•  2
    On Non-transitive “Identity”
    with Daniel Skurt
    In Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency, Springer Verlag. pp. 535-553. 2019.
    Graham Priest takes the relation of identity to be non-transitive. In this paper, we are going to discuss several consequences of identity as a non-transitive relation. We will consider the Henkin-style completeness proof for classical first-order logic with a non-transitive “identity” predicate, Leibniz-identity in Priest’s second-order minimal logic of paradox, and the question whether or not identity of individuals should be defined as Leibniz-identity.
  •  34
    Routley Star and Hyperintensionality
    with Sergei Odintsov
    Journal of Philosophical Logic 50 (1): 33-56. 2021.
    We compare the logic HYPE recently suggested by H. Leitgeb as a basic propositional logic to deal with hyperintensional contexts and Heyting-Ockham logic introduced in the course of studying logical aspects of the well-founded semantics for logic programs with negation. The semantics of Heyting-Ockham logic makes use of the so-called Routley star negation. It is shown how the Routley star negation can be obtained from Dimiter Vakarelov’s theory of negation and that propositional HYPE coincides w…Read more
  •  6
    Correction to: The nature of entailment: an informational approach
    with Yaroslav Shramko
    Synthese 1-2. forthcoming.
    The paragraph starting with “By accepting condition only,...” should be read as follows
  •  7
    New Essays on Belnap-­Dunn Logic (edited book)
    Springer Verlag. 2019.
    This edited volume collects essays on the four-valued logic known as Belnap-Dunn logic, or first-degree entailment logic. It also looks at various formal systems closely related to it. These include the strong Kleene logic and the Logic of Paradox. Inside, readers will find reprints of seminal papers written by the fathers of the field: Nuel Belnap and Michael Dunn. In addition, the collection also features a well-known but previously unpublished manuscript of Dunn, an interview with Belnap, and…Read more
  •  2
    Proofs, Disproofs, and Their Duals
    In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 483-505. 2010.
  • Tableaux for multi-agent deliberative-stit logic
    In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 503-520. 2006.
  •  1
    Connexive Modal Logic
    In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 367-383. 2005.
  •  32
    Connexive logics. An overview and current trends
    Logic and Logical Philosophy 1. forthcoming.
    In this introduction, we offer an overview of main systems developed in the growing literature on connexive logic, and also point to a few topics that seem to be collecting attention of many of those interested in connexive logic. We will also make clear the context to which the papers in this special issue belong and contribute.
  •  17
    Proof systems for various fde-based modal logics
    with Sergey Drobyshevich
    Review of Symbolic Logic 13 (4): 720-747. 2020.
    We present novel proof systems for various FDE-based modal logics. Among the systems considered are a number of Belnapian modal logics introduced in Odintsov & Wansing and Odintsov & Wansing, as well as the modal logic KN4 with strong implication introduced in Goble. In particular, we provide a Hilbert-style axiom system for the logic $BK^{\square - } $ and characterize the logic BK as an axiomatic extension of the system $BK^{FS} $. For KN4 we provide both an FDE-style axiom system and a decida…Read more
  •  1
    Dag Prawitz on Proofs and Meaning (edited book)
    Springer. 2014.
    This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD t…Read more
  •  16
    On Definability of Connectives and Modal Logics over FDE
    with Sergei P. Odintsov and Daniel Skurt
    Logic and Logical Philosophy 1. forthcoming.
  •  10
    Simplified Tableaux for STIT Imagination Logic
    with Grigory K. Olkhovikov
    Journal of Philosophical Logic 48 (6): 981-1001. 2019.
    We show how to correct the analytic tableaux system from the paper Olkhovikov and Wansing, 259–279, 2018).
  •  4
    Inference as doxastic agency. Part II: Ramifications and refinements
    with Grigory K. Olkhovikov
    Australasian Journal of Logic 14 (4): 408-438. 2017.
    Justification stit logic is a logic for reasoning about proving as a certain kind of activity, namely seeing to it that a proof is publicly available. It merges the semantical analysis of deliberatively seeing-to-it-that from stit theory and the semantics of the epistemic logic with justification from. In this paper, after recalling its language and basic semantical definitions, various ramifications and refinements of justification stit logic are presented and discussed: imposing natural restri…Read more
  •  10
    Negation as Cancellation, Connexive Logic, and qLPm
    Australasian Journal of Logic 15 (2): 476-488. 2018.
    In this paper, we shall consider the so-called cancellation view of negation and the inferential role of contradictions. We will discuss some of the problematic aspects of negation as cancellation, such as its original presentation by Richard and Valery Routley and its role in motivating connexive logic. Furthermore, we will show that the idea of inferential ineffectiveness of contradictions can be conceptually separated from the cancellation model of negation by developing a system we call qLPm…Read more
  • Advances in Modal Logic (edited book)
    with Marcus Kracht, Maarten de Rijke, and Michael Zakharyaschev
    CSLI Publications. 1998.
  •  6
    Proofs, Disproofs, and Their Duals
    In Lev Beklemishev, Valentin Goranko & Valentin Shehtman (eds.), Advances in Modal Logic, Volume 8, Csli Publications. pp. 483-505. 2010.
  •  9
    Tableaux for multi-agent deliberative-stit logic
    In Guido Governatori, Ian Hodkinson & Yde Venema (eds.), Advances in Modal Logic, Volume 6, Csli Publications. pp. 503-520. 2006.
  •  5
    Connexive Modal Logic
    In Renate Schmidt, Ian Pratt-Hartmann, Mark Reynolds & Heinrich Wansing (eds.), Advances in Modal Logic, Volume 5, Csli Publications. pp. 367-383. 2005.
  •  28
    Inference as Doxastic Agency. Part I: The Basics of Justification Stit Logic
    with Grigory K. Olkhovikov
    Studia Logica 107 (1): 167-194. 2019.
    In this paper we consider logical inference as an activity that results in proofs and hence produces knowledge. We suggest to merge the semantical analysis of deliberatively seeing-to-it-that from stit theory and the semantics of the epistemic logic with justification from. The general idea is to understand proving that A as seeing to it that a proof of A is available. We introduce a semantics of various notions of proving as an activity and present a number of valid principles that relate the v…Read more
  •  8
    A more general general proof theory
    Journal of Applied Logic 25 23-46. 2017.
  •  18
    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
  •  23
    Kripke Completeness of Bi-intuitionistic Multilattice Logic and its Connexive Variant
    with Norihiro Kamide and Yaroslav Shramko
    Studia Logica 105 (6): 1193-1219. 2017.
    In this paper, bi-intuitionistic multilattice logic, which is a combination of multilattice logic and the bi-intuitionistic logic also known as Heyting–Brouwer logic, is introduced as a Gentzen-type sequent calculus. A Kripke semantics is developed for this logic, and the completeness theorem with respect to this semantics is proved via theorems for embedding this logic into bi-intuitionistic logic. The logic proposed is an extension of first-degree entailment logic and can be regarded as a bi-i…Read more
  • 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 l…Read more
  •  35
    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.