Content
Title and Abstracts of Tutorial Lectures
 
New insights into Probabilistically Checkable Proofs (PCPs)
by Eli Ben-Sasson (Comput Sci Dept, Technion Inst of Technology, Israel)
  We revisit the celebrated PCP Theorem in light of recent simplifications to its proof and discuss new applications to error correcting codes and sub-linear time proof verification.
Reminder: The celebrated PCP Theorem was proved in the early 1990's [Arora,Safra;Arora,Lund,Motwani,Sudan,Szegedy]. Informally speaking, it says there is a format of writing proofs and a probabilistic method of verifying their correctness. In this method the verifier needs to read only a constant number of random bits from the proof (independent of the proof length) to test its validity. Good proofs of true statements are accepted with probability one, whereas any purported "proof" of a false statement is rejected with probability of at least one third.
Operational Theories of Sets
by Solomon Feferman (Depts of Mathematics and Philosophy, Stanford University, USA)
  In a kind of extension of von Neumann's axiomatization (VN) of set theory with functions at the level of classes, the language of set theory is here augmented by variables for operations in an untyped partial combinatory algebra over sets. Like the earlier approach, this language lends itself to a more natural formulation of standard set-theoretical axioms, such as those of Replacement and Choice as well as the usual closure conditions on sets. But the present formalism also has the advantage of much greater freedom than the VN approach since it permits the representation of higher order closure conditions. In particular, operational set theory is applied to obtain unified formulations of various "small" large cardinal axioms (i.e., those consistent with V=L), such as Mahlo, weakly compact, etc., in terms that are abstractly the same whether in usual set theory with the power-set operation or admissible set theory without it. The latter replaces analogue formulations in terms of recursive functions on admissible sets and schematic reflection principles.
The expanding notion of algorithm
by Yuri Gurevich (Microsoft Research, USA)
  Classical computation theory, including computational complexity theory, was a great advance in the study of algorithms but the theory has severe limitations that make it inadequate for modern engineering. In particular, the behavior of an algorithm is restricted to the input/output relation, and inputs are supposed to be string-codable. Behavioral computation theory, aka the theory of abstract state machines, overcomes these restrictions. We explain the basics of behavior computation theory and mention various applications. For those who want to do a little reading ahead of time, the best place to start is article #141 at speaker's webpage. For a broad-brush picture see #164 and #174. For those who have a greater appetite for reading and who are unafraid of technical details, there are articles #157, #166, #170, #171, #176.
Proof Mining: Applications of Proof Theory to Analysis
by Ulrich Kohlenbach (Department of Mathematics, Darmstadt University of Technology, Germany)
  In recent years (though influenced by papers of G. Kreisel going back to the 50's) an applied form of proof theory systematically evolved with sometimes is called "Proof Mining". This approach is concerned with the extraction of both new effective data as well as new qualitative information (independence of solutions from certain parameters) from typically ineffective proofs. A particularly fruitful area of applications has been functional analysis. This 2-part tutorial will give a survey on the logical background and applications of this approach.
(tba)
by Thomas Scanlon (Mathematics Department, University of California at Berkeley, USA)
Symbolic Analysis of Computer Network Security Protocols
by Andre Scedrov (Department of Mathematics, University of Pennsylvania, USA)
  While modern cryptography relies on applications of number theory, probability theory, and computational complexity, the methods of symbolic logic are contributing in significant ways to the wider area of computer security, including network security, access control, and policy languages. We will explore some of the applications of the abstract symbolic methods in these areas and in particular in the analysis of network security protocols. We will also consider several ways in which abstract symbolic methods relate to mathematical applications in cryptography.
As an example of this methodology we describe joint work with I. Cervesato, A.D. Jaggard, J.-K. Tsay, and C. Walstad on a vulnerability in PKINIT, the public key extension of the widely deployed Kerberos 5 authentication protocol. The discovery of this flaw caused an internet standards body IETF to change the specification of PKINIT and caused Microsoft to release a security update for a number of Windows operating systems. A Microsoft Security Bulletin which mentions this work is available on http://www.microsoft.com/technet/security/bulletin/MS05-042.mspx We discovered this flaw as part of an ongoing symbolic analysis of the Kerberos protocol suite, and we have verified in the symbolic model several fixes to PKINIT that prevent our attack.

