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  1. Proof Theory for Positive Logic with Weak Negation.Marta Bílková & Almudena Colacito - 2020 - Studia Logica 108 (4):649-686.
    Proof-theoretic methods are developed for subsystems of Johansson’s logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems. In particular, cut-free complete sequent calculi are introduced and used to provide a proof of the fact that the systems satisfy the Craig interpolation property. Alternative versions of the calculi are later obtained by means of an appropriate loop-checking history mechanism. Termination of the new calculi is proved, and (...)
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  • Undecidability of First-Order Modal and Intuitionistic Logics with Two Variables and One Monadic Predicate Letter.Mikhail Rybakov & Dmitry Shkatov - 2019 - Studia Logica 107 (4):695-717.
    We prove that the positive fragment of first-order intuitionistic logic in the language with two individual variables and a single monadic predicate letter, without functional symbols, constants, and equality, is undecidable. This holds true regardless of whether we consider semantics with expanding or constant domains. We then generalise this result to intervals \ and \, where QKC is the logic of the weak law of the excluded middle and QBL and QFL are first-order counterparts of Visser’s basic and formal logics, (...)
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  • Transitive Primal Infon Logic.Carlos Cotrini & Yuri Gurevich - 2013 - Review of Symbolic Logic 6 (2):281-304.
    Primal infon logic was introduced in 2009 in connection with access control. In addition to traditional logic constructs, it contains unary connectives p said indispensable in the intended access control applications. Propositional primal infon logic is decidable in linear time, yet suffices for many common access control scenarios. The most obvious limitation on its expressivity is the failure of the transitivity law for implication: \$$ \to \$$ and \$$ \to \$$ do not necessarily yield \$$ \to \$$. Here we introduce (...)
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