This Week in Logic at CUNY:

– – – – Monday, Sep 5, 2011 – – – –

– – – – Tuesday, Sep 6, 2011 – – – –

Fall Semester 2011,

Computational Logic Seminar

GC Room 3309, 2:00 – 4:00 PM,

September 6, 2011

Speaker: Sergei Artemov (Graduate Center CUNY)

Title: Toward first-order justification logic I.

Abstract: We will study first-order logic of proofs FOLP and outline first-order justification logic. In part I of this talk, we will revisit the Brouwer-Heyting-Kolmogorov semantics as the principal motivation and introduce FOLP in its current “official” form.

Reading: the first three sections of Sergei N. Artemov and Tatiana Yavorskaya (Sidon). First-Order Logic of Proofs. Technical report TR-2011005 of the Ph.D. Program in Computer Science at CUNY Graduate Center.

http://tr.cs.gc.cuny.edu/tr/techreport.php?id=418

– – – – Wednesday, Sep 07, 2011 – – – –

– – – – Thursday, Sep 08, 2011 – – – –

– – – – Friday, Sep 09, 2011 – – – –

Set Theory Seminar

Friday, September 9, 2011 10:00 am GC 6417

Mr. Brent Cody (The Graduate Center of The City University of New York) The Levinski property

Abstract. Levinski showed that given a measurable cardinal kappa there is a forcing extension that preserves the measurability of kappa in which GCH fails at every regular cardinal less than kappa and yet holds at kappa. This is in contrast to the standard fact that a measurable cardinal kappa cannot be the first regular cardinal at which GCH fails. We say that a cardinal kappa has the Levinski property if it is the least regular cardinal at which GCH holds. We will discuss a proof of Levinski’s theorem as well as some extensions of his result to other large cardinals.

Model Theory Seminar

Friday, September 9, 2011 12:30 pm GC 6417

Professor Roman Kossak (The City University of New York)

Models and types of PA, I

Abstract. Various types of arithmetic types will be defined and their properties discussed. The goal is to prove that each completion of PA has continuum many independent unbounded indiscernible types.

Logic Workshop

Friday, September 9, 2011 2:00 pm GC 6417

Professor David Marker (University of Illinois at Chicago) Zilber’s exponential field

Abstract. There are a number of basic but notoriously difficult open questions about definability in the complex field with exponentiation. Zilber constructed a non-elementary class of algebraically closed exponential fields, proved that the class is categorical in

uncountable powers and showed that definable sets behave well in this class. This leads one to ask if the complex field with exponentiation is the unique model in this class of size continuum. I will survey a number of results around this question.

Seminar in Logic and Games

Friday, September 9, 2011

** Two talks today **

CUNY Graduate Center, room 4419

4:15 PM

FILLING IN THE FOUNDATIONS OF PROBABILITY

ARTHUR PAUL PEDERSEN

Carnegie Mellon University

Abstract. This talk focuses on the foundations of probability, paying particular attention to justiﬁcations for possessing degrees of belief conforming to probabilities. Broadly speaking, these justiﬁcations can be divided into four categories: Representation Arguments (Ramsey [1926], Savage [1954]), Axiomatic Arguments (Cox [1946], Aczel [1966]), ´ Forecasting or Calibration Arguments (de Finetti [1974], Savage [1971]), and Dutch Book Arguments (de Finetti [1937], Shimony [1955]). Dutch Book Arguments have received the most attention—indeed, they have become a tradition in probability for furnishing

foundations—and they will receive more attention in this talk.

I will review the classic Dutch Book Argument due to de Finetti [1937], some well-known difﬁculties for the argument, and other difﬁculties for the argument which have received less attention. I will then review work which tries to ameliorate some of the problems we discuss.

I will thereupon consider a Dutch Book Argument advanced by way of a compelling notion of coherence, circumventing some of these problems. The notion of coherence ties in nicely with the work of van Fraassen [1995], Arlo-Costa and Parikh [2005], and Leitgeb [2010]. So-called core systems, which form the basis of this work, play a crucial role in the reduction of qualitative epistemic notions to quantitative epistemic notions. After brieﬂy reviewing core systems, we will see how qualitative aspects of core systems may be invoked in a Dutch Book Argument for possessing degrees of belief conforming to probabilities. Finally, we evaluate the argument. Parts of this talk address some of the issues I will touch upon at

Progic and so would be useful to acquire additional background.

