|14.00 - 14.40 Hs.||Patrick Blackburn. Introducing Hybrid Logics|
In this talk we will discuss the good
side of modal logic, the bad side of modal logic, and how hybrid
logic takes the good and fixes the bad.
In essence, modal logic is a simple formalism for working with relational structures (or multigraphs). But modal logic has no mechanism for referring to or reasoning about the individual nodes in such structures, and this lessens its effectiveness as a representation formalism. In their simplest form, hybrid logics are upgraded modal logics in which reference to individual nodes is possible.
But hybrid logic is a rather unusual modal upgrade. It pushes one simple idea as far as it will go: represent all information as formulas. This turns out to be the key needed to draw together a surprisingly diverse range of work (for example, feature logic, description logic and labelled deduction). Moreover, it displays a number of knowledge representation issues in a new light, notabley the importance of sorting.
|14.50 - 15.30 Hs.||Maarten Marx. Complexity of Basic Hybrid Logics|
Already the basic hybrid language provides the tools needed to
design an efficient proof system. In particular the
satisfiability operator @ let us internalize, in a
straightforward way, the key ideas behind labeled deduction and
But the basic hybrid language also has an excellent behavior in terms of complexity: the addition of nominals and @ to the basic modal logic K enhace its expressive power without modifying its complexity (except, perhaps, by a polynomial).
In this talk we will introduce model theoretic tools to investigate the complexity of the basic hybrid language and its multi-modal and tense logical cousins.
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