Advances in Modal Logic is an initiative aimed at presenting an up-to-date picture of the state of the art in modal logic and its many applications. The initiative consists of a conference series together with volumes based on the conferences.
The conference is the main international forum at which research on all aspects of modal logic is presented. The Advances in Modal Logic Initiative was founded in 1995 and the first AiML Conference was held in 1996 in Berlin, Germany. Since then the AiML Conference has been organised on an bi-annual basis with previous meetings being held in 1998 in Uppsala, Sweden, in 2000 in Leipzig, Germany (jointly with ICTL-2000), in 2002 Toulouse, France, in 2004 in Manchester, UK, and in 2006 in Noosa, Australia.
In 2008, Advances in Modal Logic will be organized by LORIA, le Laboratoire Lorrain de Recherche en Informatique et ses Applications (Lorraine Laboratory of IT Research and its Applications), in Nancy, France.
1) Invited speakers at AiML-2008 will include the following:
Mai Gehrke, Radboud Universiteit Nijmegen: "Using duality theory to export methods from modal logic".
Abstract: The rich theory of modal logic includes many powerful results and tools relating relational semantics and syntactic deduction. Mathematically, this may be seen as duality results and methods and these are pertinent in a much wider setting. The algebraic theory of canonical extensions, which formulates the canonical model construction of modal logic in an algebraic and widely available setting, has developed substantially over the last decade and this is the required 'Rosetta Stone' for translating the theorems, tools, and problems of modal logic to a wider setting. In this talk we give an introduction to this theory and illustrate the exportation with examples in substructural logic and the theory of finite semigroups and regular languages.
Guido Governatori, NICTA, Australia: "Labelled modal tableaux".
Abstract: Labelled tableaux are extensions of semantic tableaux with annotations (labels, indices) whose main function is to enrich the modal object language with semantic elements. This talk consists of three parts. In the first part we consider some options for labels: simple constant labels vs labels with free variables, logic depended inference rules vs labels manipulation based on a label algebra. In the second and third part we concentrate on a particular labelled tableaux system called KEM using free variable and a specialised label alebra. Specifically in the second part we show how labelled tableaux (KEM) can account for different types of logics (e.g., non-normal modal logics and conditional logics). In the third and final part we investigate the relative complexity of labelled tableaux systems and we show that the uses of KEM's label algebra can lead to speed up on proofs.
Agi Kurucz, King's College London: "Axiomatising many-dimensional modal logics".
Abstract: Many-dimensional propositional modal logics (multi-modal logics having productsof Kripke frames among their frames) have been studied in both pure modal logic and in computer science applications. They are also connected to algebras of relations in algebraic logic and to finite variable fragments of modal and intermediate predicate logics. In this talk we give a survey of axiomatisation problems for many-dimensional modal logics, discuss important techniques, and present some new results.
Lawrence Moss, Indiana University: "Relational syllogistic logics, and other connections between modal logic and natural logic".
Abstract: Syllogistic logics and modal logics share a number of features: they are both families of logics, both typically use relational semantics, both tend to be decidable, and both are motivated by the need to capture interesting fragments of reasoning. Despite the similarities, there is far less technical work on syllogistic logics than on modal logics. This talk will provide modal logicians with a look at much of the technical work on the other side, including: completeness theorems for some logics obtained via representations of orthoposets (rather than boolean algebras), connections to boolean modal logics, and the computational complexity of several logics (work done with Ian Pratt-Hartmann). People are interested in modal logic for many reasons; some of those reasons could also suggest an interest in this other work.
Michael Zakharyaschev, Birkbeck College: "Topology, connectedness, and modal logic".
Abstract: This talk presents a survey of topological spatial logics, taking as its point of departure the interpretation of the modal logic S4 due to McKinsey and Tarski. We consider the effect of extending this logic with the means to represent topological connectedness, focusing principally on the issue of computational complexity. In particular, we draw attention to the special problems which arise when the logics are interpreted not over arbitrary topological spaces, but over (low-dimensional) Euclidean spaces.
2) The following papers has been accepted for the conference.
Marta Bilkova, Alessandra Palmigiano and Yde Venema, "Proof systems for the coalgebraic cover modality".
Tim French and Hans van Ditmarsch, "Undecidability for arbitrary public announcement logic".
Rajeev Gore, Linda Postniece and Alwen Tiu, "Cut-elimination and proof-search for bi-intuitionistic logic using nested sequents".
Rajeev Gore and Revantha Ramanayake, "Valentini's Cut-elimination for Provability Logic Resolved".
Jens Ulrik Hansen, Thomas Bolander and Torben Brauner, "Many-Valued Hybrid Logic".
Andreas Herzig and Francois Schwarzentruber, "Proof-theoretic properties of logics of individual and group agency".
Savas Konur, "An Interval Logic for Natural Language Semantics".
Clemens Kupke, Alexander Kurz and Yde Venema, "A complete coalgebraic logic".
Antti Kuusisto, "A Modal Perspective on Monadic Second-Order Alternation Hierarchies".
Yavor Nenov and Dimiter Vakarelov, "Modal Logics for Mereotopological Relations"
Martin Otto and Robert Piro, "A Lindstrom Characterisation of the Guarded Fragment and of Modal Logic With a Global Modality".
Ilya Shapirovsky, "PSPACE-decidability of Japaridze's Poly-modal Logic".
Timofei Shatrov, "On the intermediate logic of open subsets of metric spaces".
Viorica Sofronie-Stokkermans, "Locality and subsumption testing in EL and some of its extensions".
Yoshinori Tanabe, Koichi Takahashi and Masami Hagiya, "A decision procedure for alternation-free modal mu-calculi"
Tero Tulenheimo, "Modal Logic of Time Division"
Sara L. Uckelman, "Three 13th-century views of quantified modal logic".
3) Accepted Abstracts
Francesco Belardinelli, "Counterpart Semantics at work: an Incompleteness Result in Quantified Modal Logic".
Anna Chernilovskaya and Mai Gehrke, "Generalised Kripke semantics for the Lambek-Grishin calculus".
Stas Kikot, "An extension of Kracht's theorem to monadic inductive formulas".
Hans Lycke, "Inconsistency-Adaptive Modal Logics: Part I"
Larisa Maksimova, "Restricted interpolation in modal and superintuitionistic logics"
Sergio Marcelino, "An algebraic generalization of Kripke structures"
John McCabe-Dansted, "A Tableau for RoBCTL".
Jacob Vosmaer, "Compact Hausdorff modal algebras are image-finite Kripke frames".