Proof Theoretical Studies on Semilattice Relevant Logics
نویسنده
چکیده
The semilattice relevant logics ∪R, ∪T, ∪RW, and ∪TW (slightly different from the orthodox relevant logics R, T, RW, and TW) are defined by “semilattice models” in which conjunction and disjunction are interpreted in a natural way. In this paper, we prove the equivalence between “LK-style” and “LJ-style” labelled sequent calculi for these logics. (LKstyle sequents have plural succedents, while they are singletons in LJ-style.) Moreover, using this equivalence, we give the following. (1) New Hilbert-style axiomatizations for ∪R and ∪T. (2) Equivalence between two semantics (commutative monoid model and distributive semilattice model) for the “contractionless” logics ∪RW and ∪TW.
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