Supergroup BLAST!
Shay Logan
Supergroup Talk
Speaker: Michał Godziszewski (MCMP)
Title: Modal Quantifiers, Potential Infinity, and Yablo sequences
Time and Date: Friday, September 18 0900 GMT-5
Link: https://ksu.zoom.us/j/98927095498?pwd=L0czT2Y3WENFbXBJUjVMVXNON1cydz09
Meeting ID: 989 2709 5498
Passcode: munich
Abstract: When properly arithmetized, Yablo's paradox results in a set of formulas which (with local disquotation in the background) turns out to be consistent, but $\omega$-inconsistent. Adding either uniform disquotation or the $\omega$-rule results in inconsistency. Since the paradox involves an infinite sequence of sentences, one might think that it doesn't arise in finitary contexts. We study whether it does. It turns out that the issue depends on how the finitistic approach is formalized. On one of them, proposed by M. Mostowski, all the paradoxical sentences simply fail to hold. This happens at a price: the underlying finitistic arithmetic itself is $\omega$-inconsistent. Finally, when studied in the context of a finitistic approach which preserves the truth of standard arithmetic, the paradox strikes back --- it does so with double force, for now the inconsistency can be obtained without the use of uniform disquotation or the $\omega$-rule. This is joint work with Rafał Urbaniak from the University of Gdańsk.
Talks by Other Groups:
NYU Logic and Metaphysics Seminar
Speaker: Chris Scambler (NYU
Title: Cantor's Theorem, Modalized
Time and Date: Monday, September 14 15:15 GMT-5
Meeting ID: 968 6949 1549
Passcode: 602751
Abstract: I will present a modal axiom system for set theory that (I claim) reconciles mathematics after Cantor with the idea there is only one size of infinity. I’ll begin with some philosophical background on Cantor’s proof and its relation to Russell’s paradox. I’ll then show how techniques developed to treat Russell’s paradox in modal set theory can be generalized to produce set theories consistent with the idea that there’s only one size of infinity.
Helsinki Logic Seminar
Speaker: Phokion Kolaitis (UC Santa Cruz and IBM Research - Almaden)
Title: The Query Containment Problem: Set Semantics vs. Bag Semantics
Time and Date: Wednesday, September 16 10:00 GMT-5
Link: https://helsinki.zoom.us/j/63880559261?pwd=dzViaTA3U1lkQ2YvM2NOZVNacVovdz09
Abstract: Query containment is a fundamental algorithmic task in database query processing and optimization. Under set semantics, the query-containment problem for conjunctive queries has long been known to be NP-complete. SQL queries, however, are typically evaluated under bag semantics and return multisets (bags) as answers, since duplicates are not eliminated unless explicitly specified. The exact complexity of the query-containment problem for conjunctive queries under bag semantics has been an outstanding problem for more than twenty-five years. To this date, it is not even known whether conjunctive-query containment under bag semantics is decidable. The aim of this talk is to present a comprehensive overview of results about the query-containment problem for conjunctive queries and their variants under bag semantics, including recent results that reveal tight connections between this problem and open problems in information theory.
Lógicos em Quarentena
Speaker: Damian Szmuc (IIF-SADAF/CONICET)
Title: The fragment of Classical Logic that respects the Variable-Sharing Principle
Time and Date: Thursday, September 17 14:00 GMT-5
Link: https://meet.google.com/qjd-qfiq-vof
Abstract: We provide a logical p-matrix semantics and a Gentzen-style sequent calculus for the first-degree entailments valid in R. Epstein's Relatedness Logic, which incidentally coincides with the fragment of Classical Logic that respects the Variable Sharing Principle. We achieve the former by introducing a logical p-matrix closely related to that inducing paracomplete weak Kleene logic, and the latter by presenting a calculus where the left and right rules for negation are subject to linguistic constraints.
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!
Shay Logan
Supergroup Talk
Speaker: Stewart Shapiro (OSU/UConn) and David McCarty (Indiana)
Title: Intuitionistic Sets and Numbers: the theory SST
Time and Date: Friday, September 25 1000 GMT-5
Link: https://ksu.zoom.us/j/99006967120?pwd=bElXcUlUcUpLQkNHdER5Q2dobVN4dz09
Meeting ID: 990 0696 7120
Passcode: numbers
Abstract: SST is a small intuitionistic set theory governing the hereditarily finite sets. It is based upon set induction. Simple as SST is, it seems remarkably strong: it deduces--within intuitionistic formal logic--all the axioms of ZF + AC, less the Axiom of Infinity, except that Separation is limited to decidable predicates. It is relatively straightforward to prove that SST has the usual Goedelian incompleteness properties. SST is definitionally equivalent to full, first-order intuitionistic arithmetic, aka Heyting Arithmetic. And SST manifests the attractive metamathematical properties of many intuitionistic mathematical theories--it supports a number of different realizability and topological interpretations and can be assumed to be categorical.
Talks by Other Groups:
Logic and Metaphysics Workshop (CUNY)
Speaker: Yale Weiss (CUNY)
Title: Arithmetical Semantics for Non-Classical Logic
Time and Date: Monday, September 21 15:15 GMT-5
Meeting ID: 944 4946 1647
Passcode: 583887
Abstract: I consider logics which can be characterized exactly in the lattice of the positive integers ordered by division. I show that various (fragments of) relevant logics and intuitionistic logic are sound and complete with respect to this structure taken as a frame; different logics are characterized in it by imposing different conditions on valuations. This presentation will both cover and extend previous/forthcoming work of mine on the subject.
