Equational theories

Author: tkka

August undefined, 2024

WebJul 15, 2024 · Equationality is a strengthening of stability. We show the equationality of the theory of proper extensions of algebraically closed fields and of the theory of separably … WebA partial Horn theory (S,Σ,T) is called an equational theory if • Σ contains no relation symbol, • every function symbol fin Σ is total, i.e., the sequent ⊤ ~x f(~x)↓ is a PHL-theorem of T, and • Tconsists of equations, i.e., every sequent in Thas the expression ⊤ ~x ϕ. Given an equational theory T, we will denote the category T ...

[0904.4756] Models and theories of lambda calculus - arXiv.org

WebJun 9, 2015 · Specifically, it is shown that the equational theory of an unstable involution semigroup is not finitely axiomatizable whenever the equational theory of its semigroup reduct satisfies the same property. Consequently, many results on equational properties of semigroups can be converted into results applicable to involution semigroups. WebDecision Problems for Equational Theories of Relation Algebras - H. Andréka 1997 This work presents a systematic study of decision problems for equational theories of algebras of binary relations (relation algebras). For example, an easily applicable but deep method, based on von Neumann's coordinatization theorem, is developed for establishing chris levingston orange

Minimum bases for equational theories of groups and rings: …

WebFeb 9, 2024 · We improve on Johnstone's result by showing that an equational theory is cartesian closed just when its operations have a unique hyperaffine-unary decomposition. It follows that any non-degenerate cartesian closed variety is a variety of sets equipped with compatible actions by a monoid M and a Boolean algebra B; these are the titular [B M]-sets. WebThe equational theory of A is the set of equations that hold in A. The equational theory of A is denoted E(A). Theorem 4.1 The following classes of algebras all have the same equational theory: Kleene algebras, star-continuous Kleene algebras, closed semirings, S-algebras, N-algebras, R-algebras, WebRewrite Theories in General (IV) This leads to the following general deﬁnition of a rewrite theory on membership equational logic: A rewrite theory is a 4-tuple, R= (Σ,E,φ,R), where: •(Σ,E) is a membership equational theory, with, say, kinds K, sorts S, and operations Σ •φ : Σ −→P fin(IN) is a K∗ ×K-indexed family of functions chris levy

EQUATIONAL THEORIES OF FIELDS - Cambridge Core

Equational Theories and Monads from Polynomial Cayley

WebEquational logic was developed over the years (beginning in the early 1980s) by researchers in the formal development of programs, who felt a need for an … WebThese theorems require only loose, abstract conditions on the equational theory for messages. They subsume previous results for a syntactically defined class of theories that allows basic equations for functions such as encryption, decryption, and digital signatures. chris levy sacramentoWebJun 19, 2024 · The study of equational theories of \(UT_n(\mathbb {S})\) and its subsemigroups has attracted much attention. The semigroup \(UT_{n}(\mathbb {B})\) is … geoff culbertson

"http://mathcs.chapman.edu/~jipsen/talks/BLAST2009/JipsenUAtutorial4pp.pdf " - Equational theories

Equational theories

Equational Theory - an overview ScienceDirect Topics

WebApr 5, 2024 · The equational theories that we generate in Sect. 4 are multi-sorted, which is useful for trimming down the combinatorial complexity of the result. This turns out to be, in our view, essential in understanding what computational effects they actually represent. WebJul 5, 2014 · That is, operations on processes are defined, and their equational laws are investigated. In other words, methods and techniques of universal algebra are used (see …

Did you know?

WebJul 1, 2024 · Equational logic generalizes in a similar way. For example, a module over a ring is a two-sorted algebra with two universes, an Abelian group and a ring, and …

WebThis work presents a narrowing calculus for reachability problems in order-sorted conditional rewrite theories whose underlying equational logic is composed of some theories solvable via a... WebApr 30, 2009 · Models and theories of lambda calculus. In this paper we briefly summarize the contents of Manzonetto's PhD thesis which concerns denotational semantics and equational/order theories of the pure untyped lambda-calculus. The main research achievements include: (i) a general construction of lambda-models from reflexive objects …

WebApr 5, 2024 · The equational theories that we generate in Sect. 4 are multi-sorted, which is useful for trimming down the combinatorial complexity of the result. This turns out to be, … Webequational theories of K (the dual of the lattice of sub-quasivarieties of K) is isomorphic to Con(S;+;0;F). It is known that if S is a join semilattice with 0 (and no operators), then there is a quasivariety Q such that the lattice of theories of Q is isomorphic to Con(S;+;0). We prove that if S is a semilattice having both 0 and 1 with a group G

WebThis work presents a systematic study of decision problems for equational theories of algebras of binary relations (relation algebras). For example, an easily applicable but deep method, based on von Neumann's coordinatization theorem, is developed for establishing undecidability results. The method is used to solve several outstanding problems ...

WebThe theory of equations. Another subject that was transformed in the 19th century was the theory of equations. Ever since Niccolò Tartaglia and Lodovico Ferrari in the 16th … geoff culbert redmondWeball members of A. The equational theory of A is the set of equations that hold in A. The equational theory of A is denoted E(A). Theorem 4.1 The following classes of algebras … geoff culbertson texarkanaWebIt is important to distinguish the invariant notion of Lawvere theory from the notion of equational theory. Equational theories are a form of presentation for Lawvere theories … geoff cullenWebAug 27, 2024 · Theorem 10.1. Let 〈 S, ⋆ 〉 be any twisted involution semigroup. Suppose that the reduct S is non-finitely based. Then 〈 S, ⋆ 〉 is non-finitely based. In Sect. 10.1, each twisted involution semigroup is shown to possess some … geoff cullwick lawyerWeba single sentence. Because equational logic lacks connectives, many ﬁnitely based equational theories fail to be based a just a single equation. For an equational theory T we let µT be the least among all cardinals κ so that T has a base of cardinality κ. This parameter µT oﬀers a means to diﬀerentiate among equational theories. chris levy in hammond laWebA quasi-equational theory over a signature is then a set of implications (the axioms of T) of the form ’) , with ’; 2Horn() (see [6]). The operation symbols of a quasi-equational theory are only required to be partially de ned. If t is a term, we write t #as an abbreviation for t = t, meaning ‘t is de ned’. chris levy height 2023WebEquational theories Definition (Equational theory) Given a class K of algebras of signature ˆ we say refer to a set of equations of the form Id(K) := fϵ j (8A 2 K)(A j= ϵ)g as … chris levy \u0026 associates