A Roadmap of Some Two-Dimensional Logics
Vaughan Pratt · The MIT Press eBooks · 1994
We define the notion of two-dimensional logic and diagram the relative locations of a number of such. This work was supported by the National Science Foundation under grant number CCR-8814921 and a grant from Mitsubishi. 1 Background The theme of this note is logics with more or less independent disjunction and conjunction. At JELIA'90 I described one such logic, action logic, a single-sorted finitely based equational conservative extension of the equational logic of regular expressions, with the language part of the extension consisting of new operations preimplication A!B (had A then B) and postimplication B/A (B if-ever A) [Pra90a]. The organizers of the present conference requested that I talk again on action logic. Although I had nothing new to report on this subject it seemed to me that a walk around the neighborhood of action logic should be of some interest. Action logic being what I called a two-dimensional logic, a natural selection of neighbors would be the various two-dime...