Order-sorted equational generalization algorithm revisited

Generalization, also called anti-unification, is the dual of unification. A generalizer two terms t and $t^{\prime }$ a term \prime which are substitution instances. The most general equational unifiers that least generalizers, i.e., specific anti-instances modulo equations. In previous work, we extended classical untyped generalization algorithm to: (1) an order-sorted typed setting with sorts, subsorts, subtype polymorphism; (2) work theories, where function symbols can obey any combination associativity, commutativity, identity axioms (including empty set such axioms); (3) both, results in modular, algorithm. However, Cerna Kutsia showed our generally incomplete for case counterexample was given. Furthermore, they proved that, theories elements or more, nullary, yet it finitary both linear one-unital fragments, either solutions repeated variables disregarded considered restricted to having just one symbol unit element. this show how easily extend original inference system cope non-linear fragment identify more class than one–unit finitary.