OCIE Seminar
Speaker: Bruno Bentzen (CMU)
Title: Frege's Anticipation of Simple Type Theory
Time and Date: Tuesday, September 22 18:00 GMT-5
Link: https://uci.zoom.us/j/95859575948
Abstract: In this talk, I argue that Frege's sharp distinction between terms denoting objects and terms denoting functions on the basis of their saturation anticipate a version of simple type theory, although Frege vacillates between regarding functions as closed terms of a function type and open terms formed under a hypothetical judgment. In the end, Frege fails to express his logical views consistently due to his logicist ambitions, which require him to endorse the view that value-ranges are objects.
Shay Logan
Supergroup Talk
Speaker: Alex Belikov (Lomonosov Moscow State University)
Title: On Bivalent Semantics and Natural Deduction For Some Infectious Logics
Time and Date: Friday, October 2 09:00 GMT-5
Link: https://ksu.zoom.us/j/93495801842?pwd=WERmbTNjL3ZPWmNYekxucDBSc1E3dz09
Meeting ID: 934 9580 1842
Passcode: bivalent
Abstract: In this work, I present a variant of so-called ‘informational semantics’, a technique elaborated by E. Voishvillo, for two quatervalent infectious logics, Deutsch’s Sfde and Szmuc’s dSfde in order to illuminate how incompleteness and inconsistency (understood in the ‘infectious’ way) effect on the truth and falsity conditions for conjunction and disjunction. In a nutshell, I suggest two kinds of semantical conditions: ‘affirmative’ one for logics with infected gaps and ‘rejective’ one for those where gluts are infected only. With regard to the technical part, I formalize these logics in the form of natural deduction calculi, thereby solving several problems: to fill the corresponding gap in the study of a proof- theoretical aspect of infectious logics; to revise Petrukhin’s result for Sfde; to provide simple natural deduction systems for Sfde and dSfde, representing a fundamental symmetry between them and forming a convenient basis for further extensions.
Talks by Other Groups:
Logic and Metaphysics Workshop (CUNY)
Speaker: Daniel Hoek (Virginia Tech)
Title: Coin flips, Spinning Tops and the Continuum Hypothesis
Time and Date: Monday, September 28 15:15 GMT-5
Meeting ID: 924 3989 1639
Passcode: 346380
Abstract: By using a roulette wheel or by flipping a countable infinity of fair coins, we can randomly pick out a point on a continuum. In this talk I will show how to combine this simple observation with general facts about chance to investigate the cardinality of the continuum. In particular I will argue on this basis that the continuum hypothesis is false. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. A classic theorem from Banach and Kuratowski (1929), tells us that it follows, given the axioms of ZFC, that there are cardinalities between countable infinity and the cardinality of the continuum. (Get the paper here: https://philpapers.org/archive/HOECAT-2.pdf).
Lógicos em Quarentena
Speaker: Catharina Dutilh Novaes
Title: Who's afraid of adversariality? Conflict and cooperation in argumentation
Time and Date: Tuesday, September 29, 09:00-11:00 GMT-5
Helsinki Logic SeminarAbstract: Since at least the 1980s, the role of adversariality in argumentation has been extensively discussed. Some authors criticize adversarial conceptions and practices of argumentation and instead defend more cooperative approaches, both on moral and on epistemic grounds. Others retort that argumentation is inherently adversarial, and that the problem lies not with adversariality per se but with overly aggressive manifestations therof. In this paper, I defend the view that specific instances of argumentation are (and should be) adversarial or cooperative proportionally to pre-existing conflict. What determines whether an argumentative situation should be primarily adversarial or primarily cooperative are contextual features and background conditions, in particular the extent to which the parties involved have prior conflicting or convergent interests and goals. I articulate a notion of adversariality in terms of the relevant parties pursuing conflicting interests, and argue that, while cooperative argumentation is to be encouraged whenever possible, conflict as such is an inevitable aspect of human sociality and thus cannot be completely eliminated.
Speakers: Cheryl Misak and Simon Blackburn
Time and Date: Wednesday, September 30, 06:00 GMT-5
Link: https://wiki.helsinki.fi/display/Logic/Seminar
Abstract: Cheryl Misak:
The theory of general relativity drove Russell in 1928 to argue that we can refer to unobservable theoretical entities only through an understanding of their structural properties. At the end of that decade, two eminent philosophically inclined Cambridge mathematicians explored the issue. Simon Blackburn will show how Max Newman exploded Russell’s structuralism by noting that to say of two collections that they share a specified structure asserts nothing more than that they have the same cardinality. He will also show that Frank Ramsey is thought to have developed a technique (“Ramsey Sentences”) for the empiricist who wants to reduce theory to observation. Ramsey’s technique however, seems to open him to Newman’s problem, and Simon puzzles over why this seems not to have bothered him.
Cheryl Misak will then argue that Ramsey in fact is not open to Newman’s Problem. Ramsey Sentences are much richer and much more interesting, in that they are situated in a context of inquiry and allow for refinement and improvement.
Simon Blackburn: ”Why is Newman missing?”
