Equations, order-sortedness, and inheritance in logic programming
Ulrich Furbach, Steffen Hölldobler · 1992
this paper is to show that order-sortedness can easily be expressed within the framework of equational logic programming. More precisely, by carefully designing a certain equational theory it is demonstrated that the well-known least model semantics of equational logic programming captures precisely the features of an order-sorted logic language restricted to Horn clauses. It is outlined how polymorphism, well-sortedness, order-sorted equational logic programming, attributes, and inheritance can also be treated within this framework. The equational theories developed herein are ordinary conditional equational theories. It is unnecessary to change the domain of discourse as -- for example -- in [39] or the semantics of equality as -- for example -- in [44]. The semantics of an order-sorted logic comes for free. There is no need of a relativization and a sort theorem nor is it necessary to borrow concepts from order-sorted algebra. In fact, the problem is to convince the reader that the simple equational theories developed herein are sufficient to achieve order-sortedness. This claim will be validated by many examples