scientific
landscape
| modeling |
(models, semantics)
| semiotics |
reasoning
| categories |
| relations |
| objects |
| wholes & levels |
| meta |
glossary
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formalization & symbol manipulation |
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the scientific landscape |
| representation (models, semantics) |
| logic & reasoning | complexity & metrics | sets & numbers | |||||||||
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| meaning
| linguistic glossary |
| components & datatypes | relations | ||||||||||
| truth & reality | algebras | |||||||||||||||
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Location: http://www.cs.mun.ca/~ulf/gloss/rels.html.
By Ulf Schünemann since 2002.
Please mail any comments.
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| See the status of relations |
However, it is fact that "part" is used in language not only for "real" part relations, but also for class inclusion. [ProbPW] made an analysis of Webster's Seventh Collegiate Dictionary: «[T]wo major types of part-whole relation appear very directly in the dictionary definitions of nouns: functional part and segmented whole. ... Two additional types of part-whole relationships appear in the definitions: collection-element and set-subset. These tend to be expressed by some other term such as member, or, when focus is on the whole, by including, comprising, or containing»
[TaxPW] compared the three inclusion relations
class inclusion, merological (part-whole) inclusion, and topological inclusion.
There seems to be a logical ordering of the different inclusion relations,
so that syllogisms with mixed inclusion relations
have to conclude with the "smaller" relation:
class > merological > topologic [TaxPW]:
class + mero => mero: Wings are parts of birds + Birds are creatures => Wings are parts of creatures.
class + mero => mero: Pies are a kind of dessert + Desserts are partly sugar => Pies are partly sugar.
mero + topo => topo: The wheel is part of the bike + The bike is in the garage => The wheel is in the garage.
class + topo => topo: Socrates is in Athens + Athens is a city => Socrates is in a city.
[NatSR] present two studies where subjects had to sort examples of semantic relations into groups by similiarity. [NatSR]'s first study comprised undergraduates and 31 semantic relations. The major division was between contrast and non-contrast relations. The divisions on proximity level 0-10% were
| contrast relations separates at 5% proximity | attribute similars
| ... see below
| ca 2.5% | proximity "logic" | (based on property) separates at 5% proximity class inclusion, see below
| similarity | separates at 8% proximity necessary & invited attribute
| ... see below
| "pragmantic" | separates at 7% proximity case relations, see below
| part-of relations | separates at 9% proximity measure & ingredients
| ... see below
| | |||||
| ca. 8% | ca. 10% | ca. 11% | representation & plan, separates at 25% proximity |
| class inclusion, separates at 31% proximity -> see below
| meronymic | ca. 13% stuff (constituency) separates at 20% proximity -> see below
| separates | at 17% mass-portion (homeomerous) separates at 23%
|
| ca. | 19% ca. | 21% organizational separates at 22%
| spatial, separates at 23% proximity -> see below
| ca. | 21% integral object- component | separates at 22% spatial | integral separates at 23% functional location-component: kitchen-refrigerator, classroom-desk, store-cash register
| mobile object-component, separates at 27% (the two artefacts at 29%) into:
| dramatic event, separates at 23% into
| event-feature, separates at 22% into
|
| stages | non-"has" separates at 13%
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| 15% | stages (part of process): "phase" vs. "stage" (37% similar)
| 17%
| part of scripts describing an event: "role"
| part of place | 27-28% 19%
| homeomerous | 21% 24-25%
| 29-30%
| measurement: "portion", "percentage", "share" (25% similar)
| non-homeomerous | 27-28% "part", "member", "item", "feature", "element" ~ "factor" (28%), "ingredient" ~ "component" (32%)
(similarity increasing from 21% to 25%)
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All underlining is added emphasis.
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[MB3 261] «Definition 5.32 Two different
things are bonded (or linked or coupled)
together iff at least one of them acts upon
the other. In symbols: If x and y are things,
then
where «x acts on y, or x |> y for short, iff, for some state function H determining the trajectory h(y|x), h(y|x) =/= h(y)» [MB3 258], where h(y) = {<t,G(t)> | t  S(f) }and h(y|x) = {<t,H(t)> | t S(f) }with state function G relative to a reference frame f whose time-scope is S(f), and a state function H that depends on y's own state function G as well as on x's own state function F. [MB3 262] «In principle [the set of bonds] includes couplings of all n-arities - dyadic, triadic, and so on. In practice the dyadic or binary bonds are by far the most important.» |
S
are bound (or connected or coupled)
iff some changes in x are accompanied (or preceded or followed)
by some changes in y. ...
navigation bar: Dataflow
ca. 12%
proximity
actions
separates at
28% proximity
agent
separates at
20% proximity
- agent/instrument: farmer/tractor, soldier/gun
- agent/object: baker/bread, sculptor/clay
navigation bar: State-Transition
OML: The transition from state A (before) to B (after).
