Cluster expansion and the boxdot conjecture

0468171 - MÚ 2017 RIV DE eng J - Journal Article
Jeřábek, Emil
Cluster expansion and the boxdot conjecture.
Mathematical Logic Quarterly. Roč. 62, č. 6 (2016), s. 608-614. ISSN 0942-5616. E-ISSN 1521-3870
R&D Projects: GA AV ČR IAA100190902; GA ČR GBP202/12/G061
Institutional support: RVO:67985840
Keywords : modal logic * boxdot translation * cluster expansion
Subject RIV: BA - General Mathematics
Impact factor: 0.250, year: 2016
http://onlinelibrary.wiley.com/doi/10.1002/malq.201600036/abstract

The boxdot conjecture asserts that every normal modal logic that faithfully interprets T by the well-known boxdot translation is in fact included in T. We confirm that the conjecture is true. More generally, we present a simple semantic condition on modal logics L_0 which ensures that the largest logic where L_0 embeds faithfully by the boxdot translation is L_0 itself. In particular, this natural generalization of the boxdot conjecture holds for S4, S5, and KTB in place of T.
Permanent Link: http://hdl.handle.net/11104/0266023