It is generally agreed that the idea of the Ramsey sentence of a theory has an origin in “Theories” written in note form in 1929, the last year of Ramsey’s productive life. Yet in 1928 his friend Max Newman had published, in Mind, a paper which has ever since dominated discussions of Ramsification. The paper was directed at Russell’s 1927 book The Analysis of Mind, and Russell conceded its criticism was both fundamental and correct. Why then did Ramsey ignore it— when Russell had in effect preceded him in the application of Ramsey sentences in defining “structural realism” ? I suggest that the answer is that Ramsey was not interested in anything like Russell’s foundational project (nor Carnap’s) but perhaps in something more like David Lewis’s 1970 paper “How to Define Theoretical terms”.
UConn Logic Group
Speaker: Lenore Blum (CMU)
Time and Date: Friday, October 2, 12:00 GMT-5
See supergroup calendar for further details
Speaker: Matthew Harrison-Trainor
Time and Date: Friday, October 2, 18:00 GMT-5
Link: http://logic.berkeley.edu/events.html
Title: Scott complexity of countable structures
Abstract: Dana Scott proved that every countable structure has a sentence of the infinitary logic Lω1ω which characterizes that structure up to isomorphism among countable structures. Such a sentence is called a Scott sentence, and can be thought of as a description of the structure. The least complexity of a Scott sentence for a structure can be thought of as a measurement of the complexity of describing the structure. I will give an introduction to the area, and then focus on three subtopics: connections with computability, Scott complexity of particular structures, and complexity in classes of structures.
Shay Logan
Supergroup Talk
Speaker: Damian Szmuc (CONICET and University of Buenos Aires)
Title: The fragment of Classical Logic that respects the Variable-Sharing Principle
Time and Date: Thursday, October 8 19:00 GMT-5
Link: https://ksu.zoom.us/j/95209188832?pwd=OWRuUS9UaDBlbnk5SnhzbFFJZzBOdz09
Meeting ID: 952 0918 8832
Passcode: sharing
Talks by Other Groups:
Logic and Metaphysics Workshop (CUNY)
Speaker: Oliver Marshall (UNAM)
Title: Mathematical Information Content
Time and Date: Monday, October 5, 15:15 GMT-5
Meeting ID: 932 1423 1899
Passcode: 692542
Abstract: Alonzo Church formulated several logistic theories of propositions based on three alternative criteria of identity (1949, 1954, 1989, 1993). The most coarse grained of these criteria is Alternative (2), according to which two propositions are identical iff the sentences that express them are necessarily materially equivalent. Alternative (1) is more discerning. According to Alternative (1), two propositions are identical iff the sentences that express them can be obtained from one another by the substitution of synonyms for synonyms and λ-conversion. Church said that he intended this to limn a notion of proposition closely related to Frege’s notion of gedanke, but added that it will not be sufficiently discerning if propositions in the sense of Alternative (1) are taken as objects of assertion and belief (1993). Alternative (0), the most discerning criterion, says that two propositions are identical iff the sentences that express them can be obtained from one another by the substitution of synonyms for synonyms. I argue that Alternative (1) does indeed provide insight into one of the topics that concerned Frege (1884) – namely, abstraction. Then I discuss various counterexamples to Church’s criteria (including one due to Paul Bernays, 1961). I close by proposing a criterion of identity for mathematical information content based on the various examples under discussion.
UConn Logic Group
Speaker: Sam Sanders (TU Darmstadt)
Time and Date: Friday, October 9, 10:00 GMT-5
Title: Brouwer, Plato, and classification
Abstract: Classification is an essential part of all the exact sciences, including mathematical logic. The program Reverse Mathematics classifies theorems of ordinary mathematics according to the minimal axioms needed for a proof. We show that the current scale, based on comprehension and discontinuous functions, is not satisfactory as it classifies many intuitively weak statements, like the uncountability of $\mathbb{R}$ or properties of the Riemann integral, in the same rather strong class. We introduce an alternative/complimentary scale with better properties based on (classically valid) continuity axioms from Brouwer’s intuitionistic mathematics. We discuss how these new results provide empirical support for Platonism.
Speaker: Larry Moss
Time and Date: Friday, October 9, 12:00 GMT-5
Title: Natural Logic
Link: contact Stella Moon (moo...@uci.edu) for details
Abstract: This talk reports on work in logic whose goal is the study of inference in language. This leads to what I will call “natural logic”, the enterprise of studying logical inference in languages that look more like natural language than standard logical systems.
The talk should appeal to several parts of the OCIE audience: (1) Logicians interested in completeness and complexity results, including results for logical systems that are not first-order. The talk also includes the simplest completeness theorem in all of logic. (2) Philosophers curious about modern revitalizations of term (syllogistic) logic, especially extensions which incorporate relational reasoning. (3) Anyone interested in monotonicity reasoning, where I and many co-workers have results and running programs.
Shay Logan
Supergroup Talk Number 1
Speaker: Yao Tang (La Trobe)
Title: Recursive relations on the set of words with 2 letters
Time and Date: Thursday, October 15 19:00 GMT-5
Link: https://unimelb.zoom.us/j/846890369?pwd=TktZYmlIUGlYOU9ZaXFJcCt0TFJFZz09
Abstract: Recursive functions on the natural numbers can be characterized as the class of functions generated from a specified list of initial functions and inductive conditions.
