Switch to: References

Citations of:

A note on the logic of elsewhere

Theoria 46 (2-3):183-187 (1980)

Add citations

You must login to add citations.
  1. Axiomatizability of Propositionally Quantified Modal Logics on Relational Frames.Peter Fritz - 2024 - Journal of Symbolic Logic 89 (2):758-793.
    Propositional modal logic over relational frames is naturally extended with propositional quantifiers by letting them range over arbitrary sets of worlds of the relevant frame. This is also known as second-order propositional modal logic. The propositionally quantified modal logic of a class of relational frames is often not axiomatizable, although there are known exceptions, most notably the case of frames validating the strong modal logic $\mathrm {S5}$. Here, we develop new general methods with which many of the open questions in (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Carnap’s Problem for Modal Logic.Denis Bonnay & Dag Westerståhl - 2023 - Review of Symbolic Logic 16 (2):578-602.
    We take Carnap’s problem to be to what extent standard consequence relations in various formal languages fix the meaning of their logical vocabulary, alone or together with additional constraints on the form of the semantics. This paper studies Carnap’s problem for basic modal logic. Setting the stage, we show that neighborhood semantics is the most general form of compositional possible worlds semantics, and proceed to ask which standard modal logics (if any) constrain the box operator to be interpreted as in (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Modal Logic for Other-World Agnostics: Neutrality and Halldén Incompleteness.Lloyd Humberstone - 2007 - Journal of Philosophical Logic 36 (1):1-32.
    The logic of 'elsewhere,' i.e., of a sentence operator interpretable as attaching to a formula to yield a formula true at a point in a Kripke model just in case the first formula is true at all other points in the model, has been applied in settings in which the points in question represent spatial positions, as well as in the case in which they represent moments of time. This logic is applied here to the alethic modal case, in which (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Generalizing the lottery paradox.Igor Douven & Timothy Williamson - 2006 - British Journal for the Philosophy of Science 57 (4):755-779.
    This paper is concerned with formal solutions to the lottery paradox on which high probability defeasibly warrants acceptance. It considers some recently proposed solutions of this type and presents an argument showing that these solutions are trivial in that they boil down to the claim that perfect probability is sufficient for rational acceptability. The argument is then generalized, showing that a broad class of similar solutions faces the same problem. An argument against some formal solutions to the lottery paradox The (...)
    Download  
     
    Export citation  
     
    Bookmark   78 citations  
  • Abstract modal logics.Ramon Jansana - 1995 - Studia Logica 55 (2):273 - 299.
    In this paper we develop a general framework to deal with abstract logics associated with a given modal logic. In particular we study the abstract logics associated with the weak and strong deductive systems of the normal modal logicK and its intuitionistic version. We also study the abstract logics that satisfy the conditionC +(X)=C( in I n X) and find the modal deductive systems whose abstract logics, in addition to being classical or intuitionistic, satisfy that condition. Finally we study the (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Non-finitely axiomatisable modal product logics with infinite canonical axiomatisations.Christopher Hampson, Stanislav Kikot, Agi Kurucz & Sérgio Marcelino - 2020 - Annals of Pure and Applied Logic 171 (5):102786.
    Our concern is the axiomatisation problem for modal and algebraic logics that correspond to various fragments of two-variable first-order logic with counting quantifiers. In particular, we consider modal products with Diff, the propositional unimodal logic of the difference operator. We show that the two-dimensional product logic $Diff \times Diff$ is non-finitely axiomatisable, but can be axiomatised by infinitely many Sahlqvist axioms. We also show that its ‘square’ version (the modal counterpart of the substitution and equality free fragment of two-variable first-order (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • (1 other version)On Modal Products with th Logic of 'Elsewhere'.Christopher Hampson & Agi Kurucz - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 339-347.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Intuitionistic logic and modality via topology.Leo Esakia - 2004 - Annals of Pure and Applied Logic 127 (1-3):155-170.
    In the pioneering article and two papers, written jointly with McKinsey, Tarski developed the so-called algebraic and topological frameworks for the Intuitionistic Logic and the Lewis modal system. In this paper, we present an outline of modern systems with a topological tinge. We consider topological interpretation of basic systems GL and G of the provability logic in terms of the Cantor derivative and the Hausdorff residue.
    Download  
     
    Export citation  
     
    Bookmark   25 citations  
  • Von der Ontologie des Raums zur Ontologie der Raumzeit.Niko Strobach - 2006 - History of Philosophy & Logical Analysis 9 (1):105-133.
    Download  
     
    Export citation  
     
    Bookmark  
  • The Logic of Where and While in the 13th and 14th Centuries.Sara Uckelman - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 535-550.
    Medieval analyses of molecular propositions include many non-truthfunctional connectives in addition to the standard modern binary connectives (conjunction, disjunction, and conditional). Two types of non-truthfunctional molecular propositions considered by a number of 13th- and 14th-century authors are temporal and local propositions, which combine atomic propositions with `while' and `where'. Despite modern interest in the historical roots of temporal and tense logic, medieval analyses of `while' propositions are rarely discussed in modern literature, and analyses of `where' propositions are almost completely overlooked. (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Leo Esakia on Duality in Modal and Intuitionistic Logics.Guram Bezhanishvili (ed.) - 2014 - Dordrecht, Netherland: Springer.
    This volume is dedicated to Leo Esakia's contributions to the theory of modal and intuitionistic systems. Consisting of 10 chapters, written by leading experts, this volume discusses Esakia’s original contributions and consequent developments that have helped to shape duality theory for modal and intuitionistic logics and to utilize it to obtain some major results in the area. Beginning with a chapter which explores Esakia duality for S4-algebras, the volume goes on to explore Esakia duality for Heyting algebras and its generalizations (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • On the Modal Logic of Subset and Superset: Tense Logic over Medvedev Frames.Wesley H. Holliday - 2017 - Studia Logica 105 (1):13-35.
    Viewing the language of modal logic as a language for describing directed graphs, a natural type of directed graph to study modally is one where the nodes are sets and the edge relation is the subset or superset relation. A well-known example from the literature on intuitionistic logic is the class of Medvedev frames $\langle W,R\rangle$ where $W$ is the set of nonempty subsets of some nonempty finite set $S$, and $xRy$ iff $x\supseteq y$, or more liberally, where $\langle W,R\rangle$ (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • Temporal Reference in Linear Tense Logic.M. J. Cresswell - 2010 - Journal of Philosophical Logic 39 (2):173-200.
    The paper introduces a first-order theory in the language of predicate tense logic which contains a single simple axiom. It is shewn that this theory enables times to be referred to and sentences involving ‘now’ and ‘then’ to be formalised. The paper then compares this way of increasing the expressive capacity of predicate tense logic with other mechanisms, and indicates how to generalise the results to other modal and tense systems.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Proof-Theoretic Functional Completeness for the Hybrid Logics of Everywhere and Elsewhere.Torben Braüner - 2005 - Studia Logica 81 (2):191-226.
    A hybrid logic is obtained by adding to an ordinary modal logic further expressive power in the form of a second sort of propositional symbols called nominals and by adding so-called satisfaction operators. In this paper we consider hybridized versions of S5 (“the logic of everywhere”) and the modal logic of inequality (“the logic of elsewhere”). We give natural deduction systems for the logics and we prove functional completeness results.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Decidable first-order modal logics with counting quantifiers.Christopher Hampson - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 382-400.
    Download  
     
    Export citation  
     
    Bookmark