1. Taxonomies and Laws Lecture 10

2. 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).

3. Taxonomies in Science 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. Scientists use taxonomies to classify organisms into existing taxa, to identify elementary particles by their properties, and to diagnose patients by symptoms and findings. So, although an individual’s properties may be factual, its categorization may change over time.

4. 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.

5. 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.

6. 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).

7. 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.

8. 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.

9. 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).

10. Statistical Laws The scientific laws that we described so far are deterministic, but laws may also be statistical.

11. 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.