In “Undecidability without Arithmetization”, Andrzej Grzegorczyk constructed a class GD of relations on theset of words with 2 letters, which is characterized in a similar way (as the class of relations generated from a specified list of initial relations and inductive conditions).
We want to show that GD is precisely the class of relations on the set of words with 2 letters that are also recursive sets.
Supergroup Talk Number 2
Speaker: Edson Bezerra (UNICAMP)
Title: Squeezing arguments and the plurality of informal notions
Time and Date: Friday, October 16 9:00 GMT-5
Link: https://ksu.zoom.us/j/94976439500?pwd=VmV4N01FK3pkUjE1RSthaS83a1JWZz09
Meeting ID: 949 7643 9500
Passcode: informal
Abstract: Kreisel's squeezing argument (1967) shows that there is an informal notion of validity which is irreducible to both model-theoretic and proof-theoretic validity of First-Order Logic (FOL), but coextensive with both formal notions. His definition of informal validity as truth in all structures received some criticisms in the literature for being heavily model-theoretical (Smith (2011) and Halbach (2020)). However, because of its simple and schematic form, variants squeezing argument has been presented for capturing other intuitive notions of validity closer to our pre-theoretical notion of validity (Shapiro, 2005). Therefore, the different squeezing arguments we find in the literature show that there are other informal notions of logical validity, which are coextensive with their corresponding formal definition of logical validity. In this talk, we argue for an even form of pluralism, showing that squeezing arguments cannot squeeze in the uniqueness of the corresponding informal notion. Indeed, we maintain that a complete logical system can be compatible with different notions of informal validity.
Talks by Other Groups:
Logic and Metaphysics Workshop (CUNY)
Speaker: Brian Cross Porter (CUNY)
Title: A Metainferential Hierarchy of Validity Curry Paradoxes
Time and Date: Monday, October 12, 15:15 GMT-5
Meeting ID: 933 3942 1821
Passcode: 292620
Abstract: The validity curry paradox is a paradox involving a validity predicate which does not use any of the logical connectives; triviality can be derived using only the structural rules of Cut and Contraction with intuitively plausible rules for the validity predicate. This has been used to argue that we should move to a substructural logic dropping Cut or Contraction. In this talk, I’ll present metainferential versions of the validity curry paradox. We can recreate the validity curry paradox at the metainferential level, the metametainferential level, the metametametainferential level, and so on ad infinitum. I argue that this hierarchy of meta-n-inferential validity curry paradoxes poses a problem for the standard substructural solutions to the validity curry paradox.
Lógicos em Quarentena
Speaker: Hugo Luiz Mariano
Time and Date: Thursday, October 15, 14:00 GMT-5
Title: An algebraic framework to a theory of sets based on the surreal numbers
Link: https://meet.google.com/sqh-iepr-ges
Abstract: The surreal numbers constitute a linearly ordered (proper) class $No$ containing the class of all ordinal numbers ($On$), that satisfies many interesting properties. In an attempt to codify the universe of sets directly within the surreal number class, we have founded some clues that suggest that this class is not suitable for this purpose. Carefully formalizing the definition of the class of pre-(surreal) numbers (and some variants), which is an intermediate stage in the construction of the Conway surreal numbers, we obtain structures which have copies of $No$ as well the class the universe of all sets ($V$).as well as copies of the class of surreal numbers. Thus, in particular, we gave first steps toward a certain kind of "relative set theory", in this new setting.
The main aim of this work is to isolate and explore properties of these new constructions and present the notion of (partial) SUR algebra, an attempt to obtain an "algebraic theory for surreal numbers" along the lines of the Algebraic Set Theory of Joyal and Moerdijk: to establish (abstract and general) links between the class of all surreal numbers and a universe of "surreal sets" similar to the relations between the classes $On$ and $V$, of all ordinals and the class of all sets, that respects and expands the links between the linearly ordered class $On$ and $No$ of all ordinals and of all surreal numbers.
Speaker: Ekaterina Babintseva
Time and Date: Friday, October 16, 11:00 GMT-5
Title: Of Minds and Computers: Harnessing Mathematical Creativity
Link: https://pitzer.zoom.us/j/96937631191?pwd=RkZZKzQyT2Z3Y3B2OHk0Y0I3SzZMdz09
Abstract: In the mid-20th century, “creative thinking” became a prominent category in American psychology and pedagogy. Advanced by cognitive psychologists as both a descriptive and a normative characteristic of the human self, the notion of creative thinking soon came to shape many mid-century debates in mathematics pedagogy. This paper traces the work of the educational psychologists and mathematicians at the University of Illinois who attempted to create special computer software that would teach creative thinking in mathematics. Developed for the University of Illinois’ PLATO (Programmed Logic for Automated Teaching Operations) teaching computer, this software sought to introduce students to the intuitive aspect of mathematical thinking. Following this research through the 1960s-1970s, this paper discusses how scientists used PLATO as a laboratory for testing mid-century theories of learning and approaches to math education.
