Axiomatizability of algebras of binary relations
نویسنده
چکیده
Let Λ be a signature and A = (A, Λ) be an algebra. We say that A is an algebra of binary relations if A ⊆ P(U × U) for some set U and each operation in Λ is interpreted as a natural operation on relations. 0 is the empty set. Other possible operations include reexive-transitive closure * , the residuals \ and / of composition, domain d and range r, etc. Algebras of binary relations Let Λ be a signature and A = (A, Λ) be an algebra. We say that A is an algebra of binary relations if A ⊆ P(U × U) for some set U and each operation in Λ is interpreted as a natural operation on relations. 0 is the empty set. Other possible operations include reexive-transitive closure * , the residuals \ and / of composition, domain d and range r, etc. Algebras of binary relations Let Λ be a signature and A = (A, Λ) be an algebra. We say that A is an algebra of binary relations if A ⊆ P(U × U) for some set U and each operation in Λ is interpreted as a natural operation on relations. 0 is the empty set. Other possible operations include reexive-transitive closure * , the residuals \ and / of composition, domain d and range r, etc. We denote the class of algebras of binary relations of the signature Λ by R(Λ). The quasivariety and the variety generated by R(Λ) are denoted by Q(τ) and V(Λ). The class of relational Kleene algebras is The question For which Λ is the (quasi)equational theory of R(Λ) nitely axiomatizable? We denote the class of algebras of binary relations of the signature Λ by R(Λ). The quasivariety and the variety generated by R(Λ) are denoted by Q(τ) and V(Λ). The class of relational Kleene algebras is
منابع مشابه
Residuated Algebras of Binary Relations and Positive Fragments of Relevance Logic
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