About the Spring School
The spring school is aimed at advancing logic and its applications by crosscommunity interactions among subareas in logic. The school provides nine lectures including three invited tutorials. These are aimed at master and PhD students in mathematics and computer science–especially logic, but we welcome participants from all areas.
The Workshop on Mathematical Logic is also held as part of the spring school.
Venue
The school takes place at Ishikawa Prefectural Museum of Art, which is located in the famous sightseeing spot of Kanazawa, including Kenrokuen (Six Attributes Garden), Kanazawa Castle, 21st Century Museum of Contemporary Art, etc... See Kanazawa Tourist Information Guide for more places (in particular, home → tour guide → 01).
 HirosakaBekkan of Ishikawa Prefectural Museum of Art
 21 Dewamachi, Kanazawa, Ishikawa 9200963, Japan
Registration Fee
10,000 JPY (only in cash). The fee includes lunches (6th – 8th), banquet (8th), and beverage at reception (5th).
Materials
Materials will be uploaded to here.Program
Mon  Tue  Wed  Thu  Fri  

9:00 – 12:00  MPA  CL  PE  workshop  
lunch  
14:00 – 15:20  ART  CCR  NLFS  SS  workshop 
coffee break  
15:40 – 17:00  ART  CCR  NLFS  SS (–17:30) 
workshop 
reception  banquet 
Monday
Tuesday
Wednesday
Thursday
9:00–12:00  PE: Program
Extraction Ulrich Berger In this tutorial I will give a gentle introduction to program extraction from proofs. We will study a proof calculus for constructive (or intuitionistic) firstorder logic and show that, based on ideas of Kleene and Kreisel, one can extract from every proof a program that "realizes" the proven formula, that is, the program solves the computational problem expressed by the formula. In addition, one obtains a proof that the extracted program is indeed a correct solution to the problem. Hence, program extraction is a method for program generation and verification at the same time. We will discuss some applications, mainly in constructive analysis, and demonstrate some tools for carrying out program extraction in practice implemented in the proof systems Minolg (Schwichtenberg) and Coq (Letouzey). If time permits we will also look into other methods for extracting useful information from proofs, most notably, the Friedman/Dragalin method for extracting programs from classical, that is, nonconstructive, proofs, and a monotone version of Goedel's Dialectica Interpretation for extracting bounds in approximation and fixed point theory (Kohlenbach). 
14:00–17:00  SS: Special Session 
Automated Proofs of Confluence of Term Rewrite Systems Bertram Felgenhauer Term rewrite systems are a simple but general model of computation. Confluence is a property of rewrite systems that ensures results (normal forms) to be unique. In recent years, there is increased interest in automatically proving confluence and nonconfluence of TRSs, with a number of actively developed tools (ACP, Saigawa, ...). In this talk I will give an overview of confluence criteria employed in our tool, CSI, and demonstrate how proving confluence is related to rewriting equational proofs into so called valley proofs. 

A Unified View of PTS's Conversion Vincent Siles Pure Type Systems (or PTS) are a generic framework which allow to deal with several systems (Simply Typed Lambda Calculs, System F, Calculus of Constructions,...) all at once. Those systems mostly rely on an untyped notion of equality called conversion, which is based on program evaluation. To prove some theoretical properties of those systems, like their consistency in presence of external axioms, we may need to type the process of evaluation, leading to the notion of PTS with "judgmental equality". However the theory behind this typed equality is strangely difficult to establish: the proofs of Confluence, Subject Reduction or Injectivity of Products are all linked together in a circular dependency. In this talk, I'll do a survey of the several result towards proving this equivalence, from Adams' first proof for functional PTS to my own PhD work which extends this result to *all* PTS. This result involves the description of a third "intermediate" system we called PTS with annotated typed reduction, which has all the necessary information to derive properties of PTS, even with a typed conversion. 

Gentzen's Consistency Proofs for Arithmetic Annika Siders The earliest proofs of the consistency of Peano arithmetic were presented by Gentzen, who worked out a total of four proofs between 1934 and 1939. In his best known proof from 1938 he gives a reduction procedure for derivations of the empty sequent, which represents a contradiction in the system. The proof shows that if there exists a derivation of the empty sequent, then there exists another less complex derivation, and another derivation, etc. He uses a heightline argument to construct the less complex derivations. It will be shown that the heightline construction is possible to avoid by a Howardstyle vector assignment, which makes the reductions resemble proofs of direct cut elimination without multicut. 

