Hybrid-Logical Proof Theory: With an Application to False-Belief Tasks

Torben Braüner (Roskilde) gives a talk at the MCMP Colloquium (17 January, 2013) titled "Hybrid-Logical Proof Theory: With an Application to False-Belief Tasks". Abstract: Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model (where the points represent times, possible worlds, states in a computer, or something else). This additional expressive power is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There is little consensus about proof-theory for ordinary modal logic. Many modal-logical proof systems lack important properties and the relationships between proof systems for different modal logics are often unclear. In my talk I will demonstrate that these deficiencies are remedied by hybrid-logical proof-theory. In my talk I first give a brief introduction to hybrid logic and its origin in Arthur Prior's temporal logic. I then describe essential proof-theoretical results for natural deduction formulations of hybrid logic. Finally, I show how a proof system for hybrid logic can be used to formalize what are called false-belief tasks in cognitive psychology.