Title and Abstracts of Invited Talks
 
New insights into Probabilistically Checkable Proofs (PCPs)
by Eli Ben-Sasson (Comput Sci Dept, Technion Inst of Technology, Israel)
  We revisit the celebrated PCP Theorem in light of recent simplifications to its proof and discuss new applications to error correcting codes and sub-linear time proof verification.
Reminder: The celebrated PCP Theorem was proved in the early 1990's [Arora,Safra;Arora,Lund,Motwani,Sudan,Szegedy]. Informally speaking, it says there is a format of writing proofs and a probabilistic method of verifying their correctness. In this method the verifier needs to read only a constant number of random bits from the proof (independent of the proof length) to test its validity. Good proofs of true statements are accepted with probability one, whereas any purported "proof" of a false statement is rejected with probability of at least one third.
Operational Theories of Sets
by Solomon Feferman (Depts of Mathematics and Philosophy, Stanford University, USA)
  In a kind of extension of von Neumann's axiomatization (VN) of set theory with functions at the level of classes, the language of set theory is here augmented by variables for operations in an untyped partial combinatory algebra over sets. Like the earlier approach, this language lends itself to a more natural formulation of standard set-theoretical axioms, such as those of Replacement and Choice as well as the usual closure conditions on sets. But the present formalism also has the advantage of much greater freedom than the VN approach since it permits the representation of higher order closure conditions. In particular, operational set theory is applied to obtain unified formulations of various "small" large cardinal axioms (i.e., those consistent with V=L), such as Mahlo, weakly compact, etc., in terms that are abstractly the same whether in usual set theory with the power-set operation or admissible set theory without it. The latter replaces analogue formulations in terms of recursive functions on admissible sets and schematic reflection principles.
The expanding notion of algorithm
by Yuri Gurevich (Microsoft Research, USA)
  The notion of algorithm is key in computer science. Computer programs are algorithms. This includes e.g. operating systems. Programming languages themselves can be viewed as universal algorithms that treat a particular program as part of input. A foundational problem arises: What is an algorithm? But the notion of algorithm expands and deepens as the computer revolution advances. In addition to classical sequential algorithms, we have now concurrent algorithms, distributed algorithms, real-time algorithms. Algorithms grow in size and complexity raising numerous software concerns like fault tolerance and maintainability. The variety of algorithms is bewildering. The foundational problem may seem hopeless. And yet there has been a substantial progress in the area, partially covered in our WoLLIC 2006 tutorial. Here we concentrate on issues that are not covered in the tutorial, in particular on distributed algorithms and on the question what the notion of algorithm is in its full generality. To what extent one can anticipate the limit point of the expansion of the notion of algorithm?
A logical uniform boundedness principle for abstract metric and hyperbolic spaces
by Ulrich Kohlenbach (Department of Mathematics, Darmstadt University of Technology, Germany)
  This talk will present some of the most recent applications of logical metatheorems developed in the course of proof mining to functional analysis. We will also discuss some new proof theoretic results which were prompted by these applications. This includes a powerful "nonstandard" uniform boundedness principle for abstract metric and hyperbolic spaces.
(tba)
by Thomas Scanlon (Mathematics Department, University of California at Berkeley, USA)
Symbolic Analysis of Computer Network Security Protocols
by Andre Scedrov (Department of Mathematics, University of Pennsylvania, USA)
  While modern cryptography relies on applications of number theory, probability theory, and computational complexity, the methods of symbolic logic are contributing in significant ways to the wider area of computer security, including network security, access control, and policy languages. We will explore some of the applications of the abstract symbolic methods in these areas and in particular in the analysis of network security protocols. We will also consider several ways in which abstract symbolic methods relate to mathematical applications in cryptography.
As an example of this methodology we describe joint work with I. Cervesato, A.D. Jaggard, J.-K. Tsay, and C. Walstad on a vulnerability in PKINIT, the public key extension of the widely deployed Kerberos 5 authentication protocol. The discovery of this flaw caused an internet standards body IETF to change the specification of PKINIT and caused Microsoft to release a security update for a number of Windows operating systems. A Microsoft Security Bulletin which mentions this work is available on http://www.microsoft.com/technet/security/bulletin/MS05-042.mspx We discovered this flaw as part of an ongoing symbolic analysis of the Kerberos protocol suite, and we have verified in the symbolic model several fixes to PKINIT that prevent our attack.

   
List of Accepted Papers
 
Alexandru Baltag and Sonja Smets
Conditional Doxastic Models: a Qualitative Approach to Dynamic Belief Revision
Tim Fernando
Situations as Strings
Makoto Kanazawa
Abstract Families of Abstract Categorial Languages
Laurentiu Leustean
Proof Mining in R-trees and Hyperbolic Spaces
Larisa Maksimova
To Interpolation Problem in Paraconsistent Extensions of Minimal Logic
Aleksey Nogn and Alexei Kopylov
Formalizing Type Operations Using the ``Image'' Type Constructor
Bryan Renne
Propositional Games with Explicit Strategies
Yoshitaka Suzuki
Additive Consolidation with Maximal Change
Hans-Joerg Tiede and Stephan Kepser
Monadic Second-Order Logic over Trees and Deterministic Transitive Closure Logics
Petrucio Viana, Renata P. de Freitas, Paulo A.S. Veloso and Sheila R.M. Veloso
Reasoning with Graphs
Dan Willard
The Axiom System I$\Sigma_0$ Manages to Simultaneously Obey and Evade the Herbrandized Version of the Second Incompleteness Theorem

