# New perspectives on residuated posets

The project is funded under the following programmes:

"The Project I 1923-N25" by FWF -
The Austrian Science Fund,

"The Project 15-34697L" by GAČR -
The Czech Science Foundation.

## Abstract

Residuated posets are important algebraic structures in
various disciplines, including logic and mathematics. For instance, they are
key structures for non-classical logics such as intuitionistic, linear,
many-valued, and substructural logics as well as for ring theory. Nevertheless,
with the exception of particular subclasses, the systematic description of the
structure of these partially ordered algebras has remained until now an
unsolved challenge.

This project aims at a substantial progress in the theory of residuated posets;
we intend to enlarge the presently quite limited class of those subclasses
whose structure is known in detail. To know the structure of residuated posets
as precisely as, e.g., in the case of MV- or BL-algebras would be important for
a number of long-standing problems on the side of logic. We have in mind, e.g.,
the complexity problem for the logic MTL.

Our strategy will be to take up a number of promising approaches that were
recently defined. New results exist on the extension of totally ordered
monoids, on the description of finite linearly ordered MTL-algebras, or on the
structure of pseudo-BCK algebras, to mention just a few lines of new research.
The plan is to develop these approaches further and to examine in which way
they can mutually benefit. The competences with respect to the various
approaches are spread between several working groups; to bundle these
competences is the intention of the project.