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Taxonomies and Laws
Lecture 10
Taxonomies and Laws
Taxonomies enumerate scientifically relevant classes and
organize them into a hierarchical structure, such as
• living organisms,
• psychological disorders, and
• elementary particles.
Scientific laws describe, often idealized, regularities among
instances of a class or attributes of instances, such as
• the law of microscopic reversibility (the mechanisms in a
reversible reaction are inverse to each other),
• Ohm’s law (I = V / R), and
• the Hardy-Weinberg principle (genotype and allele
frequencies are in equilibrium across generations).
Taxonomies in Science
Scientists use taxonomies
• to classify organisms into existing taxa,
• to identify elementary particles by their properties, and
• to diagnose patients by symptoms and findings.
However, taxonomies and the categories within them are
hypotheses about the world that evolve, for example
• Woese classified archaea as a separate domain of
prokaryotes (1977), updating the Linnaean system; and
• social protest led to the removal of homosexuality as a
psychological disorder in the DSM.
So, although an individual’s properties may be factual, its
categorization may change over time.
Representing Taxonomies
Informatics tools for formally specifying taxonomies center
on knowledge representations including
• description logics (e.g., OWL-DL);
• frame-based systems (e.g., Protégé-Frames); and
• semantic web languages (e.g., RDF).
Useful characteristics include the ability
• to associate attributes and properties with classes;
• to support attribute inheritance through is-a links; and
• to create instances of the classes.
Use of Taxonomies
Formal representations of taxonomies are used to organize
knowledge resources such as
• the Universal Virus Database
http://www.ncbi.nlm.nih.gov/ICTVdb/index.htm
• the Taxonomy Browser
http://www.ncbi.nlm.nih.gov/Taxonomy/
• the Tree of Life project
http://tolweb.org/tree/
Classifiers categorize instances by their properties.
These may be represented as a set of rules, a decision
tree, a neural network, or other formalisms.
Example applications involve land-use identification from
satellite imagery and protein classification from structure.
Qualitative Laws in Science
Scientists state qualitative laws to specify conditions that
reliably produce an outcome.
These laws may be causal in nature, such as
• moving a magnet through a coil produces a current of
electricity within the coil; and
• combining an alkali and an acid produces a salt.
The laws may also be purely descriptive, such as
• all metals conduct electricity;
• the growth rate of a city is independent of its size
(Gibrat’s Law); and
• an atom mutagenic if it has a hydrogen atom with a
partial charge of 0.146 (King et al., 1996).
Informatics Approaches to Qualitative Laws
Informatics tools stating qualitative laws include
• production rule languages (e.g., OPS5);
• extended first-order logical languages (e.g., CycL); and
• limited first-order logical languages (e.g., Prolog).
Formalisms for stating qualitative laws often
• represent relationships among objects and properties;
• interpret both abstract and specific quantities; and
• support predictions about scenarios or instances.
Qualitative laws appear in larger systems that reason about
phenomena and construct qualitative models.
Quantitative Laws in Science
In contrast to qualitative laws, quantitative laws encode
mathematical regularities.
The laws are descriptive and often appear definitional.
However, consider Newton’s Second Law of Motion:
Often written as F = ma, applications of the law
generally follow a = F/m.
That is, force applied to mass results in acceleration.
Compare this with Ohm’s Law, which has a causal
interpretation in all three of its forms.
Quantitative laws are treated primarily as numerical
relationships although they may have causal meaning.
Informatics Approaches to Quantitative Laws
Quantitative laws are generally represented as symbolic
equations or numeric relationships.
Informatics systems may contain routines for algebraic
manipulation of quantitative laws (e.g., Mathematica).
Statistical Laws
The scientific laws that we described so far are
deterministic, but laws may also be statistical.
Taxonomies and Laws: Summary
Scientific taxonomies and laws share the characteristic that
they are typically descriptive and definitional in nature.
Taxonomies represent a collection of hypotheses about
categories and the IS-A relationships among them.
Laws are hypotheses about general relationships among
the quantities and qualities of an object’s properties.
Informatics tools use taxonomies to organize knowledge
and to classify new observations.
Informatics approaches apply laws to predict the static and
dynamic characteristics of an entity or system.