Penn Logic and Computation Seminar 2021-2022
Logic and Computation Group
is composed of faculty and graduate students from the
Computer and Information Science,
departments, and participates in the
Institute for Research in the Cognitive Sciences.
The Logic and Computation group runs a weekly seminar.
The seminar is open to the public and all are welcome.
The seminar meets regularly during the school year
on Tuesdays at 2:00 p.m. online. Contact Henry Towsner for the link.
Any changes to this venue or schedule will be specifically noted.
Some upcoming talks:
- Nov 15: Revantha Ramanayake
- Oct 18: Denis Hirschfeldt
- Oct 11: Elaine Pimentel
University of California, Berkeley
Tuesday, October 4, 2022, online
Subsystems of classical logic and their semantics based on graphs
The starting points of my talk are two of the most important subsystems of classical logic arising in the foundations of mathematics and foundations of physics: intuitionistic logic (Heyting 1930) and orthologic (Birkhoff and von Neumann 1936). In a Fitch-style formulation of natural deduction, intuitionistic logic and orthologic can be obtained from a more basic logic, defined using only the introduction and elimination rules for the logical connectives, by the addition of rules of Reiteration and Reductio ad Absurdum, respectively. In this talk (based on https://arxiv.org/abs/2207.06993), I will characterize this "fundamental" logic both proof-theoretically and semantically. The semantic characterization is based on representation theorems for complete lattices with additional operations (e.g., negation, implication) using directed graphs.