The first invited talk of BNAIC 2013 was given by Wiebe van der Hoek and combined two studies related to modal logic. In the first part Wiebe gave some examples of statements about believes that surprisingly (to me at least) cannot be expressed in standard modal logic. These are statements with some local (in the Kripke model) aspect, such as “agent a believes his beliefs are correct, but this is not the case”. Wiebe then showed that modal logics can be extended with concepts describing such local behavior in an elegant way.

In the second part Wiebe discussed how to compare the succinctness of a logic. He proposed a method, akin to reductions in complexity theory, to prove that one logical language is exponentially more succinct than another.

After his talk there was an interesting discussion about whether succinctness is always a desirable property: there are examples of succinct logics in which reasoning is of a higher complexity. Also, as was pointed out, humans typically do not prefer the most succinct language, but one that is easy to parse. It seems that there is an interesting relation between succinctness and complexity that deserves further study.

– Mathijs de Weerdt