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In this study, a new logic called the connexive paraconsistent quantum logic is introduced as a common denominator of a paraconsistent logic and a quantum logic. A natural deduction system for this logic is introduced, and the weak normalization theorem for this system is shown. A typed lambda calculus for the implication-negation fragment of this logic is developed on the basis of the Curry-Howard...
We propose an approach for defining labeled natural deduction systems for the class of Peircean branching temporal logics, seen as logics in their own right rather than as sub logics of Ockhamist systems. In particular, we give a system for the logic UB, i.e., the until-free fragment of CTL, and show that it is sound and complete. We also study normalization and discuss how derivations may reduce...
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