Predicateinitial

Predicateinitial is a term used in logic and computer science to denote the initial or base-case predicate in a recursive or inductive definition. It identifies the starting facts or conditions from which other facts are derived.

In logic programming, Datalog, and formal semantics, many predicates are defined by a base set of facts plus recursive rules. The initial predicate provides the grounding for derivations and helps establish the least fixpoint of the definition.

Examples: In a simple definition of even numbers, the base fact even(0) is an instance of the initial predicate; a recursive rule then derives even(n) from even(n-2). In a reachability analysis, the initial predicate reachable(start) records the starting node, and a recursive rule adds nodes reachable via successive edges from already reachable nodes.

Notes: The exact label predicateinitial varies across sources; in some contexts the base clause or base facts are described without a special name. The term is primarily descriptive rather than a formal standard.

See also: base case, inductive definition, least fixpoint, recursion, Datalog, logic programming.