Fuzzy Topological Systems

Dialectica categories are a very versatile categorical model of linear logic. These have been used to model many seemingly different things (e.g., Petri nets and Lambek's calculus). In this note, we expand our previous work on fuzzy petri nets to deal with fuzzy topological systems. One basic idea is to use as the dualizing object in the Dialectica categories construction, the unit real interval [0,1], which has all the properties of a {\em lineale}. The second basic idea is to generalize Vickers's notion of a topological system.