In this paper we discuss sequent calculi for the propositional fragment of the logic of HYPE. The logic of HYPE was recently suggested by Leitgeb as a logic for hyperintensional contexts. On the one hand we introduce a simple \-system employing rules of contraposition. On the other hand we present a \-system with an admissible rule of contraposition. Both systems are equivalent as well as sound and complete proof-system of HYPE. In order to provide a cut-elimination procedure, we expand the (...) calculus by connections as introduced in Kashima and Shimura. (shrink)

In this paper we discuss sequent calculi for the propositional fragment of the logic of HYPE. The logic of HYPE was recently suggested by Leitgeb as a logic for hyperintensional contexts. On the one hand we introduce a simple \-system employing rules of contraposition. On the other hand we present a \-system with an admissible rule of contraposition. Both systems are equivalent as well as sound and complete proof-system of HYPE. In order to provide a cut-elimination procedure, we expand the (...) calculus by connections as introduced in Kashima and Shimura. (shrink)

Questions concerning the proof-theoretic strength of classical versus nonclassical theories of truth have received some attention recently. A particularly convenient case study concerns classical and nonclassical axiomatizations of fixed-point semantics. It is known that nonclassical axiomatizations in four- or three-valued logics are substantially weaker than their classical counterparts. In this paper we consider the addition of a suitable conditional to First-Degree Entailment—a logic recently studied by Hannes Leitgeb under the label HYPE. We show in particular that, by formulating the theory (...) PKF over HYPE, one obtains a theory that is sound with respect to fixed-point models, while being proof-theoretically on a par with its classical counterpart KF. Moreover, we establish that also its schematic extension—in the sense of Feferman—is as strong as the schematic extension of KF, thus matching the strength of predicative analysis. (shrink)

Cut-free sequent calculi for the predicate intermediate logic CD of constant domains have appeared only very recently in literature, even if this logic has been axiomiatized since the early seventies. In the present paper we propose a different cut-free sequent calculus for CD, in which a great care is devoted in avoiding duplications of formulas.