6 research outputs found
Characterizing specification languages which admit initial semantics
AbstractThe paper proposes an axiomatic approach to specification languages, and introduces notions of reducibility and equivalence as tools for their study and comparison. Algebraic specification languages are characterized up to equivalence. They are shown to be limited in expressive power by implicational languages
Logics of Finite Hankel Rank
We discuss the Feferman-Vaught Theorem in the setting of abstract model
theory for finite structures. We look at sum-like and product-like binary
operations on finite structures and their Hankel matrices. We show the
connection between Hankel matrices and the Feferman-Vaught Theorem. The largest
logic known to satisfy a Feferman-Vaught Theorem for product-like operations is
CFOL, first order logic with modular counting quantifiers. For sum-like
operations it is CMSOL, the corresponding monadic second order logic. We
discuss whether there are maximal logics satisfying Feferman-Vaught Theorems
for finite structures.Comment: Appeared in YuriFest 2015, held in honor of Yuri Gurevich's 75th
birthday. The final publication is available at Springer via
http://dx.doi.org/10.1007/978-3-319-23534-9_1
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Algebraic specification : syntax, semantics, structure
Algebraic specification is the technique of using algebras to model properties of a system and using axioms to characterize such algebras. Algebraic specification comprises two aspects: the underlying logic used in the axioms and algebras, and the use of a small, general set of operators to build specifications in a structured manner. We describe these two aspects using the unifying notion of institutions. An institution is an abstraction of a logical system, describing the vocabulary, the kinds of axioms, the kinds of algebras, and the relation between them. Using institutions, one can define general structuring operators which are independent of the underlying logic. In this paper, we survey the different kind of logics, syntax, semantics, and structuring operators that have been used in algebraic specification