Logics of variable inclusion

0508286 - ÚI 2020 AT eng A - Abstract
Bonzio, S. - Moraschini, Tommaso - Pra Baldi, M.
Logics of variable inclusion.
SYSMICS 2018. Second Workshop - Contributions. Vienna: University of Vienna, 2018.
[SYSMICS 2018: Workshop. Substructural logics: semantics, proof theory, and applications. /2./. 26.02.2018-28.02.2018, Vienna]
Institutional support: RVO:67985807
https://sysmics.logic.at/accepted/_left/SYSMICS-W2_abstract_8.pdf

A variety of algebras K is called strongly irregular whenever it satisfies an identity of the kind f(x, y) ≈ x, where f(x, y) is any term of the language in which x and y really occur. On the other hand, an identity ϕ ≈ ψ is said to be regular provided that exactly the same variables occur in ϕ and ψ. A variety is regular, when it is defined by regular identities. Examples of (strongly) irregular varieties abound in logic, since every variety with a lattice reduct is (strongly) irregular as witnessed by the term f(x, y) := x ∧ (y ∨ x). The algebraic study of regular varieties traces back to the pioneering work of P lonka [7], who introduced a classoperator Pl(·) nowadays called P lonka sums, and used it to prove that any regular variety K can be represented as P lonka sums of a suitable strongly irregular variety V, in symbols Pl(V) = K. In this case K is called the regularization of V.
Permanent Link: http://hdl.handle.net/11104/0299240