Bits and pieces of the theory of institutions
Proceedings of a tutorial and workshop on Category theory and computer programming
Institutions: abstract model theory for specification and programming
Journal of the ACM (JACM)
Logical support for modularisation
Papers presented at the second annual Workshop on Logical environments
Equational axiomatizability for coalgebra
Theoretical Computer Science
A Category-Based Equational Logic Semantics to Constraint Programming
Selected papers from the 11th Workshop on Specification of Abstract Data Types Joint with the 8th COMPASS Workshop on Recent Trends in Data Type Specification
An Introduction to Category-based Equational Logic
AMAST '95 Proceedings of the 4th International Conference on Algebraic Methodology and Software Technology
FCT '93 Proceedings of the 9th International Symposium on Fundamentals of Computation Theory
Mathematical Structures in Computer Science
An axiomatic approach to structuring specifications
Theoretical Computer Science
Parameterisation for abstract structured specifications
Theoretical Computer Science
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A categorical framework for equational logics is presented, together with axiomatizability results in the style of Birkhoff. The distinctive categorical structures used are inclusion systems, which are an alternative to factorization systems in which factorization is required to be unique rather than unique ‘up to an isomorphism’. In this framework, models are any objects, and equations are special epimorphisms in ℭ, while satisfaction is injectivity. A first result says that equations-as-epimorphisms define exactly the quasi-varieties, suggesting that epimorphisms actually represent conditional equations. In fact, it is shown that the projectivity/freeness of the domain of epimorphisms is what makes the difference between unconditional and conditional equations, the first defining the varieties, as expected. An abstract version of the axiom of choice seems to be sufficient for free objects to be projective, in which case the definitional power of equations of projective and free domain, respectively, is the same. Connections with other abstract formulations of equational logics are investigated, together with an organization of our logic as an institution.