Abstract
AbstractIn the early 1960s, to prove undecidability of monadic fragments of sublogics of the predicate modal logic $$\textbf{QS5}$$
QS
5
that include the classical predicate logic $$\textbf{QCl}$$
QCl
, Saul Kripke showed how a classical atomic formula with a binary predicate letter can be simulated by a monadic modal formula. We consider adaptations of Kripke’s simulation, which we call the Kripke trick, to various modal and superintuitionistic predicate logics not considered by Kripke. We also discuss settings where the Kripke trick does not work and where, as a result, decidability of monadic modal predicate logics can be obtained.
Funder
University of the Witwatersrand
Publisher
Springer Science and Business Media LLC
Reference58 articles.
1. Andréka, H., S. Givant, and I. Németi, Decision problems for equational theories of relation algebras, in Number 604 in Memoirs of the American Mathematical Society, American Mathematical Society, 1997.
2. Blackburn, P., and E. Spaan, A modal perspective on the computational complexity of attribute value grammar, Journal of Logic, Language, and Information 2:129–169, 1993.
3. Boolos, G. S., J. P. Burgesss, and R. C. Jeffrey, Computability and Logic, 5th edn, Cambridge University Press, 2007.
4. Börger, E., E. Grädel, and Y. Gurevich, The Classical Decision Problem, Springer, 1997.
5. Chagrov, A., and M. Rybakov, How many variables does one need to prove PSPACE-hardness of modal logics?, in P. Balbiani, N.-Y. Suzuki, F. Wolter, and M. Zakharyaschev, (eds), Advances in Modal Logic 4, King’s College Publications, 2003, pp. 71–82.