Taxonomy of living being made by Carolus Linnaeus is known for a couple of centuries. Although it is clear and unambiguous for biologist , an attempt to formalize it reveal certain ambiguities which arise exclusively on account of the formal languages we use. In this section we will argue that certain peculiar properties of F-Logic , such as meta-classes may be essential for the representation of Linnaean taxonomy. In this section will we will describe a simple example of food web and the taxonomy of related species just to illustrate the problems pertained to semantics of biodiversity data. In the subsequent section this data will be extensively used for the illustration of domain browsing philosophy.
Consider a fragment of food web of Illinois Wetland:
Here are the details about the species that constitute the food -web.
| Kingdom | Phylum/Division | Subphylum | Class | Order | Family | Genus | Species | |
| Earthworm | Animalia | Annelida | Oligochaeta | Opisthopora | Lumbricidae | Lumbricus | Lumbricus terrestris | |
| Spotted Salamander | Animalia | Chordata | Vertebrata | Amphibia | Urodela | Ambystoma | Ambystoma maculatum | |
| Mosquito | Animalia | Arthropoda | Insecta | Diptera | Culicidae | Aedes | Aedes aegypti | |
| North Leopard Frog | Animalia | Chordata | Vertebrata | Amphibia | Anura | Ranidae | Rana | Rana pipiens |
| Great Egret | Animalia | Chordata | Vertebrata | Aves | Herodiones | Ardeidae | Casmerodius | Casmerodius albus |
| Blue Gill fish | Animalia | Chordata | Vertebrata | Osteichthyes | Perciformes | Centrachidae | Lepomis | Lepomis macrochirus |
| Shrew (short tailed) | Animalia | Chordata | Vertebrata | Mammalia | Insectivora | Soricidae | Blarina | Blarina brevicauda |
| Cattails (plant) | Plantae | Magnoliophyta | Liliopsida | Typhales | Typhaceae | Typha | Typha latifolia | |
| Northern water snake | Animalia | Chordata | Vertebrata | Reptilia | Squamata | Colubridiae | Nerodia | Nerodia sipedon |
Earthworm='Lumbricus terrestris '
'Spotted Salamander'='Ambystoma maculatum'
Mosquito='Aedes aegypti'
The categories kingdom, phylum, class, order, family , etc are well known to biologists. However their semantic role is ambiguous. They have at least two types of semantic representation. Consider them separately:
1. All the italics word in the table
above are classes. The
Linnaean taxonomy is merely a hierarchy of classes.
Yet each class has a certain type on its own which describes the level of this
class in the whole hierarchy. For example
animalia, plantae, protista, monera, fungi
are 5 classes on the top of
hierarchy. They describe the Kingdom
where a particular organism belongs. The classes
Anneliada, Chordata, Athropoda, etc
belongs to the second level
of the hierarchy. The whole second level is called
Phylum.
This is how the taxonomy is arranged:
Kingdom
/-----------|-------------\
Phylum
Phylum
/
\
/ \
Class
Class
Class Class
/ \
/ \
/ \
/ \
Order Order Order Order
Order Order Order Order
Now we can suggest that words kingdom, phylum, class, order, family , etc represent metaclasses for those classes which are written in italics in the table above. For example animalia, plantae, protista, monera, fungi are the 5 instances of the class kingdom. We can treat them as objects and we can write:
animalia:kingdom.
plantae:kingdom.
protista:kingdom.
monera:kingdom.
fungi:kingdom.
At the same time animalia, plantae, protista, monera, fungi are classes and they have their own subclasses. For example we can write:
vertebrata::chordata::animalia.
Here is the right time to explain why in our graphic formalism we used boxes for both objects and classes. If we dealt with the language other then F-Logic it would be appropriate to device different graphic symbols for classes and their instances, because in most of the languages classes can not be treated as objects. Yet in F-Logic any class can be also treated as an object which can be an instance of some metaclass. The possibility to treat classes as objects may seem to be unnatural to a programmer. But our example of Linnaean taxonomy illustrates that in scientific taxonomies we often do treat classes as objects! And if we expect ontologies to be faithful representation of real taxonomies the last remark makes a strong case for using F-Logic as an ontology language.
2. Here is the second semantic role for categories kingdom, phylum, class, order, family , etc. They can be considered as attributes (roles or binary relations if we like to express the ideas in FOL or Description Logics). Say in F-Logic/GFL we may describe an earthworm as follows:
If we use description logic we have to describe kingdom, phylum, class, order, family , etc as roles or binary relations which will be equivalent to the representation of these categories as attributes. And if we use description logic this would be the only representation, since description logic does not allow using classes as objects! F-Logic would allow to consider both the representations at the same time and the two representations may be related. Now, after going through the issues we shall discuss the systematic F-logic representation of the data pertained to our food web example.
