Equational theories

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August undefined, 2024

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 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 …

Equational logic - Encyclopedia of Mathematics

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 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 … thick blood called

An Introduction to Equations and Equational Theories …

WebApr 10, 2006 · The extension is intended to handle equational theories which can be split into two parts, R and T, such that each equation m R can be construed as a reduction and T represents an equational ... WebFeb 11, 2024 · This can be particularly useful for specializing an overly general equational theory E whose operators may obey complex combinations of associativity, commutativity, and/or identity axioms, when being plugged into a host rewrite theory R as happens, for instance, in protocol analysis, where sophisticated equational theories for cryptography … 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 thick blood causes heart attack \u0026 stroke

Equational logic - Wikipedia

http://mathcs.chapman.edu/~jipsen/talks/BLAST2009/JipsenUAtutorial4pp.pdf saginaw school district texasWebA 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. saginaw school district michigan

"WebExamples of equational theories and varieties A binar is an algebra (A,·) with one binary operation x ·y, written xy A semigroup is an associative binar, i.e. satisﬁes (xy)z = x(yz) A band is an idempotent semigroup, i.e. satisﬁes xx = x A semilattice is a commutative band, i.e. satisﬁes xy = yx " - Equational theories

Equational theories

EQUATIONAL BASES FOR LATTICE THEORIES - JSTOR

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. 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.

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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 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.

WebFind many great new & used options and get the best deals for Equational Compactness in Rings: With Applications to the Theory of Topological at the best online prices at eBay! Free shipping for many products! 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

WebIn algebra, the theory of equations is the study of algebraic equations (also called "polynomial equations"), which are equations defined by a polynomial. The main … Weba 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.

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

WebIt 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 … thick blood causing strokesWebat in mathematics. While equational theories are related to stable theories, which is a very important notion in model theory, we wish our discussion to be more or less independent … saginaw river watershed mapWebApr 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, … thick blood causes sypmtomsWebJan 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 … thick blood cause blood clotsWebA 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 ... thick blood causes high blood pressureWebJan 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. thick blood clotsWebMar 6, 2024 · The development of simple and complete equational theories for expressive quantum circuit models opens new avenues for reasoning about quantum circuits. It … thick blood clots during pregnancy