6 found
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  1.  11
    Full Cut Elimination and Interpolation for Intuitionistic Logic with Existence Predicate.Paolo Maffezioli & Eugenio Orlandelli - 2019 - Bulletin of the Section of Logic 48 (2):137-158.
    In previous work by Baaz and Iemhoff, a Gentzen calculus for intuitionistic logic with existence predicate is presented that satisfies partial cut elimination and Craig's interpolation property; it is also conjectured that interpolation fails for the implication-free fragment. In this paper an equivalent calculus is introduced that satisfies full cut elimination and allows a direct proof of interpolation via Maehara's lemma. In this way, it is possible to obtain much simpler interpolants and to better understand and overcome the failure of (...)
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  2.  15
    Logicality, Double-Line Rules, and Modalities.Norbert Gratzl & Eugenio Orlandelli - 2019 - Studia Logica 107 (1):85-107.
    This paper deals with the question of the logicality of modal logics from a proof-theoretic perspective. It is argued that if Dos̆en’s analysis of logical constants as punctuation marks is embraced, it is possible to show that all the modalities in the cube of normal modal logics are indeed logical constants. It will be proved that the display calculus for each displayable modality admits a purely structural presentation based on double-line rules which, following Dos̆en’s analysis, allows us to claim that (...)
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  3.  17
    Free Quantified Epistemic Logics.Giovanna Corsi & Eugenio Orlandelli - 2013 - Studia Logica 101 (6):1159-1183.
    The paper presents an epistemic logic with quantification over agents of knowledge and with a syntactical distinction between de re and de dicto occurrences of terms. Knowledge de dicto is characterized as ‘knowledge that’, and knowlegde de re as ‘knowledge of’. Transition semantics turns out to be an adequate tool to account for the distinctions introduced.
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  4.  17
    Proof-Theoretic Pluralism.Filippo Ferrari & Eugenio Orlandelli - forthcoming - Synthese:1-25.
    Starting from a proof-theoretic perspective, where meaning is determined by the inference rules governing logical operators, in this paper we primarily aim at developing a proof-theoretic alternative to the model-theoretic meaning-invariant logical pluralism discussed in Beall and Restall. We will also outline how this framework can be easily extended to include a form of meaning-variant logical pluralism. In this respect, the framework developed in this paper—which we label two-level proof-theoretic pluralism—is much broader in scope than the one discussed in Beall (...)
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  5.  13
    Proof Theory for Quantified Monotone Modal Logics.Sara Negri & Eugenio Orlandelli - 2019 - Logic Journal of the IGPL 27 (4):478-506.
    This paper provides a proof-theoretic study of quantified non-normal modal logics. It introduces labelled sequent calculi based on neighbourhood semantics for the first-order extension, with both varying and constant domains, of monotone NNML, and studies the role of the Barcan formulas in these calculi. It will be shown that the calculi introduced have good structural properties: invertibility of the rules, height-preserving admissibility of weakening and contraction and syntactic cut elimination. It will also be shown that each of the calculi introduced (...)
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  6.  3
    Interpolation in Extensions of First-Order Logic.Guido Gherardi, Paolo Maffezioli & Eugenio Orlandelli - forthcoming - Studia Logica:1-30.
    We prove a generalization of Maehara’s lemma to show that the extensions of classical and intuitionistic first-order logic with a special type of geometric axioms, called singular geometric axioms, have Craig’s interpolation property. As a corollary, we obtain a direct proof of interpolation for first-order logic with identity, as well as interpolation for several mathematical theories, including the theory of equivalence relations, partial and linear orders, and various intuitionistic order theories such as apartness and positive partial and linear orders.
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