Equational Logic and Categorical Semantics for Multi-Languages
نویسندگان
چکیده
منابع مشابه
Categorical Abstract Algebraic Logic: Categorical Algebraization of Equational Logic
This paper deals with the algebraization of multi-signature equational logic in the context of the modern theory of categorical abstract algebraic logic. Two are the novelties compared to traditional treatments: First, interpretations between different algebraic types are handled in the object language rather than the metalanguage. Second, rather than constructing the type of the algebraizing c...
متن کاملA 2-categorical framework for the syntax and semantics of many-sorted equational logic
Received 30 January 2008; revised 7 July 2008 In memory of Professor Tsuyoshi Fujiwara (1923–2006) Primary: 03C05, 03F25, 08A68, 08A40, 18A23, 18C10, 18D05; Secondary: 03C95, 68Q65.
متن کاملCategorical Abstract Algebraic Logic: Ordered Equational Logic and Algebraizable PoVarieties
A syntactic apparatus is introduced for the study of the algebraic properties of classes of partially ordered algebraic systems (a.k.a. partially ordered functors (pofunctors)). A Birkhoff-style order HSP theorem and a Mal’cev-style order SLP theorem are proved for partially ordered varieties and partially ordered quasivarieties, respectively, of partially ordered algebraic systems based on thi...
متن کاملCategorical Semantics for Array Programming Languages
Background Consider the usual addition operator between (real or complex) numbers: a, b 7→ a + b This can be straightforwardly extended to give an additive structure on R for any n ∈ N: (a1, . . . , an) + (b1, . . . , bn) := (a1 + b1, . . . , an + bn) Similarly, we can extend our notion of addition to give a canonical way of adding arrays of any shape: (aijk...z) + (bijk...z) := (aijk...z + bij...
متن کاملRelating Categorical Semantics for Intuitionistic Linear Logic
There are several kinds of linear typed calculus in the literature, some with their associated notion of categorical model. Our aim in this paper is to systematise the relationship between three of these linear typed calculi and their models. We point out that mere soundness and completeness of a linear typed calculus with respect to a class of categorical models are not sufficient to identify ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Notes in Theoretical Computer Science
سال: 2020
ISSN: 1571-0661
DOI: 10.1016/j.entcs.2020.09.005