•  33
    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 conc…Read more
  •  49
    Knowledge, belief, normality, and introspection
    Synthese 195 (10): 4343-4372. 2017.
    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 conc…Read more
  •  34
    Proof-theoretic analysis of the quantified argument calculus
    Review of Symbolic Logic 12 (4): 607-636. 2019.
    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…Read more
  •  12
  •  6
    Truth, Partial Logic and Infinitary Proof Systems
    Studia Logica 106 (3): 515-540. 2018.
    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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \use…Read more
  •  36
    Is, Ought, and Cut
    Journal of Philosophical Logic 52 (4): 1149-1169. 2023.
    In this paper we use proof-theoretic methods, specifically sequent calculi, admissibility of cut within them and the resultant subformula property, to examine a range of philosophically-motivated deontic logics. We show that for all of those logics it is a (meta)theorem that the Special Hume Thesis holds, namely that no purely normative conclusion follows non-trivially from purely descriptive premises (nor vice versa). In addition to its interest on its own, this also illustrates one way in whic…Read more
  •  2
    Rezension:: Rationalität in der Angewandten Ethik
    with C. Werndl, W. F. Berger, B. Armstrong, and A. J. J. Anglberger
    Kriterion - Journal of Philosophy 19 (1): 44-54. 2005.
  •  1
    Rezension:: Rationalität in der Angewandten Ethik
    with C. Werndl, W. F. Berger, B. Armstrong, and A. J. J. Anglberger
    Kriterion - Journal of Philosophy 1 (19): 44-54. 2005.
  •  18
    Neutral Free Logic: Motivation, Proof Theory and Models
    Journal of Philosophical Logic 52 (2): 519-554. 2023.
    Free logics are a family of first-order logics which came about as a result of examining the existence assumptions of classical logic (Hintikka _The Journal of Philosophy_, _56_, 125–137 1959 ; Lambert _Notre Dame Journal of Formal Logic_, _8_, 133–144 1967, 1997, 2001 ). What those assumptions are varies, but the central ones are that (i) the domain of interpretation is not empty, (ii) every name denotes exactly one object in the domain and (iii) the quantifiers have existential import. Free lo…Read more
  •  24
    Abstract Forms of Quantification in the Quantified Argument Calculus
    Review of Symbolic Logic 16 (2): 449-479. 2023.
    The Quantified argument calculus (Quarc) has received a lot of attention recently as an interesting system of quantified logic which eschews the use of variables and unrestricted quantification, but nonetheless achieves results similar to the Predicate calculus (PC) by employing quantifiers applied directly to predicates instead. Despite this noted similarity, the issue of the relationship between Quarc and PC has so far not been definitively resolved. We address this question in the present pap…Read more
  •  37
    A More Unified Approach to Free Logics
    Journal of Philosophical Logic 50 (1): 117-148. 2020.
    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 some atomic…Read more
  •  34
    Obligation, free choice, and the logic of weakest permissions
    with Albert J. J. Anglberger, Nobert Gratzl, and Olivier Roy
    Review of Symbolic Logic 8 (4): 807-827. 2015.
    We introduce a new understanding of deontic modals that we callobligations as weakest permissions. We argue for its philosophical plausibility, study its expressive power in neighborhood models, provide a complete Hilbert-style axiom system for it and show that it can be extended and applied to practical norms in decision and game theory.
  •  70
    Truth, Partial Logic and Infinitary Proof Systems
    Studia Logica 106 (3): 1-26. 2017.
    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.
  •  25
    Logicality, Double-Line Rules, and Modalities
    Studia Logica 107 (1): 85-107. 2019.
    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…Read more
  •  14
    Two types of indefinites: Hilbert & Russell
    IfCoLog Journal of Logics and Their Applications 4 (2). 2017.
    This paper compares Hilbert’s -terms and Russell’s approach to indefinite descriptions, Russell’s indefinites for short. Despite the fact that both accounts are usually taken to express indefinite descriptions, there is a number of dissimilarities. Specifically, it can be shown that Russell indefinites - expressed in terms of a logical ρ-operator - are not directly representable in terms of their corresponding -terms. Nevertheless, there are two possible translations of Russell indefinites into …Read more
  •  13
    Double-line Harmony in a Sequent Setting
    with Orlandelli Eugenio
    In Pavel Arazim & Tomáš Lávička (eds.), The Logica Yearbook 2016, . 2017.
    This paper concentrates on how to capture harmony in sequent calculi. It starts by considering a proposal made by Tennant and some objections to it which have been presented by Steinberger. Then it proposes a different analysis which makes use of a double-line presentation of sequent calculi in the style of Dosen and it shows that this proposal is able to dismiss disharmonious operators without thereby adopting any global criterion.
  •  1
    Rhetorische Wissenschaft: Rede Und Argumentation in Theorie Und Praxis (edited book)
    with G. Kreuzbauer and E. Hiebl
    Lit. 2008.
  •  1
  •  373
    The Basics of Display Calculi
    with Tim Lyon, Christian Ittner, and Timo Eckhardt
    Kriterion - Journal of Philosophy 31 (2): 55-100. 2017.
    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.
  •  76
    A Sequent Calculus for a Negative Free Logic
    Studia Logica 96 (3): 331-348. 2010.
    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.
  •  75
    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 specif…Read more
  •  39
    Definite descriptions: Language, logic, and elimination
    In Hieke Alexander & Leitgeb Hannes (eds.), Reduction, Abstraction, Analysis, Ontos Verlag. pp. 355. 2009.
    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 met…Read more
  •  6
    Hilbert and Bernays on definite descriptions
    Studia Philosophiae Christianae 47 (4): 19-29. 2011.
  •  179
    Book review: Rationalität in der Angewandten Ethik (review)
    with A. J. J. Anglberger, B. Armstrong, W. F. Berger, and Charlotte Werndl
    Kriterion - Journal of Philosophy 19 (1): 44-54. 2005.
    Betrachtet man den Gebrauch der Worte ‘Moral’ und ‘Vernunft’ etwas genauer, so stellt man fest, dass nicht klar ist, was sie bezeichnen bzw. wie Moral und Vernunft zusammenhängen. In dem Buch ‘Rationalität in der Angewandten Ethik’, in dem sich verschiedene Autoren die Aufgabe gestellt haben, diese Umstände in das Licht der Betrachtung zu rücken, finden wir Fragen darüber, wie “Moral”, “Angewandte Ethik” und “Vernunft” (auch in der Anwendung) zu verstehen und zu vereinen sind.
  •  83
    Incomplete Symbols — Definite Descriptions Revisited
    Journal of Philosophical Logic 44 (5): 489-506. 2015.
    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…Read more