384

31

The Organization of Knowledge

of solid understanding require a certain conceptual fluidity, before the evidence in

favour of a proposition becomes overwhelming.

Formally, classifying structures can be partitions or hierarchies. A structure ss is

a partition if and only if for all c comma c prime element of s comma c intersection c Superscript prime Baseline equals normal empty set∀c, c^, ∈s, c ∩c^, = ∅, and it is a hierarchy if and only if

for all i element of upper I comma StartSet i EndSet element of s semicolon for all c comma c prime element of s comma c intersection c Superscript prime Baseline element of StartSet normal empty set comma c comma c prime EndSet∀i ∈I, {i} ∈s; ∀c, c^, ∈s, c ∩c^, ∈{∅, c, c^,}.

Problem. Draw Venn diagrams illustrating the partition

StartSet StartSet a EndSet comma StartSet b comma c EndSet comma StartSet d comma e comma f comma g EndSet EndSet comma{{a}, {b, c}, {d, e, f, g}},

and the hierarchy

StartSet StartSet a comma b comma c comma d comma e comma f comma g EndSet comma StartSet d comma e comma f comma g EndSet comma StartSet b comma c EndSet comma StartSet e comma f EndSet comma StartSet a EndSet comma StartSet b EndSet comma StartSet c EndSet comma StartSet d EndSet comma StartSet e EndSet comma StartSet f EndSet comma StartSet g EndSet EndSet period{{a, b, c, d, e, f, g}, {d, e, f, g}, {b, c}, {e, f }, {a}, {b}, {c}, {d}, {e}, { f }, {g}}.

A classifying algorithm would start by constructing the classifying structure; it must

then have a method (discrimination algorithm) for associating each item to be classi-

fied with a class (this is usually a pattern recognition problem; cf. Sect. 13.1), which

is then applied to identify the items and place them in their classes.

31.1

Ontology

Ontology is defined as that branch of metaphysics concerned with the “nature

of being”. ² Attempts have been made to define it less metaphysically and more

concretely, such as the formalization, or specification, of conceptualizations about

objects in the world—including the constraints that define them individually and

the relationships between them. Such formalization is held to be essential for being

able to communicate with others. Hence, human languages came into being, but a

problem is that they evolve: A fundamental paradox is that the desire to commu-

nicate novel, complex ideas requires individual, local innovations, which increase

linguistic diversity but reduce communicability. Certain languages seem to be better

than others in this regard, insofar as novel constructs can be understood by people

even though they have never heard them before then.

The encapsulation of biological knowledge within database schemata almost

inevitably leads to impoverishment and distortion. A good example ³ is the repre-

sentation of a protein structure obtained by X-ray crystallography as an array of the

three-dimensional coördinates of its constituent atoms. The raw diffraction data are

refined to yield a single structure, but nearly all proteins have multiple stable struc-

tures, most of which will, however, be only slightly populated under a given set of

conditions, such as those used to crystallize the protein. The protein database ignores

these alternative structures.

2 This section is complementary to Sect. 1.3.

3 Pointed out by Frauenfelder (1984).