5 papers
Conuclei on varieties of hoops
Sebastián Buss, Diego Castaño, José Patricio Díaz Varela
A conucleus on a partially ordered monoid is an interior operator that satisfies and for all $a,b \in…
Terms that define nuclei on residuated lattices: a case study of BL-algebras
Sebastián Buss, Diego Castaño, José Patricio Díaz Varela
A nucleus on a (bounded commutative integral) residuated lattice is a closure operator that satisfies the inequality for all $a…
The algebraic semantics for the one-variable monadic fragment of the predicate logic
Diego Castaño, Valeria Castaño, José Patricio Díaz Varela +1
In this article we characterize the equivalent algebraic semantics for the one-variable monadic fragment of the first-order logic defined by F. Esteva, L.…
Strong completeness for the predicate logic of the continuous t-norms
Diego Castaño, José Patricio Díaz Varela, Gabriel Savoy
The axiomatic system introduced by Hájek axiomatizes first-order logic based on BL-chains. In this study, we extend this system with the axiom $(\forall x ϕ)^2 \leftrightarrow \for…
Strong standard completeness theorems for S5-modal Lukasiewicz logics
Diego Castaño, José Patricio Díaz Varela, Gabriel Savoy
We study the S5-modal expansion of the logic based on the Lukasiewicz t-norm. We exhibit a finitary propositional calculus and show that it is finitely strongly complete with respe…