5 PM

Meaning shifts and Conditioning

Jan-Willem Romeijn (University of Groningen)

Abstract: This paper investigates the viability of the Bayesian model of belief change. Van Benthem (2003) has shown that a particular kind of information change typical for dynamic epistemic logic cannot be modelled by Bayesian conditioning. I argue that the problems described by van Benthem come about because the information change alters the semantics in which the change is supposed to be modelled by

conditioning: it induces a shift in meanings. I then show that meaning shifts can be modelled in terms of conditioning by employing a semantics that makes these changes in meaning explicit, and that the appropriate probability kinematics can be described by Dempster’s rule. The new model thereby facilitates a better understanding between probabilistic epistemology and dynamic epistemic logic.

There will be a wine and cheese reception in room 4421 after the second talk.

– – – – Saturday, Sep 10 and Sunday, Sep 11, 2011- – – –

Progic 2011 on September 10th and 11th at Columbia University http://wp.me/p1at4T-pQ

The Progic conference series is intended to promote interactions between probability and logic. The fifth installment of the series will be held at Columbia University in New York on September 10th and 11th of 2011. While several of the earlier Progic meetings included a special focus, Progic 2011 will honor Haim Gaifman’s contributions to the intersection of probability and logic. Progic 2011 will consist of 11 talks, including invited talks by the following:

Haim Gaifman (Columbia)

Rohit Parikh (CUNY)

Jeff Paris (Manchester)

Dana Scott (Carnegie Mellon)

Progic 2011 will also include a memorial session to honor Horacio Arlo-Costa (Carnegie Mellon) who was scheduled to speak at the conference but passed away on July 14, 2011.

A brief listing of talks appears below. For complete conference details see http://wp.me/p1at4T-pQ

Saturday, September 10th in 602 Hamilton Hall

9:45-10:00 Opening remarks

10:00-11:00 Mixing modality and probability (yet again), Dana Scott (Carnegie Mellon)

11:30-12:00 From Bayesian epistemology to inductive logic, Jon Williamson (Kent) 12:15-12:45 Ultralarge lotteries: dissolving the lottery paradox using non-standard analysis, Sylvia Wenmackers (Groningen)

2:25-3:25 Knowledge and Uncertainty, Rohit Parikh (Brooklyn College and CUNY Graduate Center)

3:50-4:20 Coherence based probability logic: philosophical and psychological applications, Niki Pfeifer (Munich)

4:50-5:20 Matryoshka epistemology: the role of cores in belief and decision, Paul Pedersen (Carnegie Mellon)

5:30-6:30 Memorial for Horacio Arlo Costa

Sunday, September 11th – in 403 IAB

10:25-10:30 Opening announcements

10:30-11:30 Pure inductive logic, Jeff Paris (Manchester)

12:00-12:30 Probabilities on sentences in an expressive logic, M. Hutter (ANU), J. Lloyd (ANU), K. Ng (ANU), and W. Uther (National ICT) 2:10-2:40 Confirmation as partial entailment: a representation theorem in inductive logic, Vincenzo Crupi (Munich) and Katya Tentori (Trento) 2:55-3:25 On a priori and a posteriori reasoning, Anubav Vasudevan (Chicago) 3:45-4:45 T.b.a., Haim Gaifman (Columbia)

5:05-5:15 Closing remarks

Next Week in Logic at CUNY:

– – – – Monday, Sep 12, 2011 – – – –

– – – – Tuesday, Sep 13, 2011 – – – –

– – – – Wednesday, Sep 14, 2011 – – – –

– – – – Thursday, Sep 15, 2011 – – – –

– – – – Friday, Sep 16, 2011 – – – –

Model Theory Seminar

Friday, September 16, 2011 12:30 pm GC 6417

Professor Roman Kossak (The City University of New York)

Models and types of PA, II

Abstract. Unbounded indiscernible types will be applied in

constructions of elementary pairs in countable recursively saturated models, and in saturated models.

Logic Workshop

Friday, September 16, 2011 2:00 pm GC 6417

Dr. Alice Medvedev (University of California – Berkeley)

Unions of chains of signatures

Abstract. We meditate on a particularly naive notion of a limit of a sequence of theories: a union of conservative expansions. That is, we consider a sequence of nested signatures L1 < L2 < …, each one a subsignature of the next, and a sequence of Li-theories Ti where each Ti is precisely the set of Li-consequences of Ti+1 (and hence is a subset of Ti+1). It is easy to see that many model-theoretic properties then pass from all Ti to their union T. For example, it follows immediately from the compactness theorem that T is consistent whenever all Ti are. It is surprisingly easy to show that many more complicated stability-theoretic properties also pass up in this way. Our motivating example is the theory T of fields with an action by (Q, +), seen as a limit of (theories of) fields with Z-actions.

The speaker will also give a talk in the Kolchin Seminar at 10:15 the same morning in GC 5382, entitled “Using jet spaces to understand the structure of solution sets of difference equations.” Details at http://www.sci.ccny.cuny.edu/~ksda/gradcenter.html

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