Generalized ordinal sums and translations

Generalized ordinal sums and translations

We extend the lattice embedding of the axiomatic extensions of the positive fragment of intuitionistic logic into the axiomatic extensions of intuitionistic logic to the setting of substructural logics. Our approach is algebraic and uses residuated lattices, the algebraic models for substructural logics. We generalize the notion of the ordinal sum of two residuated lattices and use it to obtain...

Generalized Ordinal Sums and the Decidability of Bl-chains

We present a general construction of a family of ordinal sums of a sequence of structures and prove an elimination theorem for the class of ordinal sums in an expanded language. From this we deduce the decidability of the class of Σ-ordinal sums of models of a decidable theory T . As an application of this result we prove that the theory of BL-chains is decidable.

Partially Ordinal Sums and P-partitions

We present a method of computing the generating function fP (x) of P -partitions of a poset P . The idea is to introduce two kinds of transformations on posets and compute fP (x) by recursively applying these transformations. As an application, we consider the partially ordinal sum Pn of n copies of a given poset, which generalizes both the direct sum and the ordinal sum. We show that the seque...

Generating Fuzzy Implications by Ordinal Sums

This paper deals with ordinal sums of fuzzy implications. Some of the known constructions are recalled and new ways of generating fuzzy implications from given ones are proposed. Sufficient properties of fuzzy implications as summands for obtaining a fuzzy implication as a result are presented.

Refinement equations for generalized translations