Deductive-nomological

The deductive-nomological, or D-N model is a formalisation of scientific explanations in natural language.

Background
The D-N model is taught implicitly in schools, and approximates our pre-theoretical conception of science, which many non-experts hold. It was initially formalised by Carl Hempel, although a sketch of it can be found in Popper's Logic of Scientific Discovery.

The model is positivist in tone and implication, devised as a prescriptive form for scientific explanations, but due to the way that the model eschews any account of causality, scientific modelling, or simplification, it is no longer accepted as dogma.

Formalisation
The model sets the following form for scientific explanation, similar to that of a sum or calculation:


 * P (Explanandum) - statements that describe the phenomenon to be explained and provide a description of the phenomena
 * S (Explanans) - statements that "explain" the statements in P, at least one of which is a specific statement, and at least one general, "law-like" statement (ex., "all Xs are Ys")

The final consideration of form pertains to the relation between the explanans (S) and the explanandum (P). This relation is one of logical entailment - given the set of explanans statements, it must be possible to deduce the explanandum.