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. 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,
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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 WebDec 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. ninyo and moore colorado
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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 … 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 ... 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 … ninyo and moore testing