Results

**1 - 1**of**1**### A New Category for Semantics

"... now is to use this idea as a unifying platform for semantics and reasoning. Our small group of faculty and students at Carnegie Mellon, namely Steven Awodey, Andrej Bauer, Lars Birkedal, and Jesse Hughes, has begun work on this program. A selection of our theses and papers is listed in the bibliogra ..."

Abstract
- Add to MetaCart

now is to use this idea as a unifying platform for semantics and reasoning. Our small group of faculty and students at Carnegie Mellon, namely Steven Awodey, Andrej Bauer, Lars Birkedal, and Jesse Hughes, has begun work on this program. A selection of our theses and papers is listed in the bibliography. Equilogical Spaces Note: We build on the known cartesian closed category CLat of continuous lattices and continuous maps. Types: Pairs X = (hXi; X ), where hXi is a continuous lattice and is a partial equivalence relation on hXi. We set jXj = fx j x xg. A type is also called an equilogical space. Equivalence Classes: [x] = fx j x g, and kXk = f[x] X j x 2 jXjg, which we regard as a topological space with the quotient topology inherited from the subspace jXj of hXi. Theorem: Each continuous lattice can be regarded as an equilogical space X where jXj = hXi and each [x] = fxg. Some Flat Lattices: We set L n = f?; 0; 1; : : : ; n 1; >g and 1 = f?; 0; 1;