Aldo Antonelli’s last paper, “Completeness and Decidability of General First-Order Logic (with a Detour Through the Guarded Fragment)” is now out in the most recent issue of the Journal of Philosophical Logic.
This paper investigates the “general” semantics for first-order logic introduced to Antonelli (Review of Symbolic Logic 6(4), 637–58, 2013): a sound and complete axiom system is given, and the satisfiability problem for the general semantics is reduced to the satisfiability of formulas in the Guarded Fragment of Andréka et al. (Journal of Philosophical Logic 27(3):217–274, 1998), thereby showing the former decidable. A truth-tree method is presented in the Appendix.
It is published together with a note on it by Hajnal Andréka, Johan van Benthem, and István Németi in the same issue.
The ASL Spring Meeting will take place on Wednesday and Thursday at the Pacific APA in Seattle! Note that the ASL Reception will take place on Thursday, April 13, 5:00–7:00 p.m. There will be snacks and wine!
Here’s the program:
WEDNESDAY MORNING, APRIL 12, 9:00 A.M.–12:00 P.M.
Invited Speaker Session: MODALITY AND MODAL LOGIC
Chair: Audrey Yap
Peter Fritz (Universitetet i Oslo), A philosophical perspective on algebraic models for modal logics.
Fenrong Liu (Tsinghua University), Social epistemic logic.
Tamar Lando (Columbia University), Topology and measure in logics for point-free spaces.
WEDNESDAY AFTERNOON, APRIL 12, 1:00–4:00 P.M.
Invited Speaker Session: INTUITONISTIC MATHEMATICS AND LOGIC
Chair: Valeria de Paiva
Mark van Atten (Centre National de la Recherche Scientifique and Université Paris 4), Intuitionism and impredicativity.
Rosalie Iemhoff (Universiteit Utrecht), Quantifiers and functions in intuitionistic logic.
Joan Rand Moschovakis (Occidental College), Realizable extensions of Brouwer’s analysis.
THURSDAY MORNING, APRIL 13, 9:00 A.M.–12:00 P.M.
Chair: Richard Zach
Joachim Mueller-Theys, Defining and simplifying the second incompleteness theorem.
Valeria de Paiva and Harley Eades III, Dialectica categories for the Lambek calculus.
Ronald Fuller, First-order logic in 13th-century accounting systems.
Rachel Boddy (University of California, Davis), Fruitful definitions.
Michael McGrady, Garbage collection (GC), Gödel numbering, and periodicity in mathematical logic.
Fabio Lampert (University of California, Davis), On the expressive power of propositional two-dimensional modal logic.
Alexei Angelides (University of San Francisco), Weak arithmetics and the bar rule.
THURSDAY AFTERNOON, APRIL 13, 1:00 P.M.–4:00 P.M.
Special Session organized by the Committee on Logic Education: INCLUSIVENESS IN LOGIC EDUCATION
Chair: Alexei Angelides
Audrey Yap (University of Victoria), Symbolic logic, accessibility, and accommodation.
Fenrong Liu (Tsinghua University), Experiences and difficulties in teaching logic at Tsinghua University.
Nicole Wyatt (University of Calgary), The Open Logic Textbook.
Maureen Eckert (University of Massachussetts, Dartmouth), The Summer Program for Diversity in Logic: Some reflections.
THURSDAY EARLY EVENING, APRIL 13, 5:00 P.M.–7:00 P.M.
I made a textbook on incompleteness for my Logic III course. See it/read about it over at the Open Logic Project.
