2 research outputs found
Cut-free sequent calculi for the provability logic D
We say that a Kripke model is a GL-model if the accessibility relation
is transitive and converse well-founded. We say that a Kripke model is
a D-model if it is obtained by attaching infinitely many worlds , and to a world of a GL-model so that . A non-normal modal logic D, which was
studied by Beklemishev (1999), is characterized as follows. A formula
is a theorem of D if and only if is true at in any
D-model. D is an intermediate logic between the provability logics GL and S. A
Hilbert-style proof system for D is known, but there has been no sequent
calculus. In this paper, we establish two sequent calculi for D, and show the
cut-elimination theorem. We also introduce new Hilbert-style systems for D by
interpreting the sequent calculi. Moreover we show a general result as follows.
Let and be arbitrary modal logics. If the relationship between
semantics of and semantics of is equal to that of GL and D, then
can be axiomatized based on in the same way as the new axiomatization
of D based on GL
Bibliography of Lewis Research Center technical publications announced in 1977
This compilation of abstracts describes and indexes over 780 technical reports resulting from the scientific and engineering work performed and managed by the Lewis Research Center in 1977. All the publications were announced in the 1977 issues of STAR (Scientific and Technical Aerospace Reports) and/or IAA (International Aerospace Abstracts). Documents cited include research reports, journal articles, conference presentations, patents and patent applications, and theses