
289The Basics of Display CalculiKriterion  Journal of Philosophy 31 (2): 55100. 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, firstorder, and modal display calculi are considered and their properties detailed.

114Book review: Rationalität in der Angewandten Ethik (review)Kriterion  Journal of Philosophy 19 (1): 4454. 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.

78Incomplete Symbols — Definite Descriptions RevisitedJournal of Philosophical Logic 44 (5): 489506. 2015.We investigate incomplete symbols, i.e. definite descriptions with scopeoperators. 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 prooftheoretic 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

73A Sequent Calculus for a Negative Free LogicStudia Logica 96 (3): 331348. 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 Cutrule. 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.

67Truth, Partial Logic and Infinitary Proof SystemsStudia Logica 106 (3): 126. 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 ωrule.

55The EpsilonReconstruction of Theories and Scientific StructuralismErkenntnis 81 (2): 407432. 2016.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 epsilonreconstruction of theories in the context of pure mathematics. The main objective here is twofold: first, to specif…Read more

33Definite descriptions: Language, logic, and eliminationIn 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 negativeparts. 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

32A More Unified Approach to Free LogicsJournal of Philosophical Logic 50 (1): 117148. 2020.Free logics is a family of firstorder 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

29Obligation, free choice, and the logic of weakest permissionsReview of Symbolic Logic 8 (4): 807827. 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 Hilbertstyle axiom system for it and show that it can be extended and applied to practical norms in decision and game theory.

22Logicality, DoubleLine Rules, and ModalitiesStudia Logica 107 (1): 85107. 2019.This paper deals with the question of the logicality of modal logics from a prooftheoretic 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 doubleline rules which, following Dos̆en’s analysis, allows us to…Read more

21Is, Ought, and CutJournal of Philosophical Logic 121. forthcoming.In this paper we use prooftheoretic methods, specifically sequent calculi, admissibility of cut within them and the resultant subformula property, to examine a range of philosophicallymotivated 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 nontrivially from purely descriptive premises (nor vice versa). In addition to its interest on its own, this also illustrates one way in whic…Read more

16Abstract Forms of Quantification in the Quantified Argument CalculusReview of Symbolic Logic 16 (2): 449479. 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

15Priority merge and intersection modalitiesReview of Symbolic Logic 15 (1): 165196. 2022.We study the logic of socalled lexicographic or priority merge for multiagent 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 dyna…Read more

12Neutral Free Logic: Motivation, Proof Theory and ModelsJournal of Philosophical Logic 52 (2): 519554. 2023.Free logics are a family of firstorder 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

12Two types of indefinites: Hilbert & RussellIfCoLog 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 ρoperator  are not directly representable in terms of their corresponding terms. Nevertheless, there are two possible translations of Russell indefinites into …Read more

10Doubleline Harmony in a Sequent SettingIn 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 doubleline 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.

1Truth, Partial Logic and Infinitary Proof SystemsStudia Logica 106 (3): 515540. 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

1Rezension:: Rationalität in der Angewandten EthikKriterion  Journal of Philosophy 1 (19): 4454. 2005.

1Rezension:: Rationalität in der Angewandten EthikKriterion  Journal of Philosophy 19 (1): 4454. 2005.

Persuasion Und Wissenschaft: Aktuelle Fragestellungen von Rhetorik Und Argumentationstheorie (edited book)Lit. 2007.
Areas of Interest
17th/18th Century Philosophy 