Ilya Shapirovsky

Products of S5 and modal logics of Hamming spaces

Joint work with Andrey Kudinov and Valentin Shehtman.

In this talk we consider unimodal logics of the relation H: sHt iff s and t are words of the same length and h(s,t)=1, where h is the Hamming distance.

Unimodal logics of this kind are closely related to many-dimensional logics. If we consider the n-dimensional product of the inequality frame over a given alphabet A, then the Hamming box-operator on words of length n acts as the conjunction of all box-operators of the product. On the other hand, we show that all modalities of the n-dimensional product of A with the universal relation can be expressed in the unimodal language with the Hamming box-operator. It follows that undecidability results for products of S5 transfer to logics of Hamming frames.