On Tue, 14 Jan 2003, Pei Wang wrote:
> I'm working on a paper to compare predicate logic and term logic. One
> argument I want to make is that it is hard to infer on uncountable nouns in
> predicate logic, such as to derive ``Rain-drop is a kind of liquid'' from
> "Water is a kind of liquid'' and ``Rain-drop is a kind of water'', (which
> can be early done in term logic, as the one used in NARS).
>
> This is a problem because predicate logic treats a predicate as a set. If
> you force a uncontable noun to be used as a set, it can be done, but it is
> not natural at all, and the distinction between "countable noun" and
> "uncountable noun" is gone.
>
> I browsed the website of CYC and cannot found how it is handled in CycL,
> which is based on predicate logic. Maybe Steve (or others) can give me a
> clue.
>
> The related conceptual issue is whether all concepts should be treated as
> sets. My answer is no.
Pei,
Here is Cyc's comment on StuffType which mentions Water:
"A collection of collections. Each instance of StuffType is a collection
that is stuff-like in at least one respect. A collection COL is stuff-like
just in case there is some sense of 'part' according to which every part
of an instance of COL is itself an instance of COL. More precisely, for a
collection to be an instance of StuffType it is sufficient that there be
some spec-pred PARTPRED of parts (that is, some predicate PARTPRED for
which (genlPreds PARTPRED parts) holds), such that if (isa OBJECT1 COL)
and (PARTPRED OBJECT1 OBJECT2), then (isa OBJECT2 COL). Here are two
examples. Consider Breathing. Take an instance of that, say a ten minute
long period in which a person is breathing. Imagine some two minute
snippet of that, one of its timeSlices (a spec-pred of parts). That, too,
is an instance of Breathing. So Breathing is a StuffType, since all
timeSlices of an instance of Breathing are also instances of Breathing.
Consider Water. Take any instance of Water -- say the water in the Pacific
Ocean. Now take any portion of that water -- say a handful of it that a
person scoops up near Honolulu, one of its physicalPortions (a spec-pred
of parts). That handful is itself an instance of Water. Hence Water is a
StuffType, in virtue of the fact that all physicalPortions of all
instances Water are themselves instances of Water. Other examples are:
AbstractInformationalThing, which is stuff-like with respect
subInformation; CharacterString, which is stuff-like with respect to
subCharacterStrings; and List, which is stuff-like with respect to
subLists. These examples are somewhat exceptional -- most StuffTypes are
like the examples of Breathing and Water. See ObjectType, for the
contrasting notion of being object-like."
And here is one of the definitional assertions for Raindrop which gives
its relationship to the concept of Water (note that Water-Fresh is a
specialization of Water):
Formula :
(genls Raindrop
(ParticleFn
(LiquidFn Water-Fresh)))
English Translation :
A raindrop is a type of fresh water particle.
LiquidFn is a function which denotes the liquid form of its argument, and
ParticleFn is a function which denotes a particle composed of its
argument.
Countable vs. uncountable nouns are easily represented by Cyc.
-Steve
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