States of Matter
I have been evaluating some of the ontologies listed on
http://ltsc.ieee.org/suo/refs.html and notice some interesting
issues in the representation of states of matter.
Russell & Norvig's upper ontology from
Russell, S., and Norvig, P. (1994), AI: A Modern Approach, Prentice-Hall
( http://ltsc.ieee.org/suo/ontologies/Russell-Norvig.txt )
represents the states of matter as:
(subclass-of Solid Stuff)
(subclass-of Liquid Stuff)
(subclass-of Gas Stuff)
(subclass-of Stuff PhysicalObjects)
(subclass-of PhysicalObjects Events)
(subclass-of Events Anything)
This is a straightforward type hierarchy that defines all Physical
Objects as existing in one of the three classes, and doesn't address
issues of time or varying states for the same object.
contrasting that with the Public Release of the Upper Cyc Ontology
( http://ltsc.ieee.org/suo/ontologies/cyc-merged-ontology.txt )
the same states of matter are represented as:
(#$genls #$SolidTangibleThing #$TangibleThing)
(#$genls #$SemiSolidTangibleThing #$TangibleThing)
(#$genls #$LiquidTangibleThing #$FluidTangibleThing)
(#$genls #$GaseousTangibleThing #$FluidTangibleThing)
(#$genls #$FluidTangibleThing #$TangibleThing)
(#$genls #$TangibleThing #$PartiallyTangible)
(#$genls #$PartiallyTangible #$SpatialThing)
(#$genls #$PartiallyTangible #$SomethingExisting)
(#$genls #$SpatialThing #$Individual)
(#$genls #$SomethingExisting #$TemporalThing)
(#$genls #$TemporalThing #$Individual)
(#$genls #$Individual #$Thing)
These hierarchies have several things in common,
with specialized classes/collections that consist of
all individuals that are in a particular state of matter
at the most specialized level. Cyc microtheories
distinguish four states of matter, whereas Russell and
Norvig distinquish only three. Interestingly enough,
plasma (the highly energized 'fourth state of matter')
is not in either list. I expect this is because
few people other than physicists encounter or think
about this state of matter.
Cyc includes semisolid as a state to facilitate
describing anomalous cases like Jello.
Fluid Tangible things are also specified to
describe the properties of materials such as sand,
which is pourable.
In the upper Cyc Ontology, there are three functions
defined to avoid an explosive growth of the knowledge
base. Each of these functions, when provided with
collection of some Tangible Stuff will produce the
collection of Tangible Things which happens to be
in the state of matter corresponding to the function.
This avoids having a multitude of constants
like #$Ice, #$Steam, and #$LiquidWater, and allows
the use of logical forms such as (#$SolidFn #$Water)
and (#$LiquidFn #$Water).
I don't know why there isn't a #$SemiSolidFn defined.
(#$isa #$SolidFn #$CollectionDenotingFunction)
(#$resultIsa #$SolidFn #$TangibleStuffStateType)
(#$resultGenl #$SolidFn #$SolidTangibleThing)
(#$arg1Isa #$SolidFn #$TangibleStuffCompositionType)
(#$isa #$LiquidFn #$CollectionDenotingFunction)
(#$resultIsa #$LiquidFn #$TangibleStuffStateType)
(#$resultGenl #$LiquidFn #$LiquidTangibleThing)
(#$arg1Isa #$LiquidFn #$TangibleStuffCompositionType)
(#$isa #$GaseousFn #$CollectionDenotingFunction)
(#$resultIsa #$GaseousFn #$TangibleStuffStateType)
(#$resultGenl #$GaseousFn #$GaseousTangibleThing)
(#$arg1Isa #$GaseousFn #$TangibleStuffCompositionType)
To further define these named states of matter, Cyc
includes definitions that define them as scalar intervals
so it makes sense to talk about the range of values
a substance takes on, from gaseous to liquid to solid.
They are also related to Physical Attributes so these names
are recognized as a possible state of matter for a
particular instance of matter.
