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  1.  20
    A More Unified Approach to Free Logics.Edi Pavlović & Norbert Gratzl - 2021 - Journal of Philosophical Logic 50 (1):117-148.
    Free logics is a family of first-order logics which came about as a result of examining the existence assumptions of classical logic. What those assumptions are varies, but the central ones are that the domain of interpretation is not empty, every name denotes exactly one object in the domain and the quantifiers have existential import. Free logics usually reject the claim that names need to denote in, and of the systems considered in this paper, the positive free logic concedes that (...)
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  2.  19
    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.  26
    Proof-Theoretic Analysis of the Quantified Argument Calculus.Edi Pavlović & Norbert Gratzl - 2019 - Review of Symbolic Logic 12 (4):607-636.
    This article investigates the proof theory of the Quantified Argument Calculus as developed and systematically studied by Hanoch Ben-Yami [3, 4]. Ben-Yami makes use of natural deduction, we, however, have chosen a sequent calculus presentation, which allows for the proofs of a multitude of significant meta-theoretic results with minor modifications to the Gentzen’s original framework, i.e., LK. As will be made clear in course of the article LK-Quarc will enjoy cut elimination and its corollaries.
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  4.  69
    A Sequent Calculus for a Negative Free Logic.Norbert Gratzl - 2010 - Studia Logica 96 (3):331-348.
    This article presents a sequent calculus for a negative free logic with identity, called N . The main theorem (in part 1) is the admissibility of the Cut-rule. The second part of this essay is devoted to proofs of soundness, compactness and completeness of N relative to a standard semantics for negative free logic.
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  5.  50
    The Epsilon-Reconstruction of Theories and Scientific Structuralism.Georg Schiemer & Norbert Gratzl - 2016 - Erkenntnis 81 (2):407-432.
    Rudolf Carnap’s mature work on the logical reconstruction of scientific theories consists of two components. The first is the elimination of the theoretical vocabulary of a theory in terms of its Ramsification. The second is the reintroduction of the theoretical terms through explicit definitions in a language containing an epsilon operator. This paper investigates Carnap’s epsilon-reconstruction of theories in the context of pure mathematics. The main objective here is twofold: first, to specify the epsilon logic underlying his suggested definition of (...)
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  6.  73
    Incomplete Symbols — Definite Descriptions Revisited.Norbert Gratzl - 2015 - Journal of Philosophical Logic 44 (5):489-506.
    We investigate incomplete symbols, i.e. definite descriptions with scope-operators. Russell famously introduced definite descriptions by contextual definitions; in this article definite descriptions are introduced by rules in a specific calculus that is very well suited for proof-theoretic investigations. That is to say, the phrase ‘incomplete symbols’ is formally interpreted as to the existence of an elimination procedure. The last section offers semantical tools for interpreting the phrase ‘no meaning in isolation’ in a formal way.
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  7.  30
    Knowledge, Belief, Normality, and Introspection.Dominik Klein, Olivier Roy & Norbert Gratzl - 2017 - Synthese 195 (10):4343-4372.
    We study two logics of knowledge and belief stemming from the work of Stalnaker, omitting positive introspection for knowledge. The two systems are equivalent with positive introspection, but not without. We show that while the logic of beliefs remains unaffected by omitting introspection for knowledge in one system, it brings significant changes to the other. The resulting logic of belief is non-normal, and its complete axiomatization uses an infinite hierarchy of coherence constraints. We conclude by returning to the philosophical interpretation (...)
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  8.  5
    Priority Merge and Intersection Modalities.Zoé Christoff, Norbert Gratzl & Olivier Roy - forthcoming - Review of Symbolic Logic:1-32.
    We study the logic of so-called lexicographic or priority merge for multi-agent plausibility models. We start with a systematic comparison between the logical behavior of priority merge and the more standard notion of pooling through intersection, used to define, for instance, distributed knowledge. We then provide a sound and complete axiomatization of the logic of priority merge, as well as a proof theory in labeled sequents that admits cut. We finally study Moorean phenomena and define a dynamic resolution operator for (...)
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  9.  64
    Truth, Partial Logic and Infinitary Proof Systems.Martin Fischer & Norbert Gratzl - 2017 - Studia Logica 106 (3):1-26.
    In this paper we apply proof theoretic methods used for classical systems in order to obtain upper bounds for systems in partial logic. We focus on a truth predicate interpreted in a Kripke style way via strong Kleene; whereas the aim is to connect harmoniously the partial version of Kripke–Feferman with its intended semantics. The method we apply is based on infinitary proof systems containing an ω-rule.
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  10.  25
    Definite Descriptions: Language, Logic, and Elimination.Norbert Gratzl - 2009 - In Hieke Alexander & Leitgeb Hannes (eds.), Reduction, Abstraction, Analysis. Ontos Verlag. pp. 355.
    Definite descriptions are in the focus of philosophical discussion at least since Russell's famous paper "On Denoting". We present in this paper a logic with descriptions in Russell's spirit. The formulation, however, is closely related to Schütte's development of predicate logic, i.e. the formulation of the calculus uses positive- and negative-parts. With respect to this slightly more sophisticated formulation it is possible to formalize Russell's convention that is originally stated in the metalanguage of his theory of descriptions within our calculus. (...)
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  11. Hilbert and Bernays on Definite Descriptions.Norbert Gratzl - 2011 - Studia Philosophiae Christianae 47 (4):19-29.
     
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  12.  18
    Knowledge, Belief, Normality, and Introspection.Dominik Klein, Olivier Roy & Norbert Gratzl - 2017 - Synthese:1-30.
    We study two logics of knowledge and belief stemming from the work of Stalnaker, omitting positive introspection for knowledge. The two systems are equivalent with positive introspection, but not without. We show that while the logic of beliefs remains unaffected by omitting introspection for knowledge in one system, it brings significant changes to the other. The resulting logic of belief is non-normal, and its complete axiomatization uses an infinite hierarchy of coherence constraints. We conclude by returning to the philosophical interpretation (...)
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  13.  83
    The Basics of Display Calculi.Tim Lyon, Christian Ittner, Timo Eckhardt & Norbert Gratzl - 2017 - Kriterion - Journal of Philosophy 31 (2):55-100.
    The aim of this paper is to introduce and explain display calculi for a variety of logics. We provide a survey of key results concerning such calculi, though we focus mainly on the global cut elimination theorem. Propositional, first-order, and modal display calculi are considered and their properties detailed.
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  14.  6
    Abstract Forms of Quantification in the Quantified Argument Calculus.Edi Pavlović & Norbert Gratzl - forthcoming - Review of Symbolic Logic:1-32.
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  15.  5
    Free Logic and the Quantified Argument Calculus.Edi Pavlović & Norbert Gratzl - 2019 - In Gabriele M. Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium. De Gruyter. pp. 105-116.
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