Graphs Identified by Logics with Counting

Graphs Identified by Logics with Counting

We classify graphs and, more generally, finite relational structures that are identified by C2, that is, two-variable first-order logic with counting. Using this classification, we show that it can be decided in almost linear time whether a structure is identified by C2. Our classification implies that for every graph identified by this logic, all vertex-colored versions of it are also identifi...

Modal Logics with Counting

We present a modal language that includes explicit operators to count the number of elements that a model might include in the extension of a formula, and we discuss how this logic has been previously investigated under different guises. We show that the language is related to graded modalities and to hybrid logics. We illustrate a possible application of the language to the treatment of plural...

Logics with Counting

Logics with Counting ESSLLI 2009

Logics with counting: Very Challenging Presentation Topics

Here is a list of very challenging topics which you might like to give a presentation on for the course Logics with Counting. They are in no particular order. All of the topics can be done (more or less successfully) by anyone who has followed the course; and none of them lacks the potential for doing serious and challenging work. Note also that these are only suggestions. If you have a better ...