Fixpoint Logic
In mathematical logic, fixed-point logics are extensions of classical predicate logic that have been introduced to express recursion. Their development has been motivated by descriptive complexity theory and their relationship to database query languages, in particular to Datalog. Least fixed-point logic was first studied systematically by Yiannis N. Moschovakis in 1974, and it was introduced to computer scientists in 1979, when Alfred Aho and Jeffrey Ullman suggested fixed-point logic as an expressive database query language. Partial fixed-point logic For a relational signature ''X'', FO FP''X'') is the set of formulas formed from ''X'' using first-order connectives and predicates, second-order variables as well as a partial fixed point operator \operatorname used to form formulas of the form operatorname_ \varphivec, where P is a second-order variable, \vec a tuple of first-order variables, \vec a tuple of terms and the lengths of \vec and \vec coincide with the arity ...
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