Journal article
On the products of Linear Modal Logics
Journal of Logic and Computation, Vol.11(6), pp.909-931
2001
Abstract
We study two‐dimensional Cartesian products of modal logics determined by infinite or arbitrarily long finite linear orders and prove a general theorem showing that in many cases these products are undecidable, in particular, such are the squares of standard linear logics like K4.3, S4.3, GL.3, Grz.3, or the logic determined by the Cartesian square of any infinite linear order. This theorem solves a number of open problems posed by Gabbay and Shehtman. We also prove a sufficient condition for such products to be not recursively enumerable and give a simple axiomatization for the square K4.3 × K4.3 of the minimal liner logic using non‐structural Gabbay‐type inference rules.
Details
- Title
- On the products of Linear Modal Logics
- Authors/Creators
- M. Reynolds (Author/Creator) - School of Computer Science and Software Engineering
- Publication Details
- Journal of Logic and Computation, Vol.11(6), pp.909-931
- Publisher
- Oxford University Press
- Identifiers
- 991005545258407891
- Copyright
- 2001 Oxford University Press
- Murdoch Affiliation
- School of Education
- Language
- English
- Resource Type
- Journal article
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- Collaboration types
- Domestic collaboration
- International collaboration
- Citation topics
- 9 Mathematics
- 9.280 Algebra & Topology
- 9.280.1047 Algebraic Logic
- Web Of Science research areas
- Computer Science, Theory & Methods
- Logic
- ESI research areas
- Computer Science