QUAD: QUantifiers And Determiners
Toulouse, Monday July 17 — Friday July 21: 17:00-18:30
ESSLLI 2017 workshop
deadline for submissions: 17 March 2017
submission website: https://easychair.org/conferences/?conf=quad2017
notification to authors: 15 April 2017
final version due: 19 May 2017
conference: 17-21 July 2017
The compositional interpretation of determiners relies on quantifiers — in a general acceptation of this later term which includes generalised quantifiers, generics, definite descriptions i.e. any operation that applies to one or several formulas with a free variable, binds it and yields a formula or possibly a generic term (the operator is then called a subnector, following Curry). There is a long history of quantification in the Ancient and Medieval times at the border between logic and philosophy of language, before the proper formalisation of quantification by Frege.
A common solution for natural language semantics is the so-called theory of generalised quantifiers. Quantifiers like « some, exactly two, at most three, the majority of, most of, few, many, … » are all described in terms of functions of two predicates viewed as subsets.
Nevertheless, many mathematical and linguistic questions remain open.
On the mathematical side, little is known about generalised , generalised and vague quantifiers, in particular about their proof theory. On the other hand, even for standard quantifiers, indefinites and definite descriptions, there exist alternative formulations with choice functions and generics or subnectors (Russell’s iota, Hilbert-Bernays, eta, epsilon, tau). The computational aspects of these logical frameworks are also worth studying, both for computational linguistic software and for the modelling of the cognitive processes involved in understanding or producing sentences involving quantifiers.
On the linguistic side, the relation between the syntactic structure and its semantic interpretation, quantifier raising, underspecification, scope issues,… are not fully satisfactory. Furthermore extension of linguistic studies to various languages have shown how complex quantification is in natural language and its relation to phenomena like generics, plurals, and mass nouns.
Finally, and this can be seen as a link between formal models of quantification and natural language, there by now exist psycholinguistic experiments that connect formal models and their computational properties to the actual way human do process sentences with quantifiers, and handle their inherent ambiguity, complexity, and difficulty in understanding.
All those aspects are connected in the didactics of mathematics and computer science: there are specific difficulties to teach (and to learn) how to understand, manipulate, produce and prove quantified statements, and to determine the proper level of formalisation between bare logical formulas and written or spoken natural language.
This workshop aims at gathering mathematicians, logicians, linguists, computer scientists to present their latest advances in the study of quantification.
Among the topics that wil be addressed are the following :
- new ideas in quantification in mathematical logic, both model theory and proof theory:
- choice functions,
- subnectors (Russell’s iota, Hilbert’s epsilon and tau),
- higher order quantification,
- quantification in type theory
- studies of the lexical, syntactic and semantic of quantification in various languages
- semantics of noun phrases
- generic noun phrases
- semantics of plurals and mass nouns
- experimental study of quantification and generics
- computational applications of quantification and polarity especially for question-answering.
- quantification in the didactics of mathematics and computer science.
Some recent relevant references:
- Anna Szabolcsi Quantification Cambridge University Press 2010
- Stanley Peters and Dag Westerstahl Quantifiers in Language and Logic Oxford Univ. Press 2010
- Mark Steedman Taking Scope – The Natural Semantics of Quantifiers MIT Press 2012
- Jakub Szymanik. Quantifiers and Cognition, Studies in Linguistics and Philosophy, Springer, 2015.
- Vito Michele Abrusci, Fabio Pasquali, and Christian Retoré. Quantification in ordinary language and proof theory. Philosophia Scientae, 20(1):185–205, 2016.
The program committee is looking for contributions introducing new viewpoints on quantification and determiners, the novelty being either in the mathematical logic framework or in the linguistic description or in the cognitive modelling. Submitting purely original work is not mandatory, but authors should clearly mention that the work is not original, and why they want to present it at this workshop (e.g. new viewpoint on already published results)
Submissions should be
- 12pt font (at least)
- 1inch/2.5cm margins all around (at least)
- less than 2 pages (references excluded)
- with an abstract of less then 100 words
- submitted in PDF by Easychair here: https://easychair.org/conferences/?conf=quad2017
In case the committee thinks it is more appropriate, some papers can be accepted as a poster with a lightning talk.
