## This Week in Logic at CUNY

Rutgers Logic Seminar

Monday September 16, 3:30pm, Rutgers University, Hill Center, Hill 705

Maxwell Levine, University of Freiburg

Namba Forcing, Minimality, and Approximations

Logic and Metaphysics Workshop

Date: Monday,September 16, 4.15-6.15pm (NY time)

Room: Graduate Center Room 4419

Speaker: Mel Fitting (CUNY)

Title: Simple tableaus for simple logics

Abstract: Consider those many-valued logic models in which the truth values are a lattice that supplies interpretations for the logical connectives of conjunction and disjunction, and which has a De Morgan involution supplying an interpretation for negation. Assume the set of designated truth values is a prime filter in the lattice. Each of these structures determines a simple many-valued logic. We show there is a single Smullyan style signed tableau system appropriate for all of the logics these structures determine. Differences between the logics are confined entirely to tableau branch closure rules. Completeness, soundness, and interpolation can be proved in a uniform way for all cases. Since branch closure rules have a limited number of variations, in fact all the semantic structures determine just four different logics, all well-known ones. Asymmetric logics such as strict/tolerant, ST, also share all the same tableau rules, but differ in what constitutes an initial tableau. It is also possible to capture the notion of anti-validity using the same set of tableau rules. Thus a simple set of tableau rules serves as a unifying and classifying device for a natural and simple family of many-valued logics.

- - - - Tuesday, Sep 17, 2024 - - - -

- - - - Wednesday, Sep 18, 2024 - - - -

The New York City Category Theory Seminar

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

Date and Time: Wednesday September 18, 2024, 7:00 - 8:30 PM. IN-PERSON TALK, Room 6417

- - - - Friday, Sep 20, 2024 - - - -

- - - - Monday, Sep 23, 2024 - - - -

Rutgers Logic Seminar

Monday September 9, 3:30pm, Rutgers University, Hill Center, Hill 705

Countable reductions in computable structure theory

Logic and Metaphysics Workshop

Date: Monday,September 23, 4.15-6.15pm (NY time)

Room: Graduate Center Room 4419

Title: Value and freedom

Abstract: In order to decide how good a society is, we need some measure of goodness. And the goodness of a society is typically obtained by somehow summing up the well beings of its members. Various approaches include Utilitarianism and Rawlsianism as well as the Leximin approach suggested by Amartya Sen. But Sen and Nussbaum have suggested that the Capability of an individual, what the individual can do, should be the real measure of well being. Another issue is that of freedom. My freedom can be diminished by some restrictive laws. But it can also be diminished by some handicap, or by certain social methods not being available. How to measure the amount of freedom I have? Is it simply the number of options I have, or does the value of the options also matter? And what is the mathematics of freedom?

Note: An extended abstract is available here.

- - - - Tuesday, Sep 24, 2024 - - - -

- - - - Wednesday, Sep 25, 2024 - - - -

The New York City Category Theory Seminar

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

Date and Time: Wednesday September 25, 2024, 7:00 - 8:30 PM. IN-PERSON TALK, Room 6417

**Noah Chrein, University of Maryland**

Title:** A formal category theory for oo-T-multicategories.**

Abstract: We will explore a framework for oo-T-multicategories. To begin, we build a schema for multicategories out of the simplex schema and the monoid schema. The multicategory schema, D_m, inherits the structure of a monad from the +1 monad on the monoid schema. Simplicial T-multicategories are monad preserving functors out of the multicategory schema, [D_m, T], into another monad T. The framework is larger than just [D_m,T]. A larger structure describes notions of yoneda lemma and fibration. Inner fibrant, simplicial T-multicategories are oo-T-multicategories. oo-T-multicategories generalize oo-categories and oo-operads: oo-operads are fm-multicategories, oo-categories are Id-multicategories.

We use this framework to study oo-fc-multicategories, or "oo - virtual double categories". In general, under various assumptions on T (which hold for fc), the collection of oo-T-multicategories [D_m, T] has other useful structure. One such structure is a join operation. This join operation points towards a synthetic definition of op/cartesian cells, which we hope will model oo-virtual equipments. If there is time, I will explain the motivation for this study as it relates to ontologies, meta-theories and type theories.

- - - - Thursday, Sep 26, 2024 - - - -

- - - - Friday, Sep 27, 2024 - - - -

CUNY Graduate Center

Friday September 27, 2:00pm-3:30pm, Room 4419

- - - - Other Logic News - - - -

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