Hierarchies of Sets in Classical and Constructive Set
Theories Albert Ziegler By iterating the powerset operation, the cumulative von Neumann hierarchy partitions the set theoretic universe into a union of sets, indexed by the ordinals. This description of the universe is a basic ingredient underlying a large part of proofs and conceptions of classical set theory. However, considering set theories with constructive instead of classical logic which lack the powerset axiom (e.g. CZF instead of ZF), the potency of the hierarchy is severely reduced as its stages cannot be proved to be sets without using the principle of the excluded middle. This talk proposes a modified hierarchy and aims at demonstrating its validity by showing how its consequences for the role of ordinals in constructive set theory can be harnessed to obtain new results. 

Characterization, Definability and Separation via
Saturated Models Facundo Matias Carreiro Three important results about the expressivity of a modal logic L are the Characterization Theorem (that identifies L as a fragment of a better known logic), the Definability theorem (that provides conditions under which a class of Lmodels can be defined by a formula or a set of formulas of L), and the Separation Theorem (that provides conditions under which two disjoint classes of Lmodels can be separated by a class definable in L). In this talk I will show general conditions under which these results can be established for a given choice of model class and modal language whose expressivity is below first order logic. Besides some basic constrains that most modal logics easily satisfy, the fundamental condition that we require is that the class of omegasaturated models in question has the HennessyMilner property with respect to the notion of observational equivalence under consideration. 

18:30 –  banquet: Waraiya 1616 Katamachi, Kanazawa map 
Friday
Please see here for the workshop programs.Lecturers
Lecturers
 Ulrich Berger (Swansea University, UK)
 Nao Hirokawa (JAIST)
 Hajime Ishihara (JAIST)
 Sara Negri (University of Helsinki, Finland)
 Mizuhito Ogawa (JAIST)
 Dirk Pattinson (Imperial College London, UK)
 Katsuhiko Sano (JAIST)
 Christian Sternagel (JAIST)
 Satoshi Tojo (JAIST)
Guest Speakers
 Facundo Matias Carreiro (University of Amsterdam, Netherlands)
 Bertram Felgenhauer (University of Innsbruck, Austria)
 Annika Siders (University of Helsinki, Finland)
 Vincent Siles (Göteborg University)
 Albert Ziegler (University of Leeds, UK)
Access to Kanazawa
from Tokyo Narita Airport to Kanazawa Station:
Please take a limousine bus to Haneda Airport (HND), fly to Komatsu Airport (KMQ), and then take an airport bus (time table) to Kanazawa. Note that there are also direct flights between Narita and Komatsu (but not many).
from Kansai International Airport to Kanazawa Station:
Please take a suitable train (type "Kansai Airport" in "From" and "Kanazawa" in "To"). Since trains are going frequently, you can simply take the next one. You must change trains at ShinOsaka. For general information, please see this website. The site describes how to get to Fukui (a city between ShinOsaka and Kanazawa) in great detail, including instructions for buying tickets and changing trains.
from Kanazawa Station to Venue and Hotels around Venue:
The easiest way is to go by taxi (approx 1,000 yen) from the station.Accommodation
For convenience we recommend to stay at a hotel in the center of the city i.e., Katamachi or Korinbou, rather than ones around Kanazawa Station. Here we list a few hotels. APA hotels (search at www.expedia.com
with e.g. keywords ``Kanazawa Japan'')
 APA Hotel KanazawaKatamachi (from $42 per night)
 APA Hotel KanazawaChuou (from $49 per night)
 APA Villa Hotel KanazawaKatamachi (from $62 per night)
 Toyoko Inn Kanazawa Kenroku (from 4480JPY per night)
 Hotel Econo
 Hotel Econo Kanazawa Asper (from 3300JPY per night)
 Hotel Econo Kanazawa Katamachi (from 3700JPY per night)
Organising Committee
 Satoshi Tojo (JAIST) chair
 Nao Hirokawa (JAIST)
 Hajime Ishihara (JAIST)
 Mizuhito Ogawa (JAIST)
 Katsuhiko Sano (JAIST)