Lattices and ordered sets play an important role in many areas of computer science. These range from lattices as models for logics, which are fundamental to understanding computation, to the ordered sets as models for computation, to the role both lattices and ordered sets play in combinatorics, a fundamental aspect of computation. In addition, many applications utilize lattices and ordered sets in fundamental ways. These include such areas as knowledge representation, text categorization and data mining, where order plays a fundamental organizing principle, to the use of lattices and ordered sets to analyze crypto-protocols in security, to inductive logic programming, where ordered sets form basic models. A number of more esoteric structures, such as Kleene algebras and quantales, also feature in recent advances to understanding computation. This workshop will bring researchers from the many areas which rely on lattices and ordered sets together with those doing research in these and related structures, in order to accomplish two goals:
1) to survey the many areas of computation where lattices and ordered sets play a role in order to better understand the problems common across these areas, and
2) to enhance the interactions between researchers in the areas of lattice theory and ordered sets, and those who utilize these structures in modeling computation and in areas of application.
It is expected that researchers in lattice theory and ordered sets will benefit by discovering new and interesting problems where their expertise can be applied, and those who work on applications will have a chance to learn of new advances in these areas that could be applied to problems where lattice theory and ordered sets traditionally have played an important role. In addition to these goals, the intention also is to present talks which are accessible to the broader public that will help those working in related areas to understand the role lattice theory and ordered sets play in theoretical computation and its applications.
The workshop will feature several plenary lectures, whose goal will be to give a broad background to the workshop, These lectures will be complimented by several shorter talks that focus on particular areas of application, as well as on recent advances in lattice theory and ordered sets. The talks by leaders in lattice theory and ordered sets will focus on applications to computer science, while the talks by leading researchers in these areas will describe how techniques from lattice theory and ordered sets have recently led to results and applications to problems in computation.