We start from representation of isa arrows. The semantic for attributes such as kingdom, phylum, class, order, family , etc is derived from the information provided by isa arrows. Here is the set of facts which represent the class hierarchies related to our example of food web of Illinois Wetland. Compare the following with the table above. Our set of facts starts from description description of vertebrata subphylum. The first fact specifies the sub tree which is common for all the vertebrata species.
'Vertebrata'::'Chordata'::'Animalia'.
'Ambystoma maculatum'::'Ambystoma'::'Urodela'::'Amphibia'::'Vertebrata'.
'Rana pipiens'::'Rana'::'Ranidae'::'Anura'::'Amphibia'::'Vertebrata'.
'Casmerodius albus'::'Casmerodius'::'Ardeidae'::'Herodiones'::'Aves'::'Vertebrata'.
'Lepomis macrochirus'::'Lepomis'::'Centrachidae'::'Perciformes'::'Osteichthyes'::'Vertebrata'.
'Blarina brevicauda'::'Blarina'::'Soricidae'::'Insectivora'::'Mammalia'::'Vertebrata'.
'Nerodia sipedon'::'Colubridiae'::'Squamata'::'Reptilia'::'Vertebrata'.
'Lumbricus terrestris' ::'Lumbricus'::'Lumbricidae'::'Opisthopora'::'Oligochaeta'::'Annelida'::'Animalia'.
'Aedes aegypti'::'Aedes'::'Culicidae'::'Diptera'::'Insecta'::'Arthropoda'::'Animalia'.
'Typha latifolia'::'Typha'::'Typhaceae'::'Typhales'::'Liliopsida'::'Magnoliophyta'::'Plantae'.
The following assertion would allow to use common name as synonym with species name:
earthworm='Lumbricus terrestris '
'spotted salamander'='Ambystoma maculatum'
mosquito='Aedes aegypti'
..........
Here are the facts that specify the meaning of the metaclasses kingdom, phylum, class, order, family , etc.
'Animalia':kingdom.
'Plantae':kingdom.
'Annelida':phylum.
'Chordata':phylum.
'Magnoliophyta':division.
'Vertebrata':subphylum.
'Oligochaeta':class.
'Amphibia':class.
'Insecta':class.
'Amphibia':class.
..............
...............
'Typha latifolia':species.
'Nerodia sipedon':species.
There are two ways of describing the respective attributes kingdom, phylum, class, order, family , etc. In the first case we may derive them with the help of the following rules:
X[kingdom*->King] :- King:kingdom, X::King.
X[phylum-*>Phyl] :- Phyl:phylum, X::Phyl.
X[class-*>Class] :- Class:class, X::Class.
....................
........................
Alternatively we can describe attributes kingdom, phylum, class, order, family , etc. with the help of the following facts:
'Animalia'[kingdom*->Animalia'].
'Plantae'[kingdom*->'Plantae'].
'Annelida'[phylum*->'Annelida'].
'Chordata'[phylum*->'Chordata']
'Magnoliophyta'[division*->'Magnoliophyta'].
'Vertebrata'[subphylum*->'Vertebrata' ].
'Oligochaeta'[class*->'Oligochaeta' ].
'Amphibia'[class*-> 'Amphibia' ].
'Insecta'[class*-> Insecta' ].
'Amphibia'[class *->Amphibia' ].
..............
...............
cattails[species*->'Typha latifolia'].
water_snake[species*->'Nerodia sipedon'].
The inheritable character of attribute kingdom in specification 'Animalia'[kingdom*->Animalia'] ensures that it will be inherited by all subclasses derived from the class Animalia'. It will be inherited for example by 'Vertebrata', 'Chordata', Ambystoma maculatum', 'Ambystoma', 'Urodela', 'Amphibia', etc.
And finally here is the description of feeding relations, i.e. those relations which form food-web
'spotted salamander'[eats*->>{ mosquito, frog , ' blue gull fish}]. //salamander eats mosquito, frog ,and blue gull fish
frog[eats*->>{mosquito , 'spotted salamander' }]. //frog eats mosquito, salamander
.................
.................
With the experience we already have we may anticipate that if we draw the whole diagram which describes the complete knowledge base of this section, this diagram will be too complex and hardly readable. Therefore we will not draw it. The knowledge base developed in this section will be used as the example in the next section.
C 2003 S. Krivov Send your comments to skrivov@zoo.uvm.edu