The Department of Logic & Philosophy of Science Colloquium Series presents
"Probabilistic Semantics for Modal Logic"
with Tamar Lando, University of California, Berkeley
Friday, November 4, 2011
Social Science Tower, Room 777
The power of modal logic lies in its ability to capture reasoning about a host of modal notions. But whether we use modal languages to say something about necessity or the deontic ‘ought’, in the standard (Kripke) semantics for modal languages, formulas are either true or false for a given model. Lando develops the formal groundwork for a probabilistic semantics for propositional modal logic, introduced in recent years by Dana Scott. In a probabilistic model, each formula acquires not just a truth value, but a probability value between 0 and 1. Lando shows that this semantics is sound and complete for the well-known modal logic S4. Lando then goes on to show that we can give a probabilistic semantics not just for the basic modal language, but for more complex, multi-modal languages. Here, Lando focuses on ‘dynamic topological logics’ which have been at the heart of a research program aimed at using logic to study ‘dynamic space’ (or space that changes over time). Lando closes with some open questions about the philosophical applications of the probabilistic semantics.
For further information, please contact Patty Jones, email@example.com or 949-824-1520.