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Modal completeness of sublogics of the interpretability logic IL
Author(s) -
Kurahashi Taishi,
Okawa Yuya
Publication year - 2021
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.202000037
Subject(s) - interpretability , completeness (order theory) , mathematics , decidability , modal logic , modal , calculus (dental) , discrete mathematics , pure mathematics , algebra over a field , artificial intelligence , computer science , mathematical analysis , medicine , chemistry , dentistry , polymer chemistry
We study modal completeness and incompleteness of several sublogics of the interpretability logic IL . We introduce the sublogic IL − , and prove that IL − is sound and complete with respect to Veltman prestructures which are introduced by Visser. Moreover, we prove the modal completeness of twelve logics between IL − and IL with respect to Veltman prestructures. On the other hand, we prove that eight natural sublogics of IL are modally incomplete. Finally, we prove that these incomplete logics are complete with respect to generalized Veltman prestructures. As a consequence of these investigations, we obtain that the twenty logics studied in this paper are all decidable.