CS 358. Lecture Topics and Suggested Reading

Spring 1995

• Apr 5. Introduction to Linear Logic. Here are some general references available electronically:
• P. Lincoln's SIGACT News column on linear logic,
• A. Scedrov's Brief Guide to Linear Logic and
• A. Scedrov's Marktoberdorf Summer School Notes on Linear Logic .
• Apr 10-12. Basic proof theory: sequent calculus and cut-elimination for classical and intuitionistic logic. Introduction to proof system for linear logic.
• Handout based in part on Girard et al., Proofs and Types.
• Recommended additional reading: Chapters 2 and 5 of Proofs and Types.
• Apr 17. Lecture canceled.
• Apr 19. Intuitive explanation of connectives of linear logic. Decision Problems.
• Handout on sequent calculus for linear logic.
• Draft reading list for future topics.
• Apr 24. (Lecture by Andre Scedrov) Overview of decision problems, permutability of rules in cut-free proofs, NP-completeness of multiplicative fragment with no propositional variables. (Proof due to Lincoln and Winkler; slides distributed Apr 26). Exercises.
• Apr 26. Phase semantics. Handout with exercises.
• May 1. Undecidability of full propositional linear logic. (Presentation by P. Lincoln, based on LMSS. ) Undecidability of second-order linear logic without exponentials using phase spaces. (Based on Lafont undecidability paper; see also Lafont and Scedrov. )
• May 3. Introduction to games. Reference: Blass, Is game semantics necessary?
• May 8-15. Continue discussion of Blass article; cover main topics from Abramsky and Jagadeesan, Games and full completeness for multiplicative linear logic.
• May 15-17. Proof games and relation to stochastic complexity classes. Reference: Lincoln, Mitchell and Scedrov, Stochastic interaction and linear logic.
• May 22. Linear lambda calculus. Handout. References: Abramsky, Computational interpretation of linear logic. Lincoln and Mitchell, Operational aspects of linear lambda calculus.
• May 24. Plan: Francois Guimbretiere, report on proof nets. Continue/complete discussion of linear lambda calculus.
• May 29. Memorial Day. No meeting.
• May 31. Report 1. Oliver Duschka, coherent spaces. Report 2. Vitaly Shmatikov, fair games. Reference: Hyland and Ong, Full completeness ...
• June 5. Plan: Proof games that are hard to even come close to winning.
• June 7. Plan: Reports: Kathleen Fisher and Julie Zelenski, Dialogue games, Pi-calculus and PCF. Reference: Reference: Hyland and Ong, Dialogue games ...