-
16A Note on “A Connexive Conditional”Logos and Episteme 13 (3): 325-328. 2022.In a recent article, Mario Günther presented a conditional that is claimed to be connexive. The aim of this short discussion note is to show that Günther’s claim is not without problems.
-
68One Heresy and One Orthodoxy: On Dialetheism, Dimathematism, and the Non-normativity of LogicErkenntnis 89 (1): 181-205. 2024.In this paper, Graham Priest’s understanding of dialetheism, the view that there exist true contradictions, is discussed, and various kinds of metaphysical dialetheism are distinguished between. An alternative to dialetheism is presented, namely a thesis called ‘dimathematism’. It is pointed out that dimathematism enables one to escape a slippery slope argument for dialetheism that has been put forward by Priest. Moreover, dimathematism is presented as a thesis that is helpful in rejecting the c…Read more
-
17Connexive Variants of Modal Logics Over FDEIn Ofer Arieli & Anna Zamansky (eds.), Arnon Avron on Semantics and Proof Theory of Non-Classical Logics, Springer Verlag. pp. 295-318. 2021.Various connexive FDE-based modal logics are studied. Some of these logics contain a conditional that is both connexive and strict, thereby highlighting that strictness and connexivity of a conditional do not exclude each other. In particular, the connexive modal logics cBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{docume…Read more
-
59Stit -logic for imagination episodes with voluntary inputReview of Symbolic Logic 16 (3): 813-861. 2023.Francesco Berto proposed a logic for imaginative episodes. The logic establishes certain (in)validities concerning episodic imagination. They are not all equally plausible as principles of episodic imagination. The logic also does not model that the initial input of an imaginative episode is deliberately chosen.Stit-imagination logic models the imagining agent’s deliberate choice of the content of their imagining. However, the logic does not model the episodic nature of imagination. The present …Read more
-
8Displaying Modal LogicSpringer. 1998.The present monograph is a slightly revised version of my Habilitations schrift Proof-theoretic Aspects of Intensional and Non-Classical Logics, successfully defended at Leipzig University, November 1997. It collects work on proof systems for modal and constructive logics I have done over the last few years. The main concern is display logic, a certain refinement of Gentzen's sequent calculus developed by Nuel D. Belnap. This book is far from offering a comprehensive presentation of generalized …Read more
-
6Advances in Modal Logic, Volume 5: Papers From the Fifth Aiml Conference, Held in Manchester, 9-11 September 2004 (edited book)King's College Publications. 2005.Modal logic is one of the most widely applied logical formalisms. Systems of modal logic are being used in many disciplines, ranging from artificial intelligence, computer science, mathematics, formal grammar and semantics to philosophy. This volume presents substantial recent advances in the relational and the algorithmic treatment of modal logics. It contains papers from the fifth conference on "Advances in Modal logic," held in Manchester (UK) in September 2004. Written by leading experts in …Read more
-
12Advances in Modal Logic, Volume 1: Papers From the First Aiml Conference, Held at the Free University of Berlin, 1996 (edited book)Cambridge University Press. 1998.Modal logic originated in philosophy as the logic of necessity and possibility. Now it has reached a high level of mathematical sophistication and has many applications in a variety of disciplines, including theoretical and applied computer science, artificial intelligence, the foundations of mathematics, and natural language syntax and semantics. This volume represents the proceedings of the first international workshop on Advances in Modal Logic, held in Berlin, Germany, October 8-10, 1996. It…Read more
-
11What is Negation? (edited book)Springer. 1999.The properties of negation, in combination with those of other logical operations and structural features of the deductibility relation, serve as gateways among logical systems. Negation therefore plays an important role in selecting logical systems for particular applications. This volume provides a thorough treatment of this concept, based on contributions written by authors from various branches of logic. The resulting 14 research papers address a variety of topics including negation in relev…Read more
-
17On Non-transitive “Identity”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.
-
79Routley Star and HyperintensionalityJournal of Philosophical Logic 50 (1): 33-56. 2020.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
-
31New 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
-
8Proofs, Disproofs, and Their DualsIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 483-505. 1998.
-
10Tableaux for multi-agent deliberative-stit logicIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 503-520. 1998.
-
28Connexive Modal LogicIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 367-383. 1998.
-
78Connexive logics. An overview and current trendsLogic 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.
-
34Proof systems for various fde-based modal logicsReview 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
-
16Dag 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
-
22Nino B. Cocchiarella and Max A. Freund. Modal logic. An introduction to its syntax and semantics. Oxford University Press, Oxford, 2008, xi + 268 pp (review)Bulletin of Symbolic Logic 16 (2): 275-276. 2010.
-
33On Definability of Connectives and Modal Logics over FDELogic and Logical Philosophy 1. forthcoming.
-
20Simplified Tableaux for STIT Imagination LogicJournal 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).
-
On Split Negation, Strong Negation, Information, Falsification, and VerificationIn Katalin Bimbó (ed.), J. Michael Dunn on Information Based Logics, Springer. 2016.
-
15Inference as doxastic agency. Part II: Ramifications and refinementsAustralasian 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
-
41Negation as Cancellation, Connexive Logic, and qLPmAustralasian 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
-
10Proofs, Disproofs, and Their DualsIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 483-505. 1998.
-
13Tableaux for multi-agent deliberative-stit logicIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 503-520. 1998.
-
24Connexive Modal LogicIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 367-383. 1998.
-
41Inference as Doxastic Agency. Part I: The Basics of Justification Stit LogicStudia 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
Areas of Specialization
Epistemology |
Logic and Philosophy of Logic |
Areas of Interest
Philosophy of Language |