Results 1 
3 of
3
Institution Morphisms
, 2001
"... Institutions formalize the intuitive notion of logical system, including syntax, semantics, and the relation of satisfaction between them. Our exposition emphasizes the natural way that institutions can support deduction on sentences, and inclusions of signatures, theories, etc.; it also introduces ..."
Abstract

Cited by 65 (18 self)
 Add to MetaCart
Institutions formalize the intuitive notion of logical system, including syntax, semantics, and the relation of satisfaction between them. Our exposition emphasizes the natural way that institutions can support deduction on sentences, and inclusions of signatures, theories, etc.; it also introduces terminology to clearly distinguish several levels of generality of the institution concept. A surprising number of different notions of morphism have been suggested for forming categories with institutions as objects, and an amazing variety of names have been proposed for them. One goal of this paper is to suggest a terminology that is uniform and informative to replace the current chaotic nomenclature; another goal is to investigate the properties and interrelations of these notions in a systematic way. Following brief expositions of indexed categories, diagram categories, twisted relations, and Kan extensions, we demonstrate and then exploit the duality between institution morphisms in the original sense of Goguen and Burstall, and the "plain maps" of Meseguer, obtaining simple uniform proofs of completeness and cocompleteness for both resulting categories. Because of this duality, we prefer the name "comorphism" over "plain map;" moreover, we argue that morphisms are more natural than comorphisms in many cases. We also consider "theoroidal" morphisms and comorphisms, which generalize signatures to theories, based on a theoroidal institution construction, finding that the "maps" of Meseguer are theoroidal comorphisms, while theoroidal morphisms are a new concept. We introduce "forward" and "seminatural" morphisms, and develop some of their properties. Appendices discuss institutions for partial algebra, a variant of order sorted algebra, two versions of hidden algebra, and...
Stretching First Order Equational Logic: Proofs with Partiality, Subtypes and Retracts
 Proceedings, Workshop on First Order Theorem Proving
, 1998
"... It is widely recognized that equational logic is simple, (relatively) decidable, and (relatively) easily mechanized. But it is also widely thought that equational logic has limited applicability because it cannot handle subtypes or partial functions. We show that a modest stretch of equational logic ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
It is widely recognized that equational logic is simple, (relatively) decidable, and (relatively) easily mechanized. But it is also widely thought that equational logic has limited applicability because it cannot handle subtypes or partial functions. We show that a modest stretch of equational logic effectively handles these features. Space limits preclude a full theoretical treatment, so we often sketch, motivate and exemplify.
Journal of Logic and Computation Advance Access published August 12, 2006 An Institutionindependent Generalization of Tarski’s Elementary Chain Theorem
"... We prove an institutional version of Tarski’s elementary chain theorem applicable to a whole plethora of ‘firstorderaccessible’ logics, which are, roughly speaking, logics whose sentences can be constructed from atomic formulae by means of classical firstorder connectives and quantifiers. These in ..."
Abstract
 Add to MetaCart
(Show Context)
We prove an institutional version of Tarski’s elementary chain theorem applicable to a whole plethora of ‘firstorderaccessible’ logics, which are, roughly speaking, logics whose sentences can be constructed from atomic formulae by means of classical firstorder connectives and quantifiers. These include the unconditional equational, positive, ð [ Þ 0 n and full firstorder logics, as well as less conventional logics, used in computer science, such as hidden or rewriting logic.