Coming Friday, October 25, LEGO will feature Balder ten Cate with a try-out talk for a conference in London (KCL)

Abstract:

Craig's interpolation property is generally considered to be a desirable property of logics, comparable to completeness and decidability. This talk will be about interpolation for extensions of the basic modal language, focusing on hybrid languages. That is, extensions of the basic modal language involving reference to individual states.

We will discuss a number of results of the following form:

L' is the least expressive extension of L that has interpolation

For example, every extension of the basic modal language with a 'difference operator' that has interpolation (on a class of frames K), has full first-order expressivity (on the class of frames K).

As a corollary, given a reasonable definition of 'hybrid language', we will show that every hybrid language with interpolation is undecidable.