Final versions of accepted papers may be slightly longer. They will be published on line. We also plan to publish postproceedings
- Christian Retoré (Université de Montpellier & LIRMM-CNRS)
- Mark Steedman (University of Edinburgh)
- Vito Michele Abrusci (Università di Roma tre)
- Mathias Baaz (University of Technology, Vienna)
- Daisukke Bekki (Ochanomizu University, Tokyo)
- Oliver Bott (Universität Tübingen)
- Francis Corblin (Université Paris Sorbonne)
- Martin Hakl (Massachusetts Institute of Technology, Cambridge MA)
- Makoto Kanazawa (National Institute of Informatics, Tokyo)
- Dan Lassiter (Stanford University)
- Zhaohui Luo (Royal Holloway College, London)
- Alda Mari (CNRS Institut Jean Nicod, Paris)
- Wilfried Meyer-Viol (King’s college, London)
- Michel Parigot (CNRS IRIF, Paris)
- Anna Szabolcsi (New-York University)
- Jakub Szymanik (Universiteit van Amsterdam)
- Dag Westerstahl (Stockholm University)
- Bruno Woltzenlogel Paleo (University of Technology, Vienna)
- Richard Zach (University of Calgary)
- Roberto Zamparelli (Università di Trento)
It is with great sadness that we announce that Professor Jack Howard Silver died on Thursday, December 22, 2016. Professor Silver was born April 23, 1942 in Missoula, Montana. After earning his A.B. at Montana State University (now the University of Montana) in 1961, he entered graduate school in mathematics at UC Berkeley. His thesis, Some Applications of Model Theory in Set Theory, completed in 1966, was supervised by Robert Vaught. In 1967 he joined the mathematics department at UC Berkeley where he also became a member of the Group in Logic and the Methodology of Science. He quickly rose through the ranks, obtaining promotion to associate professor in 1970 and to full professor in 1975. From 1970 to 1972 he was an Alfred P. Sloan Research Fellow. Silver retired in 2010. At UC Berkeley he advised sixteen students, three of whom were in the Group in Logic (Burgess, Ignjatovich, Zach).
His mathematical interests included set theory, model theory, and proof theory. His production was not extensive but his results were deep. Professor Silver was skeptical of the consistency of ZFC and even of third-order number theory. As Prof. Robert Solovay recently put it: “For at least the last 20 years, Jack was convinced that measurable cardinals (and indeed ZFC) was inconsistent. He strove mightily to prove this. If he had succeeded it would have been the theorem of the century (at least) in set theory.”
He will be greatly missed.
Jack’s contributions to set theory, according to Wikipedia (used under CC-BY-SA):
Silver has made several deep contributions to set theory. In his 1975 paper “On the Singular Cardinals Problem,” he proved that if κ is singular with uncountable cofinality and 2λ = λ+ for all infinite cardinals λ < κ, then 2κ = κ+. Prior to Silver’s proof, many mathematicians believed that a forcing argument would yield that the negation of the theorem is consistent with ZFC. He introduced the notion of master condition, which became an important tool in forcing proofs involving large cardinals. Silver proved the consistency of Chang’s conjecture using the Silver collapse (which is a variation of the Levy collapse). He proved that, assuming the consistency of a supercompact cardinal, it is possible to construct a model where 2κ=κ++ holds for some measurable cardinal κ. With the introduction of the so-called Silver machines he was able to give a fine structure free proof of Jensen’s covering lemma. He is also credited with discovering Silver indiscernibles and generalizing the notion of a Kurepa tree (called Silver’s Principle). He discovered 0# in his 1966 Ph.D. thesis. Silver’s original work involving large cardinals was perhaps motivated by the goal of showing the inconsistency of an uncountable measurable cardinal; instead he was led to discover indiscernibles in L assuming a measurable cardinal exists.
[Photo ©Steven Givant. Picture taken on the occasion of the Tarski Symposium at UC Berkeley in 1971.]