What are hybrid languages? (English) Zbl 0911.03009

Blackburn, Patrick; Seligman, Jerry

Kracht, Marcus (ed.) et al., Advances in modal logic. Vol. 1. Selected papers of the 1st AiML conference, Free University of Berlin, Germany, October 1996. Stanford, CA: Center for the Study of Language and Information (CSLI). CSLI Lect. Notes. 87, 41-62 (1998).

The authors consider several hybridisations of usual modal and tense logic respectively, i.e., enrichments of the corresponding propositional languages by individual variables, certain quantifiers, and further operators relating variables and formulas. After a careful introduction of the syntax and semantics, a hierarchy of hybrid languages with respect to expressiveness is discussed. The main technical issues of the paper concern decidability of the satisfiability problem of the hybrid language at the bottom of that hierarchy and undecidability of this problem for some languages higher up. Finally, the usefulness of hybrid languages is pointed out from a couple of points of view, including a linguistic one.
For the entire collection see [Zbl 0897.00022].

Reviewer: Bernhard Heinemann (Hagen)

MSC:

03B45

Modal logic (including the logic of norms)

Keywords:

modal logic; tense logic; hybridisation; expressiveness; decidability; undecidability; hierarchy of hybrid languages; satisfiability problem