On Monday, April 7, there will be three talks on the general theme of logic and knowledge.

At 10:10, Jelle Gerbrandy will speak on "Common Knowledge and Belief Change", in Ballantine 137.

The remaining two talks will be in Lindley Hall 101. At 11:15, Alexandru Baltag will speak on "Modal Logic and Topology: Multidimensional Frames". And at 12:30, Michael Dunn will speak on "Partiality and Its Dual."

There are some abstracts posted below. For more on any of these, please write to Larry Moss.

Abstract for Jelle Gerbrandy's talk "Common Knowledge and Belief Change"

This talk consists of two parts which are both about the relation between information states of a group of agents considered seperately and the common ground in that group. In the first part, I will show how Jon Barwise's situation-theoretic analysis of several definitions for common knowledge (in `On the model theory of Common Knowledge') fares in a more classical possible worlds framework. It turns out that the three definitions are equivalent when considered in a classical framework.

Abstract for Alexandru Baltag's talk "Modal Logic and Topology: Multidimensional Frames"

I am proposing a modal logic with indexed modalities, having two natural interpretations: "n-dimensional Kripke frames" and n-dimensional topological spaces(-a generalization for McKinsey's semantics for S4).The two natural interpretations: "n-dimensional Kripke frames" and n-dimensional topological spaces(-a generalization for McKinsey's semantics for S4). The language considered can express various modal (e.g.connectivity, antisymmetry, irreflexivity) and topological (e.g. "Hausdorff") properties, that are not expressible in the standard modal language. For n=2 (square frames), I have a complete and decidable system for S5-frames, which might have some knowledge-theoretical relevance. This logic can be regarded as a generalization of the so-called "cylindric modal logic" (see Yde Venema, Cylindric Modal Logic, the Journal of Symbolic Logic, vol.60, no. 2 (1995),pp.591-623 ).

Abstract for Michael Dunn's talk "Some Partial Logics and their Duals"

I explore the impact of allowing truth value assignments to be underdetermined (no truth values) and overdetermined (both truth values), examine some natural consequence relations that arise from these decisions, show how they are interrelated, and in turn related to existing non-classical logics in the literature. These include Lukasiewicz's three-valued logic, Kleene's three valued logic, Anderson and Belnap's (first-degree) relevant entailments, Priest's "Logic of Paradox," and the first-degree fragment of the Dunn-McCall system "R-mingle." None of these systems have nested implications, and I investigate natural extensions containing nested implications, all of which can be viewed as coming from natural variations on Kripke's semantics for intuitionistic logic. I shall also briefly mention applications in terms of epistemic logic.