a 3.31
quadruple is an object x such that (i) the
community of xs users (including its author)
ascribes x situations from Purpose as its
purposes, (ii) the set of situations in which x
actually occurs involves the full design of
x, (iii) the author (manufacturer(s)) of x
employs the information from the set Knowledge
when he designs (manufacture) x, (iv) the
community from (i) ascribes x situations from Use
so that x may bring about one of its purposes
from Purpose.
24
Dimensions of artifacts

• The Polish national anthem Dabrowskis Mazurka.
• For my ancestors the anthem served as a symbol of
  their fight for national independence. For my
• contemporaries it serves as a symbol of the unity
  of the sovereign motherland. In both cases its
• purpose is to rise the national emotions. If y
  was of Polish nationality in XIXth century, then
  the
• situation that somey desires that Poland should
  regain its independence belongs to Purpose(Polish
  
• anthem, y). But if y is a Polish citizen in XXIth
  century, then the set Purpose(Polish anthem, y)
• contains the situation that some y desires that
  Poland should retain its unity as an independent
• state but does not contain the former situation.
  The design of the anthem is its musical score.
  The
• background knowledge is a complex conceptual
  structure that consists at least of physiology of
  
• hearing, psychology of music, sociology of
  nations, and history of Poland. The use of Polish
  
• anthem involves the standard instructions for
  listening to a piece of music (e.g. a listener
  stands
• within a short distance from the source of sound,
  a listener does not think about dinner, etc.),
  the
• standard requirements for listeners of Polish
  songs (e.g. a listener should understand Polish
• language), and the special commands regarding
  national symbols (e.g. a listener to an anthem
• stands straight with her head bare, a listener
  knows and esteems Polish history, etc.). On the
• ground of the background knowledge we predict
  that if one follows these instructions of use,
  then
• the anthem is likely to arouse her national
  emotions. If you are of Polish origin and live in
  XIXth
• century, then you are likely to desire that
  Poland should regain its independence. If you are
  a Polish

25
Aims and functions

• If x?Purpose(y, z) and z is a rational agent,
  then x is an aim for y.
• If x?Purpose(y, z) and z is an artifact, then x
  is a function of y.

26
Functions
The Zener diode sets the reference voltage at 5
volts.

• The Zener diode performs this function in a power
  supply since
• (i) the function is a situation specified by the
  design of the power supply,
• (ii) the diode occurs in that situation,
• (iii) the relevant design of the diode is less
  specific than the design of the power supply.

27
Functions

• (3.19) An artifact x has a function y (plays a
  role y) in an artifact z iff
• (i) y is a situation from a design of z,
• (ii) x occurs in y,
• (iii) a design of x is less specific than the
  design of z referred to in (i).
• (3.33) x is a functional part of y iff there is
  some role that x plays in y.

28
Functional parts vs. mereological parts

• The functional parthood is irreflexive.
• The functional parthood is asymmetric.
• Is the functional parthood transitive?
• SSP?
• General Sum Principle?

29
Functional parts vs. mereological
partsTransitivity

• The relation of functional parthood is not
  transitive.

30
Functional parts vs. mereological
partsSupplementation principles

• If x is a proper part of y, then ?z(z is a proper
  part of y and z does not overlap x).
• If x is not a part of y, then ?z (z is a part of
  x and z does not overlap y).

31
Functional parts vs. mereological
partsExtensionality
32
Functional parts vs. mereological partsGeneral
Sum Principle