   
Book Exhibition
 
The following publishers are expected to be exhibiting various books from their catalogue, prospectuses, journal samples, etc., and there will be a chance to order items at promotional prices. It is likely that a few other international publishers will also take part in the book exhibit.
  The MIT Press click here
Springer-Verlag click here
A K Peters click here
Kluwer Academic Publishing click here
Cambridge University Press click here
CSLI Publications (Stanford University) click here
Oxford University Press click here
World Scientific click here
 
Call for Papers
 
The 13th Workshop on Logic, Language, Information and Computation (WoLLIC'2006), the thirteenth version of a series of workshops which started in 1994 with the aim of fostering interdisciplinary research in pure and applied logic, will be held at Stanford, California, USA, from July 18th to 21st, 2006.
Contributions are invited in the form of short papers (12 10pt pages) in all areas related to logic, language, information and computation, including:
  • context and situation theory
• formal semantics of natural language
• information update and belief revision; agent systems
• logic, arithmetic and complexity
• logic and databases
• logic and game theory
• logic and verification
• logic programming and algebraic semantics
• logical grammars
• model theory, descriptive complexity
• proof complexity
• proof theory, lambda calculus, categorical logic
• real computation, algebraic complexity
• set theory
• zero-knowledge proofs, probabilistic proofs, randomized computation
Scientific Sponsorship
The 13th WoLLIC has the scientific sponsorship of:
  Association for Symbolic Logic (ASL)
Interest Group in Pure and Applied Logics (IGPL)
European Association for Logic, Language and Information (FoLLI)
European Association for Theoretical Computer Science (EATCS)
Sociedade Brasileira de Computação (SBC)
Sociedade Brasileira de Lógica (SBL)
Guest Speakers
  Eli Ben-Sasson (Comput Sci Dept, Technion Inst of Technology, Israel)
Solomon Feferman (Depts of Mathematics and Philosophy, Stanford University, USA)
Yuri Gurevich (Microsoft Research, USA)
Ulrich Kohlenbach (Department of Mathematics, Darmstadt University of Technology, Germany)
Thomas Scanlon (Mathematics Department, University of California at Berkeley, USA)
Andre Scedrov (Department of Mathematics, University of Pennsylvania, USA)
Location
CSLI - Center for the Studies of Language and Information, Stanford
  Cordura Hall
210 Panama Street
Palo Alto, CA 94305
Submission
Papers (up to 12 pages 10pt) must be submitted (NEW DEADLINE!) by MARCH 7th, 2006.
Papers must be written in English and give enough detail to allow the programme committee to assess the merits of the work. Papers should start with a brief statement of the issues, a summary of the main results, and a statement of their significance and relevance to the workshop. References and comparisons with related work is also expected. Technical development directed to the specialist should follow. Results must be unpublished and not submitted for publication elsewhere, including the proceedings of other symposia or workshops. One author of each accepted paper will be expected to attend the conference in order to present it. Authors will be notified of acceptance by APRIL 21st, 2006, and final versions will have to be delivered (in LaTeX format) by MAY 12th, 2006. The abstracts of the papers will be published in a "Conference Report" section of the Logic Journal of the IGPL (ISSN 1367-0751) (Oxford Univ Press) as part of the meeting report. The proceedings will appear as a volume in the Elsevier series Electronic Notes in Theoretical Computer Science (ISSN 1571-0661). Full version of papers will be refereed again for publication in a special issue of the Annals of Pure and Applied Logic (TO BE CONFIRMED).
Instructions for Submission
Visit the EasyChair submission page for WoLLIC'2006.
  There are two zones: (1) Registered User and (2) New User. The first time you use the system you will have to use the New User fields. Shortly after that a password will be emailed to you. You can use this password to access the system thereafter as a registered user.
On this page you can enter the title, authors, contact author information and abstract. The abstract has to be under 300 words. It can be typed in directly or pasted in with a browser. You can upload your paper (extended abstract) using the web page. Using this submission system you can manage your papers submitted to WoLLIC'2006. You can submit new papers, resubmit previously submitted papers, or change information about authors.
Extended abstracts must be in postscript or pdf format.
The NEW deadline for submitting extended abstracts is March 7th, 2006 by midnight EST.
Student Grants
ASL sponsorship of WoLLIC'2006 also will permit student ASL members to apply for (limited) ASL travel funds that we hope to make available for sponsored meetings that take place in 2006 (see http://www.aslonline.org/studenttravelawards.html).
Important Dates
Submission:
March 7, 2006: (NEW!) Paper submission deadline
April 21, 2006: Author notification
May 12, 2006: Delivery of final version