A production rule pairs a condition (the antecedent) with an action or conclusion (the consequent). A production system combines a rule base, a working memory holding the facts of the case, and an interpreter that repeats a cycle: it finds the rules whose conditions hold, picks one if several conflict, "fires" it, and updates the memory. The formalism has logical roots (Post, 1943) and was central to Newell and Simon's models of problem solving.
An example. Witten et al. (2017) show rules learned from a small weather dataset (2017, pp. 10–11):
IF outlook = sunny AND humidity = high THEN play = no
IF outlook = rainy AND windy = true THEN play = no
IF outlook = overcast THEN play = yes
IF humidity = normal THEN play = yes
IF none of the above THEN play = yes
Read in order (a decision list) they classify every example correctly; taken one at a time, some are false.
Species. Expert systems are production systems: MYCIN had about six hundred rules obtained by interviewing physicians, combined logic and probabilities, and could explain its reasoning (M. Mitchell, 2019, ch. 2; Shortliffe, 1976). ELIZA answered with pattern-and-reassembly rules (Weizenbaum, 1966). And rules can also be learned: one can be read off each leaf of a Decision tree (ID3/C4.5) (Witten et al., 2017, p. 75).
Modularity is partial. Rules look like independent "nuggets" of knowledge: one can be added without touching the others. But Witten et al. (2017) warn that this independence is "something of an illusion" (2017, p. 78): the outcome depends on the order of execution and on how conflicts are resolved.
Linguistic and philosophical angles. The term returns in formal grammars: S → NP VP is
a production (Chomsky, 1957). Buckner (2024) stresses that a transformer produces grammatical
language without explicit production rules (2024, p. 298). Here lies the debate
between GOFAI and connectionism: in a production system the rules are written down
and cause the behavior; in a network, behavior may conform to rules that are represented
nowhere. The distinction between following a rule and merely acting in accordance with it
has been, since Wittgenstein, a philosophical problem in its own right.