Equational theories

Author: djqu

August undefined, 2024

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.

Characterizing the Equational Theory - Cornell University

Webtheorems for equational theories P. D. Bacsich 45 We classify a family of 216 interpolation principles for formulas in equational theories and show that those in a natural subfamily … WebEquational logic is a fragment of first-order logic. It constitutes that part which deals exclusively with sentences in the form of identities--theuniversal closure of equalities between terms--andthe classes of structures defined by'iden- tities. Equational logic plays a special role in the metamathe- matics of algebra since lapsi ja sota

[2303.03117] Simple Complete Equational Theories for …

WebA novel approach is described for the combination of unification algorithms for two equational theories E 1 and E 2 which share function symbols. We are able to identify a set of restrictions and a combination method such that if the restrictions are satisfied the method produces a unification algorithm for the union of non-disjoint equational theories. WebEquational 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 … WebThe equational theories of lattices — or more briefly, lattice theories — are the theories containing these six equations. Thus the smallest lattice theory is the theory A, which … asta kiel ulrike

EQUATIONAL BASES FOR LATTICE THEORIES - JSTOR

Equational Compactness in Rings: With Applications to the Theory …

WebFeb 14, 2024 · In his 1963 doctoral dissertation, Bill Lawvere introduced a new categorical method for doing universal algebra, alternative to the usual way of presenting an algebraic concept by means of its logical signature (with generating operations satisfying equational axioms). 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 … lapsikeskeinenWebIt 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 … asta kneipe

"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 … " - Equational theories

Equational theories

[2302.04402] Cartesian closed varieties I: the classification theorem

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... 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,

Did you know?

WebThe Cambridge mathematician Edward Waring published treatises in 1762 and 1770 on the theory of equations. In 1770 Lagrange presented a long expository memoir on the … WebAug 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 …

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. 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 …

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. http://mathcs.chapman.edu/~jipsen/talks/BLAST2009/JipsenUAtutorial4pp.pdf

WebIn category theory, a Lawvere theory (named after American mathematician William Lawvere) is a category that can be considered a categorical counterpart of the notion of an equational theory . Definition [ edit] Let be a skeleton of the category FinSet of …

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. asta kovaliovaWebJan 4, 2024 · This allows for equational reasoning about the class of models defined by a partial theory. We demonstrate the expressivity of such equational theories by considering a number of examples, including partial combinatory … asta kpopWeba 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 … lapsikorotus ansiopäivärahaWebEquational 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 … lapsikirjaWebA 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 ... lapsi ja tvWebJan 11, 2024 · We develop theories of abstract and term-based systems, refining cornerstone results of rewriting theory (such as Newman’s Lemma, Church-Rosser Theorem, and critical pair-like lemmas) to a metric and quantitative setting. lapsikeskeisen kasvatuksen ydinkysymyksiäWebDecision 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 astaksantinas kaina