Shay Logan
Supergroup Talk
Speaker: Ana Claudia Golzio (UNICAMP)
Title: Swap structures semantics for some logics of formal inconsistency
Time and Date: Friday, October 23 09:00 GMT-5
Link: https://ksu.zoom.us/j/99677150172?pwd=MFFBcXlDdVpuRjRXaGVRU1ZwUmdOdz09
Meeting ID: 996 7715 0172
Passcode: structures
Abstract: Multialgebras (or hyperalgebras) are algebras which at least one of the operations (called multioperations) returns a subset instead of a single element of the domain. Multialgebras have been very much studied in the literature and in the realm of Logic, they were considered by Avron and his collaborators, under the name of non-deterministic matrices (or Nmatrices), as a useful semantics tool for characterizing some logics of formal inconsistency (LFIs). In particular, these logics of formal inconsistency are not algebraizable by any method, including Blok and Pigozzi general theory. Carnielli and Coniglio introduced a semantics of swap structures for LFIs, which are Nmatrices constructed over triples in a Boolean algebra, generalizing Avron’s non-deterministic matrices. In this work we develop the first steps towards an algebraic theory of swap structures for LFIs. The logic mbC is the weakest system in the hierarchy of LFIs and the system QmbC is the extension of mbC to first-order language. The goal of this talk is to present the first steps towards a theory of non-deterministic algebraization of logics by swap structures. Specifically, a formal study of swap structures for logics of formal inconsistency is developed, by adapting concepts of universal algebra to multialgebras in a suitable way and we introduce also an algebraic semantics for QmbC. From the algebraic point of view these structures enable us to obtain properties of first-order logic QmbC and in the proof of the Soundness Theorem we can see interesting particularities of the first-order swap structures, especially with respect to the Substitution Lemma. This study opens new avenues for dealing with non-algebraizable logics through by the more general methodology of multialgebraic semantics.
Talks by Other Groups:
Logic and Metaphysics Workshop (CUNY)
Speaker: Michael Glanzberg (Rutgers)
Title: Models, Model Theory, and Modeling
Time and Date: Monday, October 19th 15:15 GMT-5
Meeting ID: 920 5635 8765
Passcode: 281885
Abstract: In this paper, I shall return to the relations between logic and semantics of natural language. My main goal is to advance a proposal about what that relation is. Logic as used in the study of natural language—an empirical discipline—functions much like specific kinds of scientific models. Particularly, I shall suggest, logics can function like analogical models. More provocatively, I shall also suggest they can function like model organisms often do in the biological sciences, providing a kind of controlled environment for observations. My focus here will be on a wide family of logics that are based on model theory, so in the end, these claims apply equally to model theory itself. Along the way towards arguing for my thesis about models in science, I shall also try to clarify the role of model theory in logic. At least, I shall suggest, it can play distinct roles in each domain. It can offer something like scientific models when it comes to empirical applications, while at the same time furthering conceptual analysis of a basic notion of logic.
IU Logic Seminar
Speaker: Siddharth Bhaskar (University of Copenhagen)
Title: Traversal-Invariant Definability and Logarithmic Space
Time and Date: Wednesday, October 21st 13:00 GMT-5
Meeting ID: 953 2639 9432
Passcode: Smullyan
GROLOG (Groningen Logic Group)Abstract: Presentation invariance is the phenomenon in which a quantity is defined in terms of some additional structure (or "presentation") but is then shown to be independent of it. Common examples are the dimension of a vector space (defined as the cardinality of basis), or Euler characteristic of a surface (defined in terms of a triangulation). Presentation invariance is a prominent theme in descriptive complexity theory, which deals with finite structures encoded as strings, but insists that queries must be independent of the encoding.
In this talk, I will give characterizations of deterministic and nondeterministic logarithmic space in terms of first-order queries in the language of graphs, with invariant usage of a traversal, a particular linear ordering of the vertices of a graph. This is the first such characterization of these classes that I know of which does not have an obvious mechanism for "computation," such as a fixed-point operator; rather, all the computation is "hidden" in the presentation itself.
I then describe how to extend traversal-invariant definability to classes of infinite structures. To do this, we need to bypass the Craig interpolation theorem, which is commonly thought of as an obstacle to presentation-invariant definability over arbitrary structures. I conclude with some ideas of how to investigate traversal-invariant definability from the perspective of abstract model theory. This work is joint with Steven Lindell and Scott Weinstein.
Speaker: Prof. dr. Allard Tamminga (Universität Greifswald)
Title: Expressivity Results for Deontic Logics of Collective Agency
Time and Date: Thursday, October 22nd 08:15 GMT-5
Meeting ID: 870 7195 5060
Passcode: 561643
Abstract: We use a deontic logic of collective agency to study reducibility questions about collective agency and collective obligations. The logic that is at the basis of our study is a multi-modal logic in the tradition of stit ('sees to it that') logics of agency. Our full formal language has constants for collective and individual deontic admissibility, modalities for collective and individual agency, and modalities for collective and individual obligations. We classify its twenty-seven sublanguages in terms of their expressive power. This classification enables us to investigate reducibility relations between collective deontic admissibility, collective agency, and collective obligations, on the one hand, and individual deontic admissibility, individual agency, and individual obligations, on the other. (Joint work with Hein Duijf and Frederik Van De Putte)
Speaker: Marcos Silva (UFPE)
Title: Revision of Logic, Reflexive Equilibrium and Normative Bidirectionality
Time and Date: Thursday, October 22nd 14:00 GMT-5
Abstract: How could we rationally justify our logical principles, if the very possibility of rational justification presupposes them? To what extent is it possible to revise something as fundamental as logical principles? How could we justify a set of basic principles of logic as the correct one without circularity or infinite regress? In our paper, we will explore a pragmatist and normative approach to the epistemic problem of justification and revision of the most basic logical rules. We defend that logic is a science analogous to normative disciplines as defended by Prawitz (1978) and Peregrin e Svoboda (2017). This pragmatist method defends the revision of logic based on the notion of reflexive equilibrium in relation to our general theoretical considerations and local instances as particular inferences, revising any of these elements, whenever necessary, in order to obtain an acceptable coherence among them. We will develop the notion of normative bidirectionality and argue that what we call upward normative pressure adequately expresses the dynamical aspect in the revision of logical principles.
