Equational logic of circular data type specification

Specification and Proof in Membership Equational Logic

Abs t rac t This paper is part of a long-term effort to increase expressiveness of algebraic specification languages while at the same time having a simple semantic basis on which efficient execution by rewriting and powerful theorem-proving tools can be based. In particular, our rewriting techniques provide semantic foundations for Maude's functional sublanguage, where they have been efficient...

Circumscription in Data Logic for Data Type Specification

In this paper we present a logical speciication of data types. This speciication is built upon a previously given speciication for a data type that we want to extend by introducing new constructing objects and deened operations. The extended data type is speciied by superposing a circumscription principle to some speciication axioms. Circumscription formalizes in second-order logic some forms o...

Equational Logic and Equational Theories of Algebras

Equational Specification of Dynamic Objects

An equational language to specify object-oriented conceptual models is defined. Objects are considered to be characterized by a unique object identifier and have static and dynamic structure. Examples of static structure are classification, aggregation, generalization and grouping, examples of dynamic structure are events, processes, local (intra-object) and global (inter-object) and communicat...

Relative Equational Specification and Semantics

Standard concepts of initial and final algebra semantics are generalised in a modular hierarchical manner. The resulting relative formalism allows a unified view on the relationship between initial and final algebra semantics and gives a dualised notion of consistency. Using this, a modular hierarchical approach to proof by consistency is taken by which only top-level equations need be consider...