Supergroup BLAST
Shay Logan
Supergroup Talk Number 1:
Speaker: Sophia Knight (University of Minnesota-Duluth)
Title: Some work on strategy logic with imperfect information
Time and Date: Thursday, September 10 20:00GMT-5
Link: https://unimelb.zoom.us/j/846890369?pwd=TktZYmlIUGlYOU9ZaXFJcCt0TFJFZz09
Abstract: There is a great deal of work on logics for games in multi-agent systems. These logics are concerned with formally defining statements like "If Alice and Bob cooperate, they can follow a strategy so that they are certain to achieve their goal," or "no matter what Cath does, she cannot be sure of achieving her goal," or "Alice can ensure that either Bob is certain not to reach his goal, no matter what he does, or Cath is cerain to reach her goal if she follows the right strategy." My talk will be focused on how to include imperfect information in these systems: if the agents do not have full information about the current state of the system, how does this change their power to act strategically in order to achieve their goals? In particular, I will discuss my current work with Bastien Maubert on some approaches to the formal expression of agents' knowledge and strategic abilities in multi-agent systems with imperfect information.
I will begin by presenting Alternating-time Temporal Logic (ATL), a logic describing the abilities of coalitions of agents in concurrent game structures. I will describe some difficulties with adapting variants of ATL to imperfect information settings. Next I will introduce Strategy Logic (SL), a logic with a similar purpose to ATL, which differs in that it takes strategies to be explicit objects in the logic, making it more powerful but less decidable than ATL. For example, SL can state the existence of Nash equilibria, whereas ATL cannot. I will describe our current work on an imperfect information variant of SL, the addition of epistemic operators, the difficulties in restricting SL to only consider uniform strategies, and a solution to this difficulty.
Supergroup Talk Number 2:
Speaker: Sara Uckelman (Durham)
Title: What Problem Did Ladd-Franklin (Think She) Solve(d)?
Time and Date: Friday, September 11 10:00GMT-5
Link: https://ksu.zoom.us/j/94305374304?pwd=cjArb1lNNjJXRGF2d3BTbGwvYmxzdz09
Meeting ID: 943 0537 4304
Passcode: ThinkShe
Abstract: Christine Ladd-Franklin is often hailed as a guiding star in the history of women in logic—not only did she study under C.S. Peirce and was one of the first women to receive a PhD from Johns Hopkins, she also, according to many modern commentators, solved a logical problem which had plagued the field of syllogisms since Aristotle. In this paper, we revisit this claim, posing and answering two distinct questions: Which logical problem did Ladd-Franklin solve in her thesis, and which problem did she \emph{think} she solved? We show that in neither case is the answer ``a long-standing problem due to Aristotle''. Instead, what Ladd-Franklin solved was a problem due to Jevons that was first articulated in the 19th century.
Talks by Other Groups:
Colloquium Logicae & OCIE
Speaker: Alfredo Roque Freire (Centre for Logic, Epistemology and the History of Science University of Campinas-Unicamp, Brazil)
Title: Intentional theory dichotomy and twisted models of set theory
Time and Date: Tuesday, September 8 18:00GMT-5
Abstract: Two modes of description were familiar to modern mathematicians: (i) descriptions of mathematical types to be satisfied by various structures, such as rings, fields, monoids; and (ii) intentional descriptions, which seek to specify mathematical objects as in geometry, arithmetic and real analysis. Due to the various limiting theorems in relation to formal systems (e.g. G\"odel's incompleteness and Loweinhein-Skolem theorems), it has become common to maintain that there is no sharp boundary between intentional and non-intentional theories. Since it is not possible to fix a single model for first order arithmetic, its axioms work in a similar way to axioms of general algebraic structures. This conclusion is the result of the following dichotomy: either there are precise and unambiguous ways to describe general collections of objects or there is no clear boundary between intentional theories and non-intentional theories. However, recent results on interpretability [1,2,3] develop restricted versions of absoluteness regarding theories historically considered to be intentional. In fact, models of arithmetic and set theory are unique
with respect to bi-interpretations. We will argue that these results allow us not only to recover the dichotomy that separates intentional from non-intentional theories, but still remain compatible with pluralism regarding theories such as arithmetic and set theory.
