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  1.  13
    Gödel justification logics and realization.Nicholas Pischke - 2022 - Logic Journal of the IGPL 30 (3):343-408.
    We study the topic of realization from classical justification logics in the context of the recently introduced Gödel justification logics. We show that the standard Gödel modal logics of Caicedo and Rodriguez are not realized by the Gödel justification logics and moreover, we study possible extensions of the Gödel justification logics, which are strong enough to realize the standard Gödel modal logics. On the other hand, we study the fragments of the standard Gödel modal logics, which are realized by the (...)
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  2.  23
    A Note on Strong Axiomatization of Gödel Justification Logic.Nicholas Pischke - 2020 - Studia Logica 108 (4):687-724.
    Justification logics are special kinds of modal logics which provide a framework for reasoning about epistemic justifications. For this, they extend classical boolean propositional logic by a family of necessity-style modal operators “t : ”, indexed over t by a corresponding set of justification terms, which thus explicitly encode the justification for the necessity assertion in the syntax. With these operators, one can therefore not only reason about modal effects on propositions but also about dynamics inside the justifications themselves. We (...)
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  3.  16
    Logical metatheorems for accretive and (generalized) monotone set-valued operators.Nicholas Pischke - 2023 - Journal of Mathematical Logic 24 (2).
    Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of certain set-valued mappings between function spaces. This paper deals with the computational properties of these accretive and (generalized) monotone set-valued operators. In particular, we develop (and extend) for this field the theoretical framework of proof mining, a program in mathematical logic that seeks to extract computational information from prima facie “non-computational” proofs from the mainstream literature. To this end, we establish logical metatheorems (...)
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  4.  10
    On intermediate justification logics.Nicholas Pischke - forthcoming - Logic Journal of the IGPL.
    We study arbitrary intermediate propositional logics extended with a collection of axioms from justification logics. For these, we introduce various semantics by combining either Heyting algebras or Kripke frames with the usual semantic machinery used by Mkrtychev’s, Fitting’s or Lehmann and Studer’s models for classical justification logics. We prove unified completeness theorems for all intermediate justification logics and their corresponding semantics using a respective propositional completeness theorem of the underlying intermediate logic. Further, by a modification of a method of Fitting, (...)
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