In the theory of lattice-ordered groups, there are interesting examples of properties — such as projectability — that are defined in terms of the overall structure of the lattice-ordered group, but are entirely determined by the underlying lattice structure. In this paper, we explore the extent to which projectability is a lattice-theoretic property for more general classes of algebras of logic...

We focus on some important fuzzy logic algebras on residuated lattices. These interesting algebraic structures and their main properties are reviewed, and their relationships are clarified. Corresponding formal deductive systems for fuzzy logic are

We give the simple general principle of studying the relations among fuzzy t-filters on residuated lattices. Using the general principle, we can easily determine the relations among fuzzy t-filters on different logical algebras.

Action logic is the algebraic (inequational theory) of residuated Kleene lattices. One operations this star, which axiomatized by an induction scheme. For a stronger system that uses -rule instead (infinitary action logic), Buszkowski and Palka (2007) proved $\Pi _1^0$?> -completeness (thus, undecidability). Decidability itself was open question, raised Kozen in 1994. In articl...

The main ‘philosophical’ outcome of this article is to demonstrate that the structural description of residuated lattices requires the use of the co-residuated setting. A construction, called skew symmetrization, which generalizes the well-known representation of an ordered Abelian group obtained from the positive (or negative) cone of the algebra is introduced here. Its definition requires lea...