Finally, we will show to what extent conditions of absoluteness may be used as sufficient to incorporate non-classical set theories to the multiverse. We believe this absoluteness conditions are possibly obtained for the novel twisted valued models developed by Carnielli and Coniglio [4]. We will argue that these paraconsistent models have the virtue of being sufficiently rigid, and thus may be successfully included in the multiverse.
[1] Friedman, H. M., & Visser, A. (2014). When bi-interpretability implies synonymy. Logic Group Preprint Series, 320, 1-19.
[2] Enayat, A. (2017). Variations on a Visserian theme. arXiv preprin
arXiv:1702.07093.
[3] Freire, A. R., & Hamkins, J. D. (2020). Bi-interpretation in weak set theories. arXiv preprint arXiv:2001.05262.
[4] Carnielli, W., & Coniglio, M. E. (2019). Twist-valued models for three-valued paraconsistent set theory.
Logic and Logical Philosophy,, ON LINE FIRST:
https://apcz.umk.pl/czasopisma/index.php/LLP/article/view/LLP.2020.015
Indiana University Logic Group
Speaker: Sergei Artemov (Graduate Center CUNY)
Title: The Provability of Consistency
Time and Date: Wednesday, September 9 15:00GMT-5
Link: https://iu.zoom.us/j/95326399432?pwd=VmVUWGxHeG5KQjEzQVozb3pCRHJVZz09
Abstract: We argue that there is a class of widely used informal arithmetical reasonings which are not captured by the standard notion of a formal proof of a formula in Peano Arithmetic PA but yet are naturally formalizable in PA. Specifically, informal “contentual” arithmetic can prove a property S (think of the "strong induction" property) without reducing S to a single formula. On this basis, we offer a mathematical proof of consistency for Peano Arithmetic PA in its original Hilbert's formulation as a property of finite sequences of formulas and demonstrate that this proof is formalizable in PA. Our consistency proof is not ruled out by Gödel’s Second Incompleteness Theorem which prohibits only PA-proofs of the internalized PA-consistency presented as a specific arithmetical formula.
The above renders the popular impossibility reading of Gödel's Theorem, that there is no consistency proof of a system that can be formalized within the system itself, unwarranted.
Lógicos em Quarentena
Speaker: Diogo Henrique Bispo Dias
Title: There is no good argument for logical monism
Time and Date: Thursday, September 10 14:00GMT-5
Link: https://meet.google.com/utd-uqvh-txh
Abstract: The aim of this talk is to investigate some arguments for logical monism, and to show how, with minor modifications, these arguments could be used to defend the adequacy of different logics. Hence, as a defence of logical monism, they all fail.
Nonclassical Logic Seminar
Speaker: Francesco Paoli (Cagliari)
Title: On Paraconsistent Weak Kleene Logic
Time and Date: Friday, September 11 11:00GMT-5
Abstract: Paraconsistent Weak Kleene Logic (PWK) is the 3-valued propositional
logic defined on the weak Kleene tables and with 2 designated values.
In this survey talk, we intend to explore some intriguing connections
between this logic and the algebraic theories of regular varieties and
of Plonka sums over semilattice direct systems of algebras. By a
recourse to this toolbox, it is possible to discover some interesting
properties of PWK from the point of view of Abstract Algebraic Logic.
We also present a Gentzen system for PWK and show that PWK has only
one nontrivial proper extension apart from Classical Logic.
The results we present are due to S. Bonzio, J. Gil Férez, T.
Moraschini, L. Peruzzi, M. Pra Baldi, and the speaker.
Other Notes and Announcements:
The Logic Supergroup has a YouTube channel! Recordings of almost all talks are available at https://www.youtube.com/channel/UCqOAS8SHP-5nGjYEE2FE6xw
Yay for logic!