(#$isa #$SolidStateOfMatter #$StateOfMatter-SolidLiquidGaseous)
(#$isa #$SemiSolidStateOfMatter #$StateOfMatter-SolidLiquidGaseous)
(#$isa #$GaseousStateOfMatter #$StateOfMatter-SolidLiquidGaseous)
(#$isa #$LiquidStateOfMatter #$StateOfMatter-SolidLiquidGaseous)
(#$genls #$StateOfMatter-SolidLiquidGaseous #$ScalarInterval)
(#$genls #$StateOfMatter-SolidLiquidGaseous #$PhysicalAttribute)
(#$genls #$ScalarInterval #$NTupleInterval)
(#$genls #$ScalarInterval #$AttributeValue)
(#$genls #$PhysicalAttribute #$AttributeValue)
(#$genls #$NTupleInterval #$Tuple)
(#$genls #$NTupleInterval #$AttributeValue)
(#$genls #$AttributeValue #$IntangibleIndividual)
(#$genls #$AttributeValue #$Individual)
(#$genls #$Tuple #$MathematicalObject)
(#$genls #$Tuple #$Situation)
(#$genls #$Situation #$Individual)
(#$genls #$MathematicalObject #$IntangibleIndividual)
(#$genls #$MathematicalObject #$MathematicalOrComputationalThing)
(#$genls #$IntangibleIndividual #$Intangible)
(#$genls #$IntangibleIndividual #$Individual)
(#$genls #$Intangible #$Thing)
(#$genls #$Individual #$Thing)
Finally, there is also a predicate used to indicate the state of matter
for a particular partially tangible thing. In Cyc, a partially tangible
thing must have a tangible part and a temporal extent.
The state of matter applies to the tangible part of thing,
within the time specified by the temporal extent.
It isn't clear in the Upper Cyc Ontology what occurs when the tangible
part is in multiple states of matter during the temporal extent,
such as what state an ice cube that is first melted and then vaporized
should have. It is clear that there are subabstractions of that tangible
part which have only one state.
I also expect there are genlPreds for this predicate that aren't listed
in the Public release of the Upper Cyc Ontology.
(#$isa #$stateOfMatter #$IntervalBasedQuantitySlot)
(#$isa #$stateOfMatter #$TangibleSubstancePredicate)
(#$arg1Isa #$stateOfMatter #$PartiallyTangible)
(#$arg2Isa #$stateOfMatter #$StateOfMatter-SolidLiquidGaseous)
According to the CNR-ITBM ontology,
( http://saussure.irmkant.rm.cnr.it/onto/ )
*Solid, *Liquid, and *Gas are reified properties, and as such
are 'non-rigid' classes of a theory of Physical concepts.
In this ontology, there is no logical distinction between a
monadic predicate (unary relation) and a type (class).
Each relation is a set of tuples that represents a relationship
among objects in the universe of discourse.
I'm not sure why there is not, but from my examination of
this ontology, it would be consistent to have a
reified-physical-property corresponding to the state of matter
for a particular object.
Such exist for consistency, and other properties, so
either this part of the ontology is still being developed, or
there is a subtle difference between these properties that I
don't see. Each of these are subrelations of the
Relation PHYSICAL-CATEGORY and are defined as compliant with
Gruber's units of measure ontologies.
This representation choice if it existed would have
'state-of-matter' as a function, single states of matter
as properties, and the 'reified-state-of-matter' concept as
range of state-of-matter relation. This choice is good at talking
directly of states of matter by properties, like natural language does,
while the function with a specialized range is good at talking
of 'the state of matter' of some object.
Class *SOLID Subclass-Of: Substance, _solid
Meta: 'Reified-property
Class *LIQUID Subclass-Of: Substance, _liquid
Meta: 'Reified-property
Class *GAS Subclass-Of: Substance, _gaseous
Meta: 'Reified-property
Class _SOLID Subrelation-Of: _physical-state
Class _LIQUID Subrelation-Of: _physical-state
Class _GASEOUS Subrelation-Of: _physical-state
Class _PHYSICAL-STATE Subrelation-Of: Physical-property
Class PHYSICAL-PROPERTY Subrelation-Of: Structuring-property
Class STRUCTURING-PROPERTY Subrelation-Of: Unary-tuple
Class UNARY-TUPLE Alias: Unary-relation
Class UNARY-RELATION Subclass-Of: Relation
Class RELATION Subclan Attribute, since the state of matter
for a particular entity is actually the property of the entity as a
continuant. I'm not sure if the state of matter is a Characteristic,
(which makes sense because this is a subtype whose instances are properties
of entities, such as color or length), or if it is an Attribute,
which is the property of some object.
Since Sowa's KR ontology is not based on a fixed hierarchy of categories,
but rather is based on a framework of distinctions, it is important
to understand which distinctions properly characterise the state-of-matter.
From this we can determine where in the automatically generated hierarchy it
is appropriate to place the concepts of Solid, Liquid, and Gaseous.
David (whitten@netcom.com) (713) 791-1414 ext 6116