Partial evaluation (PE) is a powerful and general program optimization technique with many successful applications. However, it has never been investigated in the context of expressive rule-based languages like Maude, CafeOBJ, OBJ, ASF+SDF, and ELAN, which support: 1) rich type structures with sorts, subsorts and overloading; 2) equational rewriting modulo axioms such as commutativity, associat...

The notions of meta-ontology enhance the ability to process knowledge in information systems; in particular, ontological property classification deals with the kinds of properties in taxonomic knowledge based on a philosophical analysis. The goal of this paper is to devise a reasoning mechanism to check the ontological and logical consistency of knowledge bases, which is important for reasoning...

Computer algebra systems are large collections of routines for solving mathematical problems algorithmically e ciently and above all symbolically The more advanced and rigorous computer algebra systems for example Axiom use the concept of strong types based on order sorted algebra and category theory to ensure that operations are only applied to expressions when they make sense In cases where A...

We present an encoding of Zermelo-Fraenkel set theory into many-sorted first-order logic, the input language of state-of-the-art smt solvers. This translation is the main component of a back-end prover based on smt solvers in the TLA Proof System.

In the field of ontology, several property classifications have been defined as meta-ontologies wherein the properties of individuals are rigorously classified as sortal/non-sortal, rigid/anti-rigid/non-rigid, etc. through philosophical analysis. The notions ofsuch meta-ontologies enable the processing of properties that allow us to reason abouttaxonomic knowledge in information...

In this paper, we extend the results on the modularity of con uence and termination of single-sorted TRSs[3][6][7] to order-sorted ones. Order-sorted TRSs build a good framework for handling overloaded functions and subtypes. For proving modularity of completeness of ordersorted TRSs, we rst transform a TRS with overloaded functions to a non-overloaded one, and then we demonstrate that our tran...

Knowledge representation in logics, even in the order-sorted logic that includes a sort hierarchy, tends to lose the conciseness and the nuances of natural language. If we could construct a logic that includes both predicates and terms as classes in the hierarchies, it would be very useful for connecting general knowledge to specic knowledge. Although there are actually logics that are equipped...

The purpose of this paper is to study the problem of complete type inferencing for polymorphic order-sorted logic programs. We show that previous approaches are incomplete even if one does not employ the full power of the used type systems. We present a complete type inferencing algorithm that covers the polymorphic order-sorted types in PROTOS-L, a logic programming language that allows for po...

HiLog enhances the modeling capabilities of deductive databases and logic programming with higher-order and meta-data constructs, complex objects, and schema browsing. Its distinctive feature, a higher-order syntax with a rst-order semantics, allows for eecient implementation with speeds comparable to Prolog. In fact, HiLog implementation in XSB 30, 26] together with tabulated query evaluation ...