UML: «become» between snapshots of the same object at different times
UML: «copy» between objects ???
NB: Flow relationships are not causal relations
- the cause for a transition is the input, the effect is the output;
even epsilon transitions mean non-deterministic behavior,
and not that the pre-state causes the post-state.
- iconic (see at similarity relations)
- indexical (see at causal relations)
- symbolic (see at representation relations)
money/millionaire, copyright/author, bicycle/Jenny [TaxPW]
earring/ear, antenna/chimney, hook/fishing line [TaxPW]
«The contents often have an outside existence
independent of their location within a container.
... [A] container can be empty ...
[A] container typically does not use»
the containment relationship for interacting with its contents [OML/RR].
the wine is in the cooler, the prisoner is in the cell, the meeting is in the morning [TaxPW]
ca. 5%
proximity
ca. 15%
proximity
ca. 25%
proximity
The subdivisions had proximity levels 35-40%,
here ordered in decreasing proximity:
= Attribution [TaxPW, OML]
- The attribution relation relates an object with a "descriptive attribute" [OML]
= AttributeLink [UML]
towers are tall, the joke was funny, coal burns [TaxPW]
Distinguishing between attribution and whole-part association
in object-oriented modeling requires attention [CompoAD]:
«Are the start-point and end-point attributes or parts of a line segment?
The answer depends on the context: are the delimiting points
used just as information holders, to store and provide access
to their coordinates,
or do they have behaviour that can be invoked by their LineSegment or other objects?
In the latter case the two points should be modelled as part objects.»
ca. 8%
proximity
ca. 18%
proximity
ca. 25%
proximity
ca. 17%
proximity
navigation bar: Class Inclusion
Such a relation defines some entity A based on an existing entity B [OML].
The class inclusion relations cluster, distinguished by different kinds of entities [NatSR] I
by property by essence / accindent (?)
According to [TaxPW], Wierzbicka (1984) distinguishes
a glas of water, hundred grams of rice, the tail of an ox, two apples [Midwinter]
object A instance-of class B [OML]
class A conforms-to ???interface??? B
cars are vehicles, roses are flowers, theft is-a crime, fear is-an emotion [TaxPW]
study II
ca. 31% proximity
ca.
33%
study I
ca. 12%
proximity
ca. 27%
proximity
ca.
30%
ca.
33%
"geographical"
ca. 24%
proximity
navigation bar: Wholes and Parthood
wholes & system composition levels
part-whole relations
different kinds of parthood and compositeness
aggregates (concrete)
=/= sets (conceptual)
ontological status of wholes vs. parts
holism, atomism (allied with reductionism), systemism
«To say that something is a part is to say that it is something which is
part and has some further addtional properties. It is not altogether
easy to say what this 'extra' consists in ... For artefacts, something is a
part when it is a component of a thing, a piece typically existing
as a unit before the whole artefact assembled, capable of unitary replacement,
capable of surviving dismemberment of the whole, perhaps in addition
fulfilling a unitary function. For things other than aretfacts this meaning
is inapplicable, and if sth is a part it may be because it is a salient or
prominently delimited part, or because it is functionally unitary,
like an organ. But 'part' does not normally mean 'component' where the
whole is not created by assembly, or at least ... where it is not
unitarily replaceable. Since, then, a component or unitary part is part
of something satisfying certain further conditions, we feel entitled to
follow Sharvy in saying that mereology (part-whole theory) is as such
concerned with the wider or weaker notion of 'part'. The boundaries of
the stronger concept (or concepts?) are harder to draw ... » [Parts 235]
by homology by "part-of" patterns
[Manuel Kolp: Integrating Aggregation Mechanisms into the CLOS Metaobject Protocol; 1997?]
There are four different forms of part-of (in the context of made-of) [Part 234f]:
«As Sharvy has pointed out 'are part of' is the plural of 'is part of'
whereas 'are parts of' is the plural of 'is a part of'. ...
The fact that we can use (1) even for singular count nouns [not just masses]
suggests that, among individuals, there is some difference between
the 'is part of' and the 'is a part of' relations, as these find
expression in ordinary language. And indeed there is a difference:
whatever is a part of something is also part of it, but not vice versa.
The front half of a car ... is part of, but not a part of, the car.» [235]
(continued here).
"b is part of a" when b is a mass or an individual
"b are part of a" when b is a plurality
"b is a part of a" when b is an individual
"b are parts of a" when each of b is a part of a
The part/whole relations cluster [NatSR] I
ca. 9%
proximity
a-part-of
ca. 19%
proximity
ca. 30%
proximity
= (individual)
is a-part-of
= made-of(?)
ca.
