FO(.)

rdf:langString FO(.)

rdf:langString In computer science, FO(.) (a.k.a. FO-dot) is a knowledge representation language based on first-order logic (FO). It extends FO with types, aggregates (counting, summing, maximising ... over a set), arithmetic, inductive definitions, partial functions, and intensional objects. By itself, a FO(.) knowledge base cannot be run, as it is just a "bag of information", to be used as input to various generic reasoning algorithms. Reasoning engines that use FO(.) include IDP-Z3, IDP and FOLASP. As an example, the IDP system allows generating models, answering set queries, checking entailment between two theories and checking satisfiability, among other types of inference over a FO(.) knowledge base. FO(.) has four types of statements: * Type, function and predicate declarations, * Axioms, i.e., logic sentences about possible worlds, * Definitions that specify a unique interpretation of a defined symbol, given the interpretation of its parameters. Definitions can be inductive. * Enumerations, i.e., definitions of symbols by enumeration.