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Logic seminar

usually takes place each Monday at 16:00 in IM, rear building, ground floor
Chair: Pavel Pudlak, Neil Thapen, Jan Krajíček
More information on the old seminar web page. The programme is announced via the mailing list.

Automating Resolution Is NP-Hard

Albert Atserias
Universitat Politècnica de Catalunya
Monday, 25. November 2019 - 13:30 to 15:00
We show that the problem of finding a Resolution refutation that is at most polynomially longer than a shortest one is NP-hard. In the parlance of proof complexity, Resolution is not automatizable unless P = NP. Indeed, we show that it is NP-hard to distinguish between formulas that have Resolution refutations of polynomial length and those that do not have subexponential length refutations. This also implies that Resolution is not automatizable in subexponential time or quasi-polynomial time unless NP is included in SUBEXP or QP, respectively.

This is joint work with Moritz Müller

Systems of second order arithmetic and well-ordering principles

Fedor Pakhomov
Institute of Mathematics
Monday, 18. November 2019 - 13:30 to 15:00
In the present talk I'll give a brief introduction to systems of second-order arithmetic and the study of their proof-theoretic ordinals. Further the focus will be on well-ordering principles and the approach to ordinal analysis based on functorial ordinal notation systems.

Forcing with partial structures

Moritz Müller
Universitat Politècnica de Catalunya
Wednesday, 13. November 2019 - 14:00 to 15:30
Define a finitary combinatorial principle to be a first-order sentence which is valid in the finite but falsifiable in the infinite. We aim to compare the strength of such principles over bounded arithmetics. We distinguish “weak” and “strong” principles based on their behaviour with respect to finite structures that are only partially defined. We show that over relativized T^1_2 “weak” principles do not imply “strong” ones. The proof applies a general forcing method to produce models of relativized T^1_2.

The symmetric calculus and monotone interpolation, Part 2

Pavel Pudlák
Institute of Mathematics
Monday, 11. November 2019 - 13:30 to 15:00
In this talk I will say a little bit more about the topic that I presented this spring. First I will ask and explain the problem whether the symmetric calculus simulates Frege systems. Then I show how one can strengthen the characterization of the canonical and interpolation pairs. The result can be viewed as monotone interpolation by certain generalizations of monotone Boolean circuits, called bounded depth game schemas. I will also show simulations of point-line game schemas by depth-2 games and vice versa.