24%
ca.
29%
part-of
ca. 12%= (mass) is part-of
= (individual) is part-of
«These different stances with respect to aggregation [in [6KC]] are somewhat
reminiscent of the different modeling positions with respect to null values.
Although over twenty kinds of null have been distinguished in the literature, ...»
[ORM8].
by category
A linguistic analysis of possible categorial combinations
in the common sense notion of "made-of" aka "composed-of" [Parts 232]
category of whole individual mass collection
can be made of
1 individual this chair/this box - is not composition but "serves-as" or "constitutes"
?some gold/one gold atom?
?committee/one person?
individuals wall/stones
gold/gold atoms
pack/wolves
1 individual+mass(es) toffee-apple/an apple+some toffee
?some martini / some gin+some vermouth+one olive?
?
individuals+mass(es) fruit-cake/currants+some dough
blood/plasma+blood cells
toffee-apples/apples+some toffee
(correct example?)
mass(es) sweater/some wool
dough/flower+water
snowballs/some snow
collection ? ? ? leage of clubs/several clubs
made-of vs part: can we say "part" for what something is made-of?
«What happens if we ... ask after the relation of something to what helps to make it up?
In many cases it is natural to speak here of parts.
A stone is part of a wall, the toffee is part of the toffee-apple, and so on.
Where we have plurality, the currants are part of the cake,
the bolld cells are part of the blood.
Only when something consists solely of certain individuals does the word
'part' jar, simply because in natural language it means 'proper part'.
The wolves are not part of the pack, but all of it.
... But because the wolves are all of the pack ...
we are are not entitled to say they are (i.e. are identical with)
the pack, because 'the wolves' is a simple plural term referring to
just these animals, whereas 'the pack' refers to a group, and the group and plurality,
while they here coincide in membership, have different identity conditions.
The wolves are the matter of the pack» [Parts 233f]
-- counted as configurational (structural, but not functional) by [OPEN/CC].
Splits with 20% proximity into
An external scheme is applied to (the (atomic) parts or amorpheous substance of) a whole
to pick out some selection - this selection is a part of the whole.
«One cannot have a piece of pie before the pie exists, nor does a section of fruit exist without reference to the whole fruit» [ProbPW]
There are many variations of this principle:
But how is this compatible with "selection by an external scheme"?
the red parts of a painting, the annoying parts of the evening television program, all people who are female and over fifty
Portions of complexes may coincide with a component: the wooden part of a knife (= handle ?)
NB: the steelen part of the bike =/= the steel of the bike (stuff) [Midwinter]
fat is the best or richest part, elite is the choicest part, grip is the part by which sth is grasped, extension is the part constituting an addition [ProbPW]
the upper right corners of the cube [Midwinter]
Segments of complexes may coincide with a component: The upper part of the house = roof(?). The beginning phase of the story = introduction(?) [Midwinter]
a portion identified as significant part: gulf/ocean, knee/garment, ford/body-of-water, echo/wave, light/range [ProbPW]
measured part of temporal/spatial sequence: episode/series, hour/day, evening/day [ProbPW]
generic locative selection: front is forward part, interior is the inland part, height is the highest part [ProbPW]
portion/mass [TaxPW] = homogeneous whole [Midwinter] = masses or amorphous wholes [ProbPW]:
If the object has no obvious parts (hence often named by mass nouns),
then segments are the only parts which the object can be said to have.
Portions of unspecified masses, like "glass of water", are in instance/kind relationship (see above);
the mass must be (generically) individuated to have a part-of relationship [Midwinter].
by cutting up a typewriter we obtain pieces (parts) of the typewriter [TaxPW]
slice/pie [TaxPW]
this hunk is part of my clay [TaxPW]
[actually instance/kind according to Midwinter] grain of salt, yard/mile [TaxPW]
[actually instance/kind according to Midwinter] pile of sand, bunch of pebbles [ProbPW]
«Because the portions of masses are arbitrary, we can divide and apportion masses
by means of standard measures such as inches, ounces, gallons, hours, and so forth» [TaxPW].
"some amount of a certain <mass noun>": hundred grams of the rice in the saucepan, five minutes of a soccer game, the majority of the vote [Midwinter]
[instance/kind according to Midwinter] cup of rice, pail of sand, inch of ..., ... [ProbPW]
[OPEN/R] "Connexions" are classified into:
[Kolp 37] Seven "Generic Relationships":
[BSpec] "Generic Relationships"
«There are not too many generic relationship types.
They are encountered in, and reused by, all applications» [BSpec 256].
[components]---[C>---[composite] |
[dependent]---[D>---[parent] |
[reference]---[Ref>---[maintained] |
[participants]---[S>---[symm. relsh. object] |
[OSA] "Relationship Sets" are classified into: