Switch to: References

Citations of:

Displaying Modal Logic

Studia Logica 66 (3):421-426 (2000)

Add citations

You must login to add citations.
  1. (1 other version)Partiality and Adjointness in Modal Logic.Wesley H. Holliday - unknown - In Rajeev Gore (ed.), Advances in modal logic, volume. pp. 313-332.
    Following a proposal of Humberstone, this paper studies a semantics for modal logic based on partial “possibilities” rather than total “worlds.” There are a number of reasons, philosophical and mathematical, to find this alternative semantics attractive. Here we focus on the construction of possibility models with a finitary flavor. Our main completeness result shows that for a number of standard modal logics, we can build a canonical possibility model, wherein every logically consistent formula is satisfied, by simply taking each individual (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • Proof analysis in intermediate logics.Roy Dyckhoff & Sara Negri - 2012 - Archive for Mathematical Logic 51 (1):71-92.
    Using labelled formulae, a cut-free sequent calculus for intuitionistic propositional logic is presented, together with an easy cut-admissibility proof; both extend to cover, in a uniform fashion, all intermediate logics characterised by frames satisfying conditions expressible by one or more geometric implications. Each of these logics is embedded by the Gödel–McKinsey–Tarski translation into an extension of S4. Faithfulness of the embedding is proved in a simple and general way by constructive proof-theoretic methods, without appeal to semantics other than in the (...)
    Download  
     
    Export citation  
     
    Bookmark   32 citations  
  • Proof Theory for Modal Logic.Sara Negri - 2011 - Philosophy Compass 6 (8):523-538.
    The axiomatic presentation of modal systems and the standard formulations of natural deduction and sequent calculus for modal logic are reviewed, together with the difficulties that emerge with these approaches. Generalizations of standard proof systems are then presented. These include, among others, display calculi, hypersequents, and labelled systems, with the latter surveyed from a closer perspective.
    Download  
     
    Export citation  
     
    Bookmark   22 citations  
  • Reasoning About Collectively Accepted Group Beliefs.Raul Hakli & Sara Negri - 2011 - Journal of Philosophical Logic 40 (4):531-555.
    A proof-theoretical treatment of collectively accepted group beliefs is presented through a multi-agent sequent system for an axiomatization of the logic of acceptance. The system is based on a labelled sequent calculus for propositional multi-agent epistemic logic with labels that correspond to possible worlds and a notation for internalized accessibility relations between worlds. The system is contraction- and cut-free. Extensions of the basic system are considered, in particular with rules that allow the possibility of operative members or legislators. Completeness with (...)
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • Quine and Slater on paraconsistency and deviance.Francesco Paoli - 2003 - Journal of Philosophical Logic 32 (5):531-548.
    In a famous and controversial paper, B. H. Slater has argued against the possibility of paraconsistent logics. Our reply is centred on the distinction between two aspects of the meaning of a logical constant *c* in a given logic: its operational meaning, given by the operational rules for *c* in a cut-free sequent calculus for the logic at issue, and its global meaning, specified by the sequents containing *c* which can be proved in the same calculus. Subsequently, we use the (...)
    Download  
     
    Export citation  
     
    Bookmark   27 citations  
  • Display to Labeled Proofs and Back Again for Tense Logics.Agata Ciabattoni, Tim Lyon, Revantha Ramanayake & Alwen Tiu - 2021 - ACM Transactions on Computational Logic 22 (3):1-31.
    We introduce translations between display calculus proofs and labeled calculus proofs in the context of tense logics. First, we show that every derivation in the display calculus for the minimal tense logic Kt extended with general path axioms can be effectively transformed into a derivation in the corresponding labeled calculus. Concerning the converse translation, we show that for Kt extended with path axioms, every derivation in the corresponding labeled calculus can be put into a special form that is translatable to (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • (1 other version)Dag Prawitz on Proofs and Meaning.Heinrich Wansing (ed.) - 2014 - Cham, Switzerland: Springer.
    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 thesis published in 1934. The book opens with an (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Knowledge, belief, normality, and introspection.Dominik Klein, Olivier Roy & Norbert Gratzl - 2017 - Synthese 195 (10):4343-4372.
    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 conclude by returning to the philosophical interpretation (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • The Basics of Display Calculi.Tim Lyon, Christian Ittner, Timo Eckhardt & Norbert Gratzl - 2017 - Kriterion - Journal of Philosophy 31 (2):55-100.
    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.
    Download  
     
    Export citation  
     
    Bookmark  
  • Combining linear-time temporal logic with constructiveness and paraconsistency.Norihiro Kamide & Heinrich Wansing - 2010 - Journal of Applied Logic 8 (1):33-61.
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • An Algebraic View of the Mares-Goldblatt Semantics.Andrew Tedder - 2024 - Journal of Philosophical Logic 53 (2):331-349.
    An algebraic characterisation is given of the Mares-Goldblatt semantics for quantified extensions of relevant and modal logics. Some features of this more general semantic framework are investigated, and the relations to some recent work in algebraic semantics for quantified extensions of non-classical logics are considered.
    Download  
     
    Export citation  
     
    Bookmark  
  • Double-line Harmony in a Sequent Setting.Gratzl Norbert & Orlandelli Eugenio - 2017 - In Arazim Pavel & Lávička Tomáš (eds.), The Logica Yearbook 2016. College Publications.
    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.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • A novel approach to equality.Andrzej Indrzejczak - 2021 - Synthese 199 (1-2):4749-4774.
    A new type of formalization of classical first-order logic with equality is introduced on the basis of the sequent calculus. It serves to justify the claim that equality is a logical constant characterised by well-behaved rules satisfying properties usually regarded as essential. The main feature of this approach is the application of sequents built not only from formulae but also from terms. Two variants of sequent calculus are examined, a structural and a logical one. The former is defined in accordance (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Logics and Falsifications: A New Perspective on Constructivist Semantics.Andreas Kapsner - 2014 - Cham, Switzerland: Springer.
    This volume examines the concept of falsification as a central notion of semantic theories and its effects on logical laws. The point of departure is the general constructivist line of argument that Michael Dummett has offered over the last decades. From there, the author examines the ways in which falsifications can enter into a constructivist semantics, displays the full spectrum of options, and discusses the logical systems most suitable to each one of them. While the idea of introducing falsifications into (...)
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  • Natural Deduction, Hybrid Systems and Modal Logics.Andrzej Indrzejczak - 2010 - Dordrecht, Netherland: Springer.
    This book provides a detailed exposition of one of the most practical and popular methods of proving theorems in logic, called Natural Deduction. It is presented both historically and systematically. Also some combinations with other known proof methods are explored. The initial part of the book deals with Classical Logic, whereas the rest is concerned with systems for several forms of Modal Logics, one of the most important branches of modern logic, which has wide applicability.
    Download  
     
    Export citation  
     
    Bookmark   13 citations  
  • A labelled natural deduction system for linear temporal logic.Andrzej Indrzejczak - 2003 - Studia Logica 75 (3):345 - 376.
    The paper is devoted to the concise description of some Natural Deduction System (ND for short) for Linear Temporal Logic. The system's distinctive feature is that it is labelled and analytical. Labels convey necessary semantic information connected with the rules for temporal functors while the analytical character of the rules lets the system work as a decision procedure. It makes it more similar to Labelled Tableau Systems than to standard Natural Deduction. In fact, our solution of linearity representation is rather (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Semi De Morgan Logic Properly Displayed.Giuseppe Greco, Fei Liang, M. Andrew Moshier & Alessandra Palmigiano - 2020 - Studia Logica 109 (1):1-45.
    In the present paper, we endow semi De Morgan logic and a family of its axiomatic extensions with proper multi-type display calculi which are sound, complete, conservative, and enjoy cut elimination and subformula property. Our proposal builds on an algebraic analysis of the variety of semi De Morgan algebras, and applies the guidelines of the multi-type methodology in the design of display calculi.
    Download  
     
    Export citation  
     
    Bookmark  
  • Proof Theory for Functional Modal Logic.Shawn Standefer - 2018 - Studia Logica 106 (1):49-84.
    We present some proof-theoretic results for the normal modal logic whose characteristic axiom is \. We present a sequent system for this logic and a hypersequent system for its first-order form and show that these are equivalent to Hilbert-style axiomatizations. We show that the question of validity for these logics reduces to that of classical tautologyhood and first-order logical truth, respectively. We close by proving equivalences with a Fitch-style proof system for revision theory.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Display calculi and other modal calculi: a comparison.Francesca Poggiolesi - 2010 - Synthese 173 (3):259-279.
    In this paper we introduce and compare four different syntactic methods for generating sequent calculi for the main systems of modal logic: the multiple sequents method, the higher-arity sequents method, the tree-hypersequents method and the display method. More precisely we show how the first three methods can all be translated in the fourth one. This result sheds new light on these generalisations of the sequent calculus and raises issues that will be examined in the last section.
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • Logical Connectives for Constructive Modal Logic.Heinrich Wansing - 2006 - Synthese 150 (3):459-482.
    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.
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • The Power of Belnap: Sequent Systems for SIXTEEN ₃. [REVIEW]Heinrich Wansing - 2010 - Journal of Philosophical Logic 39 (4):369 - 393.
    The trilattice SIXTEEN₃ is a natural generalization of the wellknown bilattice FOUR₂. Cut-free, sound and complete sequent calculi for truth entailment and falsity entailment in SIXTEEN₃, are presented.
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  • A Contraction-free and Cut-free Sequent Calculus for Propositional Dynamic Logic.Brian Hill & Francesca Poggiolesi - 2010 - Studia Logica 94 (1):47-72.
    In this paper we present a sequent calculus for propositional dynamic logic built using an enriched version of the tree-hypersequent method and including an infinitary rule for the iteration operator. We prove that this sequent calculus is theoremwise equivalent to the corresponding Hilbert-style system, and that it is contraction-free and cut-free. All results are proved in a purely syntactic way.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Neighborhood Semantics for Modal Logic.Eric Pacuit - 2017 - Cham, Switzerland: Springer.
    This book offers a state-of-the-art introduction to the basic techniques and results of neighborhood semantics for modal logic. In addition to presenting the relevant technical background, it highlights both the pitfalls and potential uses of neighborhood models – an interesting class of mathematical structures that were originally introduced to provide a semantics for weak systems of modal logic. In addition, the book discusses a broad range of topics, including standard modal logic results ; bisimulations for neighborhood models and other model-theoretic (...)
    Download  
     
    Export citation  
     
    Bookmark   37 citations  
  • Display calculi for logics with relative accessibility relations.Stéphane Demri & Rajeev Goré - 2000 - Journal of Logic, Language and Information 9 (2):213-236.
    We define cut-free display calculi for knowledge logics wherean indiscernibility relation is associated to each set of agents, andwhere agents decide the membership of objects using thisindiscernibility relation. To do so, we first translate the knowledgelogics into polymodal logics axiomatised by primitive axioms and thenuse Kracht's results on properly displayable logics to define thedisplay calculi. Apart from these technical results, we argue thatDisplay Logic is a natural framework to define cut-free calculi for manyother logics with relative accessibility relations.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Logical Multilateralism.Heinrich Wansing & Sara Ayhan - 2023 - Journal of Philosophical Logic 52 (6):1603-1636.
    In this paper we will consider the existing notions of bilateralism in the context of proof-theoretic semantics and propose, based on our understanding of bilateralism, an extension to logical multilateralism. This approach differs from what has been proposed under this name before in that we do not consider multiple speech acts as the core of such a theory but rather multiple consequence relations. We will argue that for this aim the most beneficial proof-theoretical realization is to use sequent calculi with (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • The nature of entailment: an informational approach.Yaroslav Shramko & Heinrich Wansing - 2019 - Synthese 198 (S22):5241-5261.
    In this paper we elaborate a conception of entailment based on what we call the Ackermann principle, which explicates valid entailment through a logical connection between sentences depending on their informational content. We reconstruct Dunn’s informational semantics for entailment on the basis of Restall’s approach, with assertion and denial as two independent speech acts, by introducing the notion of a ‘position description’. We show how the machinery of position descriptions can effectively be used to define the positive and the negative (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Linear time in hypersequent framework.Andrzej Indrzejczak - 2016 - Bulletin of Symbolic Logic 22 (1):121-144.
    Hypersequent calculus, developed by A. Avron, is one of the most interesting proof systems suitable for nonclassical logics. Although HC has rather simple form, it increases significantly the expressive power of standard sequent calculi. In particular, HC proved to be very useful in the field of proof theory of various nonclassical logics. It may seem surprising that it was not applied to temporal logics so far. In what follows, we discuss different approaches to formalization of logics of linear frames and (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • A Hypersequent Solution to the Inferentialist Problem of Modality.Andrew Parisi - 2022 - Erkenntnis 87 (4):1605-1633.
    The standard inferentialist approaches to modal logic tend to suffer from not being able to uniquely characterize the modal operators, require that introduction and elimination rules be interdefined, or rely on the introduction of possible-world like indexes into the object language itself. In this paper I introduce a hypersequent calculus that is flexible enough to capture many of the standard modal logics and does not suffer from the above problems. It is therefore an ideal candidate to underwrite an inferentialist theory (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Necessity of Thought.Cesare Cozzo - 2014 - In Heinrich Wansing (ed.), Dag Prawitz on Proofs and Meaning. Cham, Switzerland: Springer. pp. 101-20.
    The concept of “necessity of thought” plays a central role in Dag Prawitz’s essay “Logical Consequence from a Constructivist Point of View” (Prawitz 2005). The theme is later developed in various articles devoted to the notion of valid inference (Prawitz, 2009, forthcoming a, forthcoming b). In section 1 I explain how the notion of necessity of thought emerges from Prawitz’s analysis of logical consequence. I try to expound Prawitz’s views concerning the necessity of thought in sections 2, 3 and 4. (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • Labeled sequent calculi for modal logics and implicit contractions.Pierluigi Minari - 2013 - Archive for Mathematical Logic 52 (7-8):881-907.
    The paper settles an open question concerning Negri-style labeled sequent calculi for modal logics and also, indirectly, other proof systems which make (more or less) explicit use of semantic parameters in the syntax and are thus subsumed by labeled calculi, like Brünnler’s deep sequent calculi, Poggiolesi’s tree-hypersequent calculi and Fitting’s prefixed tableau systems. Specifically, the main result we prove (through a semantic argument) is that labeled calculi for the modal logics K and D remain complete w.r.t. valid sequents whose relational (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • The Stories of Logics.Andreas Kapsner - 2019 - Australasian Journal of Logic 16 (4):133-158.
    In this paper, I investigate how far we can use stories to learn about logic. How can we engage with fiction in order to come to find out what logical principles are actually valid? Is that possible at all? I claim that it is, and I propose two case studies to make the point.
    Download  
     
    Export citation  
     
    Bookmark  
  • Classical and Empirical Negation in Subintuitionistic Logic.Michael De & Hitoshi Omori - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 217-235.
    Subintuitionistic (propositional) logics are those in a standard intuitionistic language that result by weakening the frame conditions of the Kripke semantics for intuitionistic logic. In this paper we consider two negation expansions of subintuitionistic logic, one by classical negation and the other by what has been dubbed “empirical” negation. We provide an axiomatization of each expansion and show them sound and strongly complete. We conclude with some final remarks, including avenues for future research.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Essay Review.H. Wansing - 1999 - History and Philosophy of Logic 20 (2):115-120.
    Download  
     
    Export citation  
     
    Bookmark