• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Book chapter

On modal logics of Hamming spaces

P. 395-410.
Kudinov A., Shehtman V. B., Shapirovsky I.

 

With a set S of words in an alphabet A we associate the frame (S; H), where sHt i ff s and t are words of the same length and h(s; t) = 1 for the Hamming distance h. We investigate some unimodal logics of these frames. We show that if the length of words n is fi xed and fi nite, the logics are closely related to many-dimensional products of logic S5, so in many cases they are undecidable and not fi nitely axiomatizable. The relation H can be extended to infi nite sequences. In this case we prove some completeness theorems characterizing the well-known modal logics DB and TB in terms of the Hamming distance.

 

In book

Edited by: T. Bolander, T. Brauner, S. Ghilardi. Iss. 9. L.: College Publications, 2012.