6 papers · 1 filter
Duality for finitely valued algebras
Marco Abbadini, Adam Přenosil
The theory of natural dualities provides a well-developed framework for studying Stone-like dualities induced by an algebra which acts as a dualizing object when equip…
Nagata products of bimodules over residuated lattices
Adam Přenosil, Constantine Tsinakis
We study the (restricted) Nagata product construction, which produces a partially ordered semigroup from a bimodule consisting of a partially ordered semigroup acting on a (pointed…
Equivalence of multiset-based consequence relations
Ali Madanshekaf, Adam Přenosil, Zeinab Khanjanzadeh Seresti +1
The pioneering work of Blok and Jónsson and its further development by Galatos and Tsinakis initiated an abstract study of consequence relations using the tools of module theory, w…
Equational definitions of logical filters
Michele Pra Baldi, Adam Přenosil
A finitary propositional logic can be given an algebraic reading in two different ways: by translating formulas into equations and logical rules into quasi-equations, or by transla…
The lattice of super-Belnap logics
Adam Přenosil
We study the lattice of extensions of four-valued Belnap--Dunn logic, called super-Belnap logics by analogy with superintuitionistic logics. We describe the global structure of thi…
Semisimplicity, Glivenko theorems, and the excluded middle
Tomáš Lávička, Adam Přenosil
We formulate a general, signature-independent form of the law of the excluded middle and prove that a logic is semisimple if and only if it enjoys this law, provided that it satisf…