Invited speakers at AiML-2008 will include the following:
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.
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.
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.
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.
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.