productionrule

A production rule is a rule used in two related areas: formal language theory and rule-based artificial intelligence. In formal grammars, it defines how symbols can be rewritten to generate strings. In rule-based AI, it specifies conditional actions triggered by facts held in memory.

In formal grammars, a production rule has the form A -> α, where A is a nonterminal and α is a string of terminals and nonterminals. Applying rules step by step builds derivations that generate sentences of the language. A set of such rules, together with a start symbol, constitutes a grammar. Multiple rules may apply to the same nonterminal, leading to different derivations and, potentially, ambiguity in the grammar.

In rule-based AI, a production rule is typically written as IF condition(s) THEN action(s). The rules form a production system along with a working memory and an inference engine. The engine uses a control strategy to decide the order in which rules fire, such as forward chaining (data-driven) or backward chaining (goal-driven). Production systems underpin many expert systems and rule-based programming environments, including legacy systems and contemporary CLIPS- and OPS5-inspired tools.

Applications and challenges differ by domain. In AI, production rules enable modular knowledge bases and incremental updates but can suffer from conflicts, redundancy, or inefficient rule firing without proper design and conflict-resolution strategies. In formal grammars, production rules are central to parsing and language description, with considerations such as termination, ambiguity, and expressiveness shaping their use.