UConn Logic Group
Speaker: Tyler Markkanen (Springfield College)
Title: Computing Perfect Matchings in Graphs
Time and Date: Friday, October 23rd 13:00 GMT-5
Meeting ID: 824 1530 0828
Abstract: A matching of a graph is any set of edges in which no two edges share a vertex. Steffens gave a necessary and sufficient condition for countable graphs to have a perfect matching (i.e., a matching that covers all vertices). We analyze the strength of Stephens’ theorem from the viewpoint of computability theory and reverse mathematics. By first restricting to certain kinds of graphs (e.g., graphs with bounded degree and locally finite graphs), we classify some weaker versions of Stephens’ theorem. We then analyze Stephens’ corollary on the existence of maximal matchings, which is critical to his proof of the main theorem. Finally, using methods of Aharoni, Magidor, and Shore, we give a partial result that helps hone in on the computational strength of Stephens’ theorem. Joint with Stephen Flood, Matthew Jura, and Oscar Levin.Passcode: 8q8aAk
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 If you are part of a member group, are recording talks, and would like the supergroup to host them, then let us know! We'd be happy to help.
Yay for logic!
Shay Logan
Supergroup Talk 1
Speaker: Koji Tanaka (ANU)
Title: Empirical and Normative Arguments for Paraconsistency
Time and Date: Thursday, October 29th 19:00 GMT-5
Link: https://unimelb.zoom.us/j/846890369?pwd=TktZYmlIUGlYOU9ZaXFJcCt0TFJFZz09
Abstract: How can we know which inferences are valid and which ones are not? In particular, how can we know that ex contradictione quodlibet (ECQ) (A, ¬A ⊨ B for every A and B) is invalid as paraconsistent logicians claim? A popular view to answer these questions in recent years is abductivism. According to this view, we should accept a logical theory which best explains the relevant data. One central tenet of abductivism as it is used by paraconsistent logicians is a broadly empirical methodology. Paraconsistent logicians consider empirically observable data and use this to argue that ECQ is invalid. In this paper, I will defend this empirical methodology. First, I will show that some paraconsistent logicians employ an empirical methodology in arguing for the paraconsistent nature of logic. Second, I will present a view of normativity that is compatible with an empirical methodology. Third, I will develop an anti-exceptionalist view that takes logic to be normative, yet continuous with empirical sciences. Fourth, I will argue against the a priori conception of logic. My conclusion will be that the empirical methodology employed by some paraconsistent logicians is defensible.
Supergroup Talk 2
Speaker: Gisele Secco (UFSM)
Title: How are they the same? Notes on the identity of the proofs of the Four-Colour Theorem
Time and Date: Friday, October 30th 9:00 GMT-5
Link: https://ksu.zoom.us/j/96049039729?pwd=REVWcDFrU1ZPbEhyazRPT3NkYjQxUT09
Meeting ID: 960 4903 9729
Passcode: proofs
Abstract: The Four-Color Theorem (4CT, delivered in [1] and [2]) is the first case of an original mathematical result obtained through the massive use of computing devices. Despite having been the subject of exceptional amounts of advertising and philosophical commentary, this notorious mathematical result is still relevant as a case study in the philosophy of mathematical practice and, more broadly, in the history of mathematics, for two reasons. In the one hand, given the existence of (at least) two other versions of the proof ([3] and [4]) the case suggests a discussion about the criteria for establishing the identity of computer-assisted proofs (with a corollary question about the identity of computer programs, proof assistants etc..). On the other hand, a vital dimension of the proof has not yet been analysed: the interplay between its computational and the diagrammatical elements. Building on the methodological guidelines suggested in [5], I offer a partial description of [1] and [2], showing how computing devices interact with diagrams in these texts. With such a description, I offer a new way of tackling the question about the identity of proofs, articulating both reasons for defending the relevance of the 4CT for the history and the philosophy of mathematical practice.
