•  21
    A more general general proof theory
    Journal of Applied Logic 25 23-46. 2017.
  •  45
    Disentangling FDE -Based Paraconsistent Modal Logics
    with Sergei P. Odintsov
    Studia Logica 105 (6): 1221-1254. 2017.
    The relationships between various modal logics based on Belnap and Dunn’s paraconsistent four-valued logic FDE are investigated. It is shown that the paraconsistent modal logic \, which lacks a primitive possibility operator \, is definitionally equivalent with the logic \, which has both \ and \ as primitive modalities. Next, a tableau calculus for the paraconsistent modal logic KN4 introduced by L. Goble is defined and used to show that KN4 is definitionally equivalent with \ without the absur…Read more
  •  4
    "This volume comprises the proceedings of the First All-Berlin Workshop on Nonclassical Logics and Information Processing, held at the Free University of Berlin, November 9-10, 1990. The scope of the ten papers in the volume is broad, covering various different subfields of logic - particularly nonclassical logic - and its applications in artificial intelligence. The papers are grouped according to the four major topics that emerged at the meeting: modal systems, logic programming, nonmonotonic …Read more
  •  40
    Proof theory of modal logic (edited book)
    Kluwer Academic Publishers. 1996.
    Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.
  •  34
    Book review (review)
    Erkenntnis 64 (3): 415-418. 2006.
  •  66
    Reprint of: A more general general proof theory
    Journal of Applied Logic 25 23-46. 2017.
    In this paper it is suggested to generalize our understanding of general (structural) proof theory and to consider it as a general theory of two kinds of derivations, namely proofs and dual proofs. The proposal is substantiated by (i) considerations on assertion, denial, and bi-lateralism, (ii) remarks on compositionality in proof-theoretic semantics, and (iii) comments on falsification and co-implication. The main formal result of the paper is a normal form theorem for the natural deduction pro…Read more
  •  20
    Bemerkungen Zur Semantik Nicht‐Normaler Möglicher Welten
    Mathematical Logic Quarterly 35 (6): 551-557. 1989.
  •  49
    Semantics-based Nonmonotonic Inference
    Notre Dame Journal of Formal Logic 36 (1): 44-54. 1995.
    In this paper we discuss Gabbay's idea of basing nonmonotonic deduction on semantic consequence in intuitionistic logic extended by a consistency operator and Turner's suggestion of replacing the intuitionistic base system by Kleene's three-valued logic. It is shown that a certain counterintuitive feature of these approaches can be avoided by using Nelson's constructive logic N instead of intuitionistic logic or Kleene's system. Moreover, in N a more general notion of consistency can be defined …Read more
  •  52
    Nested deontic modalities: Another view of parking on highways (review)
    Erkenntnis 49 (2): 185-199. 1998.
    A suggestion is made for representing iterated deontic modalities in stit theory, the “seeing-to-it-that” theory of agency. The formalization is such that normative sentences are represented as agentive sentences and therefore have history dependent truth conditions. In contrast to investigations in alethic modal logic, in the construction of systems of deontic logic little attention has been paid to the iteration... of the deontic modalities.
  •  32
    Hypersequent and Display Calculi – a Unified Perspective
    with Agata Ciabattoni and Revantha Ramanayake
    Studia Logica 102 (6): 1245-1294. 2014.
    This paper presents an overview of the methods of hypersequents and display sequents in the proof theory of non-classical logics. In contrast with existing surveys dedicated to hypersequent calculi or to display calculi, our aim is to provide a unified perspective on these two formalisms highlighting their differences and similarities and discussing applications and recent results connecting and comparing them.
  •  105
    Anti-realistic conceptions of truth and falsity are usually epistemic or inferentialist. Truth is regarded as knowability, or provability, or warranted assertability, and the falsity of a statement or formula is identified with the truth of its negation. In this paper, a non-inferentialist but nevertheless anti-realistic conception of logical truth and falsity is developed. According to this conception, a formula (or a declarative sentence) A is logically true if and only if no matter what is to…Read more
  •  6
    Reasoning About Belief Revision
    with Caroline Semmling
    In Erik J. Olson Sebastian Enqvist (ed.), Belief Revision Meets Philosophy of Science, Springer. pp. 303--328. 2011.
  •  5
    Advances in Modal Logic, Volume
    with F. Wolter, M. de Rijke, and M. Zakharyaschev
    We study a propositional bimodal logic consisting of two S4 modalities £ and [a], together with the interaction axiom scheme a £ϕ → £ aϕ. In the intended semantics, the plain £ is given the McKinsey-Tarski interpretation as the interior operator of a topology, while the labelled [a] is given the standard Kripke semantics using a reflexive and transitive binary relation a. The interaction axiom expresses the property that the Ra relation is lower semi-continuous with respect to the topology. The c…Read more
  •  45
    Connexive logic
    Stanford Encyclopedia of Philosophy. 2008.
  •  34
    Synchronized Linear-Time Temporal Logic
    with Norihiro Kamide
    Studia Logica 99 (1-3): 365-388. 2011.
    A new combined temporal logic called synchronized linear-time temporal logic (SLTL) is introduced as a Gentzen-type sequent calculus. SLTL can represent the n -Cartesian product of the set of natural numbers. The cut-elimination and completeness theorems for SLTL are proved. Moreover, a display sequent calculus δ SLTL is defined.
  •  18
    Completeness and cut-elimination theorems for trilattice logics
    with Norihiro Kamide
    Annals of Pure and Applied Logic 162 (10): 816-835. 2011.
    A sequent calculus for Odintsov’s Hilbert-style axiomatization of a logic related to the trilattice SIXTEEN3 of generalized truth values is introduced. The completeness theorem w.r.t. a simple semantics for is proved using Maehara’s decomposition method that simultaneously derives the cut-elimination theorem for . A first-order extension of and its semantics are also introduced. The completeness and cut-elimination theorems for are proved using Schütte’s method.
  • Review (review)
    Theoria 72 (4): 336-340. 2006.
  • Editorial
    with Roy Dyckhoff
    Studia Logica 69 (2): 195-196. 2001.
  •  28
    A rule-extension of the non-associative Lambek calculus
    Studia Logica 71 (3): 443-451. 2002.
    An extension L + of the non-associative Lambek calculus Lis defined. In L + the restriction to formula-conclusion sequents is given up, and additional left introduction rules for the directional implications are introduced. The system L + is sound and complete with respect to a modification of the ternary frame semantics for L.
  •  77
    Logical Connectives for Constructive Modal Logic
    Synthese 150 (3): 459-482. 2006.
    Model-theoretic proofs of functional completenes along the lines of [McCullough 1971, Journal of Symbolic Logic 36, 15–20] are given for various constructive modal propositional logics with strong negation.
  •  18
    Editorial
    Journal of Logic, Language and Information 7 (3): 3-4. 1998.
  •  48
    An Axiomatic System and a Tableau Calculus for STIT Imagination Logic
    with Grigory K. Olkhovikov
    Journal of Philosophical Logic 47 (2): 259-279. 2018.
    We formulate a Hilbert-style axiomatic system and a tableau calculus for the STIT-based logic of imagination recently proposed in Wansing. Completeness of the axiom system is shown by the method of canonical models; completeness of the tableau system is also shown by using standard methods.
  •  88
    Diamonds are a philosopher's best friends
    Journal of Philosophical Logic 31 (6): 591-612. 2002.
    The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the unwanted disappearance of the diamond may be escaped. The emphasis is not laid on a discussion of the contentious premise of the knowability paradox, namely that all truths are possibly known, but on how from this assumption the conclusion is derived …Read more