In this paper x denotes a set and R denotes a non empty poset. Next we state two propositions: (1) For all order sorted sets X, Y of R holds X ∩Y is an order sorted set of R. (2) For all order sorted sets X, Y of R holds X ∪Y is an order sorted set of R. Let R be a non empty poset and let M be an order sorted set of R. A many sorted subset indexed by M is said to be an order sorted subset of M ...

This thesis presents the foundations for relational logic programming over polymorphically order-sorted data types. This type discipline combines the notion of parametric polymorphism, which has been developed for higher-order functional programming, with the notion of order-sorted typing, which has been developed for equational rst-order speci cation and programming. Polymorphically order-sort...

We extend first-order order-sorted unification by permitting regular expression sorts for variables and in the domains of function symbols. The set of basic sorts is finite. The corresponding unification problem is infinitary. We conjecture that this unification problem is decidable and give a complete unification procedure.

Built-in equality and inequality predicates based on comparison of canonical forms in algebraic specifications are frequently used because they are handy and efficient. However, their use places algebraic specifications with initial algebra semantics beyond the pale of theorem proving tools based, for example, on explicit or inductionless induction techniques, and of other formal tools for chec...

We compare and contrast Description Logic (DL) and Order-Sorted Feature (OSF) Logic from the perspective of using them for expressing and reasoning with knowledge structures of the kind used for the Semantic Web. Introduction The advent of the Semantic Web has spurred a great deal of interest in various Knowldege Representation formalisms for expressing, and reasoning with, so-called formal ont...

Recently, a model theoretic semantics for lazy functional programming combining parametric and inclusion polymorphism has been proposed in 2]. The aim of the present work is to provide the previous one with the incorporation of a typed lazy narrowing calculus for goal solving which combines lazy uniication, sharing and type checking at run-time. Furthermore, we state soundness and completeness ...

I have been studying the following work on description logic, which is closely related to my main work on extensions of order-sorted logic and logic programming [4, 3, 2]. Title: Negation in Description Logics: Contraries, Contradictories and Subcontraries (under submission) Abstract: We propose an alternative description logic ALC∼ with classical negation and strong negation. In particular, we...

Order-sorted logic has been formalized as first-order logic with sorted terms where sorts are ordered to build a hierarchy (called a sort-hierarchy). These sorted logics lead to useful expressions and inference methods for structural knowledge that ordinary first-order logic lacks. Nitta et al. pointed out that for legal reasoning a sort-hierarchy (or a sorted term) is not sufficient to describ...