Talks by Other Groups:
Logic and Metaphysics Workshop (CUNY)
Speaker: Lisa Warenski (CUNY)
Title: The Metaphysics of Epistemic Norms
Time and Date: Monday, October 26th 15:15 GMT-5
Link: https://gc-cuny.zoom.us/j/96888694042?pwd=cERxN3hhT3k2TmZvdlQzL3dPdzhyZz09
Meeting ID: 968 8869 4042Passcode: 847819
Abstract: A metanormative theory inter alia gives an account of the objectivity of normative claims and addresses the ontological status of normative properties in its target domain. A metanormative theory will thus provide a framework for interpreting the claims of its target first-order theory. Some irrealist metanormative theories (e.g., Gibbard 1990 and Field 2000, 2009) conceive of normative properties as evaluative properties that may attributed to suitable objects of assessment (doxastic states, agents, or actions) in virtue of systems of norms. But what are the conditions for the acceptability of systems of norms, and relatedly, correctness of normative judgment? In this paper, I take up these questions for epistemic norms. Conditions for the acceptability of epistemic norms, and hence correctness of epistemic judgment, will be based on the critical evaluation of norms for their ability to realize our epistemic aims and values. Epistemic aims and values, in turn, are understood to be generated from the epistemic point of view, namely the standpoint of valuing truth.
Helsinki Logic Seminar
Speaker: Yurii Khomskii (Amsterdam University College and Universität Hamburg)
Title: Bounded Symbiosis and Upwards Reflection
Time and Date: Wednesday, October 28th 05:00 GMT-5
Abstract: In [1], Bagaria and Väänänen developed a framework for studying the large cardinal strength of Löwenheim-Skolem theorems of strong logics using the notion of Symbiosis (originally introduced by Väänänen in [2]). Symbiosis provides a way of relating model theoretic properties of strong logics to definability in set theory. We continue the systematic investigation of Symbiosis and apply it to upwards Löwenheim-Skolem theorems and upwards reflection principles. To achieve this, the notion of Symbiosis is adapted to what we call "Bounded Symbiosis". As an application, we provide some upper and lower bounds for the large cardinal strength of upwards Löwenheim-Skolem principles of second order logic.
This is joint work with Lorenzo Galeotti and Jouko Väänänen.
[1] Joan Bagaria and Jouko Väänänen, “On the Symbiosis Between Model-Theoretic and Set-Theoretic Properties of Large Cardinals”, Journal of Symbolic Logic 81 (2) P. 584-604
[2] Jouko Väänänen, "Abstract logic and set theory. I. Definability.” In Logic Colloquium ’78 (Mons, 1978), volume 97 of Stud. Logic Foundations Math., pages 391–421. North-Holland, Amsterdam-New York, 1979.
Lógicos em Quarentena
Speaker: Daniele Nantes
Title: Nominal Equational Problems
Time and Date: Wednesday, October 28th 14:00 GMT-5
Abstract: We consider nominal equational problems of the form \exists \vec{W} \forall \vec{Y} :P, where P consists of conjunctions and disjunctions of equations s\approx_\alpha t (read: ``s is \alpha-equivalent to t''), freshness constraints a# t (read: ``a is fresh for t'') and their negations s \not \approx_\alpha t and \neg(a# t), where a is an atom and s, t are nominal terms. In addition to existential and universally quantified variables, problems can also have free variables. We give a general definition of solution parametric on the algebra used to provide semantics to the problem, and a set of simplification rules that can be used to compute solutions in the nominal term algebra. For the latter, we define notions of solved form from which solutions can be easily extracted, and show that the simplification rules are sound, preserving and complete. With a particular strategy of application for the rules, the simplification process terminates, specifying an algorithm to solve nominal equational problems. In particular, the algorithm can be used to decide the validity of a first-order equational formula in the nominal term algebra.
Speaker: Marko Malink (NYU) and Anubav Vasudevan (University of Chicago)
Title: Peripatetic Connexive Logic
Time and Date: Wednesday, October 28th 15:00 GMT-5
Link: https://iu.zoom.us/j/95326399432?pwd=VmVUWGxHeG5KQjEzQVozb3pCRHJVZz09
Meeting ID: 953 2639 9432
Password: SmullyanAbstract: Ancient Peripatetic logicians sought to establish the priority of categorical over propositional logic by reducing various modes of propositional reasoning to categorical form. In the context of such a reduction, the conditional φ-->ψ is interpreted as a categorical proposition A holds of all B, in which B corresponds to the antecedent φ and A to the consequent ψ. Under this interpretation, Aristotle’s law of subalternation (A holds of all B, therefore A holds of some B) corresponds to a version of Boethius' Thesis (φ-->ψ, therefore not-(φ-->not-ψ)). Jonathan Barnes has argued that this consequence renders the Peripatetic program of reducing propositional to categorical logic inconsistent. In this paper, we will challenge Barnes's verdict. We will argue that the system of connexive logic that most closely aligns with the reduction of propositional to categorical logic envisioned by the ancient Peripatetics is both non-trivial and consistent. Such consistency is achieved by limiting the system to first-order conditionals, in which both the antecedent and the consequent are simple categorical propositions.
