Equational theories
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 ... 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...
Equational theories
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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. WebJun 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 …
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 … 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 …
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 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 …
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.
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, … organophosphate medicationWebat 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 … organophosphate mechanismWebExamples 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 how to use slack videoWebA 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’. how to use slam storage ultrakillWebRewrite 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 how to use slack in ms projectWebDec 24, 2024 · We demonstrate how to prove decidability of various algebraic theories in the literature. It includes the equational theories of monad and λ-calculi, Plotkin and Power’s theory of states and bits, and Stark’s theory of π-calculus. We also demonstrate how this methodology can solve the coherence of monoidal categories. organophosphate moaWebEquational 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 … how to use slam on more games