January 23, 2026
Linear Logic and Pi Calculus: Formal Protocol Theory Discussion
Participants: _vgr, simpalaxy, _ergod, anurajenp, senthil_d1sc0rd, artemishelios, austinjacobs_33961, plague_year, maparent, ediblebadger, mtraven
The SIGFPT group convened to explore linear logic and pi calculus as formal frameworks for protocol theory. Simpalaxy provided preparatory reading materials on linear logic semantics, interaction nets, and their relationships to established logical systems. The discussion touched on foundational concepts including constructivism, Brouwer's intuitionism, and the rejection of excluded middle, establishing that linear logic operates within a purely constructionist paradigm with interesting computational properties. A significant portion of the meeting focused on practical applications, particularly how linear logic and linear types can model real-world systems. The kitchen metaphor for processor behavior emerged as a compelling application area, where concepts like maximizing throughput and speculative execution map naturally onto linear logic operations, with exception handling modeled as time-reversal contradictions. The group also discussed probabilistic reasoning within the formalism and potential connections to industrial protocol questions, suggesting a structured approach moving from atomic protocol questions upward through pi calculus, interaction nets, and linear logic frameworks.
- Linear logic can be understood as a constructionist formalism with graph-reduction/transformation grammars that function like a physics engine for protocol behavior.
- Interaction nets generalize proof structures in linear logic and serve as a bridge between intuitionistic logic and pi calculus, similar to how lambda calculus relates to intuitionistic logic.
- Linear types can effectively express liveness properties and model processor behavior, including speculative execution as exception handling through time-reversal semantics.
- The group identified a potential research direction connecting linear logic/linear types to atomic protocol questions, with connections to temporal logic frameworks (LTL/TLA).