منابع مشابه
Morita equivalence of many-sorted algebraic theories
Algebraic theories are called Morita equivalent provided that the corresponding varieties of algebras are equivalent. Generalizing Dukarm’s result from one-sorted theories to many-sorted ones, we prove that all theories Morita equivalent to an S-sorted theory T are obtained as idempotent modifications of T . This is analogous to the classical result of Morita that all rings Morita equivalent to...
متن کاملMore on the Lattice of Many Sorted Equivalence Relations
(4) ⊥EqRelLatt(M) = idM. (5) >EqRelLatt(M) = [[M,M]]. (6) Every subset of EqRelLatt(M) is a family of many sorted subsets indexed by [[M,M]]. (7) Let a, b be elements of EqRelLatt(M) and A, B be equivalence relations of M. If a = A and b = B, then av b iff A⊆ B. (8) Let X be a subset of EqRelLatt(M) and X1 be a family of many sorted subsets indexed by [[M,M]]. Suppose X1 = X . Let a, b be equiv...
متن کاملOn the Trivial Many Sorted Algebras and Many Sorted Congruences
In this paper a, I denote sets and S denotes a non empty non void many sorted signature. The scheme MSSExD deals with a non empty set A and a binary predicate P , and states that: There exists a many sorted set f indexed by A such that for every element i of A holds P [i, f (i)] provided the following condition is met: • For every element i of A there exists a set j such that P [i, j]. Let I be...
متن کاملMany - Sorted Natural Semantics
We present an extension of natural semantics which can be used to describe the static semantics of imperative and object-oriented programming languages. Furthermore we show that the semantic analysis can be generated from these descriptions. As a side eeect, we get a precise deenition of which properties of a programming language are statically decidable and which properties can only be checked...
متن کاملConnecting Many-Sorted Theories
Basically, the connection of two many-sorted theories is obtained by taking their disjoint union, and then connecting the two parts through connection functions that must behave like homomorphisms on the shared signature. We determine conditions under which decidability of the validity of universal formulae in the component theories transfers to their connection. In addition, we consider varian...
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 1988
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1093638017