We propose to use order-sorted algebras (OSA) on multiple levels to describe languages together with their type systems. It is demonstrated that even advanced aspects can be modeled, including, parametric polymorphism, complex relationships between diierent sorts of an operation's rank, the speciication of a variable number of parameters for operations, and type constructors using values (and n...

The notions of state and observable behaviour are fundamental to many areas of computer scjpnce. Hidden sorted algebra, an extension of many sorted al~bra. captures these notions through hidden sorts and the behavioural satisfaction of equations. This makes it a powerful formalisation of abstract machines, and many results suggest that it is also suitable for the semanticl:i of the object parad...

This paper presents an encoding of a non-temporal fragment of the TLA language, which includes untyped set theory, functions, arithmetic expressions, and Hilbert’s ε operator, into many-sorted firstorder logic, the input language of state-of-the-art smt solvers. This translation, based on encoding techniques such as boolification, injection of unsorted expressions into sorted languages, term re...

In formal ontology, entity types and relationships are philosophically defined, and the properties of objects are classified on the basis of sortality, rigidity, and identity (called property classification). Sorts and unary predicates are semantically identical in order-sorted logic, but they are respectively sortal and non-sortal (i.e., they are distinguished) in a formal ontology. This ontol...

The Schoenfinkel-Bernays-Ramsey class is a fragment of first-order logic with the Finite Model Property: a sentence in this class is satisfiable if and only if it is satisfied in a finite model. Since an upper bound on the size of such a model is computable from the sentence, the satisfiability problem for this family is decidable. Sentences in this form arise naturally in a variety of applicat...

This paper presents several extensions of order-sorted logic based on the notion of property classification in formal ontology. The refined order-sorted language contains types (as rigid sorts), anti-rigid sorts, and unary predicates in order to distinctly express the following properties: substantial sorts, nonsubstantial sorts, and non-sortal properties. For many separated knowledge bases con...

Equational presentations with ordered sorts encompass partially deened functions and subtyping information in an algebraic framework. In this work we address the problem of computing in order-sorted algebras, with very few restrictions on the allowed presentations. We adopt an algebraic framework where equational, membership and existence formulas can be expressed. A complete deduction calculus...

In recent years various sorted logics have been developed, mostly to facilitate knowledge representation and to speed up automated deduction. We present a polymorphic order-sorted logic that can be implemented e ciently. Because the polymorphism is almost unrestricted, it is possible for two terms to have an exponential number of maximally general uni ers. To guarantee a single most general uni...

Integrating ontologies and rules on the Semantic Web enables software agents to interoperate between them; however, this leads to two problems. First, reasoning services in SWRL (a combination of OWL and RuleML) are not decidable. Second, no studies have focused on distributed reasoning services for integrating ontologies and rules in multiple knowledge bases. In order to address these problems...

LIFE uses matching on order-sorted feature structures for passing arguments to functions. As opposed to uniication which amounts to normalizing a conjunction of constraints, solving a matching problem consists of deciding whether a constraint (guard) or its negation are entailed by the context. We give a complete and consistent set of rules for entailment and disentailment of order-sorted featu...