UConn Logic Group
Speaker: Ethan Brauer, Øystein Linnebo, and Stewart Shapiro
Title: Divergent potentialism: A modal analysis with an application to choice sequences
Time and Date: Friday, October 30 10:00 GMT-5
Abstract: Modal logic has recently been used to analyze potential infinity and potentialism more generally. However, this analysis breaks down in cases of divergent possibilities, where the modal logic is weaker than S4.2. This talk has three aims. First, we use the intuitionistic theory of free choice sequences to motivate the need for a modal analysis of divergent potentialism and explain the challenge of connecting the ordinary theory of choice sequences with our modal explication. Then, we use the so-called Beth-Kripke semantics for intuitionistic logic to overcome those challenges. Finally, we apply the resulting modal analysis of divergent potentialism to make choice sequences comprehensible in classical terms.Link: https://us02web.zoom.us/j/85801711433?pwd=QVBTYW1UaUJsMytJV1ZnaUEweDJUQT09
Meeting ID: 858 0171 1433
Passcode: choice
Berkeley Logic Colloquium
Speaker: Anush Tserunyan
Title: A backward ergodic theorem and its forward implications
Abstract: In the classical pointwise ergodic theorem for a probability measure preserving (pmp) transformation T, one takes averages of a given integrable function over the intervals {x, T(x), T2(x), …, Tn(x)} in front of the point x. We prove a “backward” ergodic theorem for a countable-to-one pmp T, where the averages are taken over subtrees of the graph of T that are rooted at x and lie behind x (in the direction of T − 1). Surprisingly, this theorem yields forward ergodic theorems for countable groups, in particular, one for pmp actions of finitely generated groups, where the averages are taken along set-theoretic (but right-rooted) trees on the generating set. This strengthens Bufetov’s theorem from 2000, which was the most general result in this vein. This is joint work with Jenna Zomback.Time and Date: Friday, October 30 18:10 GMT-5
Shay Logan
Logic and Metaphysics Workshop (CUNY)
Speaker: Heinrich Wansing
Title: A Note on Synonymy in Proof-Theoretic Semantics
Time and Date: Monday, November 2nd, 15:15 GMT-6
Link: https://gc-cuny.zoom.us/j/95564820696?pwd=RWRObUN3RFQ1M0ZBS0lKR2ZpK3lKQT09
Meeting ID: 955 6482 0696Passcode: 381972
Abstract: The topic of identity of proofs was put on the agenda of general (or structural) proof theory at an early stage. The relevant question is: When are the differences between two distinct proofs (understood as linguistic entities, proof figures) of one and the same formula so inessential that it is justified to identify the two proofs? The paper addresses another question: When are the differences between two distinct formulas so inessential that these formulas admit of identical proofs? The question appears to be especially natural if the idea of working with more than one kind of derivations is taken seriously. If a distinction is drawn between proofs and disproofs (or refutations) as primitive entities, it is quite conceivable that a proof of one formula amounts to a disproof of another formula, and vice versa. The paper develops this idea.
Helsinki Logic Seminar
Speaker: Ralf Schindler
Title: Martin's Maximum^++ implies the P_max axiom (*)
Time and Date: Wednesday, November 4th 04:00 GMT-6
Abstract: Forcing axioms spell out the dictum that if a statement can be forced, then it is already true. The P_max axiom (*) goes beyond that by claiming that if a statement is consistent, then it is already true. Here, the statement in question needs to come from a resticted class of statements, and "consistent" needs to mean "consistent in a strong sense." It turns out that (*) is actually equivalent to a forcing axiom, and the proof is by showing that the (strong) consistency of certain theories gives rise to a corresponding notion of forcing producing a model of that theory. This is joint work with D. Asperó building upon earlier work of R. Jensen and (ultimately) Keisler's "consistency properties."
Lógicos em Quarentena
Speaker: Carlos Olarte
Title: The L-Framework*: Structural Proof Theory in Rewriting Logic
Time and Date: Thursday, November 5th 13:00 GMT-6
Abstract: Structural properties such as admissibility and invertibility of rules are crucial in proof theory, and they can be used for establishing other key properties such as cut-elimination and completeness of focusing in sequent systems. Finding proofs for these properties requires inductive reasoning over the provability relation, which is often quite elaborated, exponentially exhaustive, and error prone. We propose automatic procedures for proving structural properties of sequent systems. Our techniques are based on the rewriting logic metalogical framework, and use rewrite- and narrowing-based reasoning. They have been fully mechanized in Maude and the resulting framework is generic and modular since cut-freeness, admissibility, and invertibility can be proved incrementally. The L-Framework achieves a great degree of automation when used on several sequent systems. Case studies include intuitionistic, classical, substructural and modal logics.
Logic Webinar@IITK
Speaker: Prof Friedrich Wehrung (Universite de Caen, France)
Title: Purity and freshness (in categorial model theory)
Time and Date: Friday, November 6th 04:30 GMT-6
Link: https://zoom.us/j/91420898789?pwd=WnRqWGhYRVEvd0pwZXpkaEd6WDB1dz09
Meeting ID: 914 2089 8789
Passcode: 874519
Abstract: The aim of this talk is to introduce the basic concepts of a technique enabling to prove that certain naturally defined classes of structures are ``intractable’’ in the sense that they cannot be described as classes of models of any infinitely formula (or more generally, of any class of $L_{\infty,\lambda}$ formulas, for any infinite cardinal $\lambda$).
The main idea is that for any suitably ``continuous’’ functor $F$, from the category of all subsets of some set $X$ and one-to-one maps between those, to a category $C$ of models, all large enough morphisms in the range of $F$ are elementary embeddings with respect to large infinitary languages.
This yields the concept of anti-elementarity, which entails intractability.
In particular, this applies to classes such as (1) the class of all posets of finitely generated ideals in rings, (2) the class of all ordered $K_0$ groups of unit-regular rings, (3) the class of all lattices of principal $l$-ideals of abelian lattice-ordered groups (yields a negative answer to the so-called MV-spectrum problem).