Results for 'Two dimensional temporal logic'

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  1.  34
    Handling database updates in two-dimensional temporal logic.Marcelo Finger - 1992 - Journal of Applied Non-Classical Logics 2 (2):201-224.
    ABSTRACT We introduce a two-dimensional temporal logic as a formalism which enables the description of both the history of a world and the evolution of an observer's views about the history. We apply such formalism to the description of certain problems that occur in historical database systems due to updates. The historical dimension describes the history of a world according to an observer's view at a certain moment in time. The transaction dimension describes the evolution of an (...)
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  2.  21
    A two‐dimensional metric temporal logic.Stefano Baratella & Andrea Masini - 2020 - Mathematical Logic Quarterly 66 (1):7-19.
    We introduce a two‐dimensional metric (interval) temporal logic whose internal and external time flows are dense linear orderings. We provide a suitable semantics and a sequent calculus with axioms for equality and extralogical axioms. Then we prove completeness and a semantic partial cut elimination theorem down to formulas of a certain type.
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  3.  90
    Two dimensional Standard Deontic Logic [including a detailed analysis of the 1985 Jones–Pörn deontic logic system].Mathijs Boer, Dov M. Gabbay, Xavier Parent & Marija Slavkovic - 2012 - Synthese 187 (2):623-660.
    This paper offers a two dimensional variation of Standard Deontic Logic SDL, which we call 2SDL. Using 2SDL we can show that we can overcome many of the difficulties that SDL has in representing linguistic sets of Contrary-to-Duties (known as paradoxes) including the Chisholm, Ross, Good Samaritan and Forrester paradoxes. We note that many dimensional logics have been around since 1947, and so 2SDL could have been presented already in the 1970s. Better late than never! As a (...)
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  4.  57
    Two dimensional Standard Deontic Logic [including a detailed analysis of the 1985 Jones–Pörn deontic logic system].Mathijs de Boer, Dov M. Gabbay, Xavier Parent & Marija Slavkovic - 2012 - Synthese 187 (2):623-660.
    This paper offers a two dimensional variation of Standard Deontic Logic SDL, which we call 2SDL. Using 2SDL we can show that we can overcome many of the difficulties that SDL has in representing linguistic sets of Contrary-to-Duties (known as paradoxes) including the Chisholm, Ross, Good Samaritan and Forrester paradoxes. We note that many dimensional logics have been around since 1947, and so 2SDL could have been presented already in the 1970s. Better late than never! As a (...)
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  5.  25
    The temporal logic of two dimensional Minkowski spacetime is decidable.Robin Hirsch & Mark Reynolds - 2018 - Journal of Symbolic Logic 83 (3):829-867.
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  6. Combining Temporal Logic Systems.Marcelo Finger & Dov Gabbay - 1996 - Notre Dame Journal of Formal Logic 37 (2):204-232.
    This paper investigates modular combinations of temporal logic systems. Four combination methods are described and studied with respect to the transfer of logical properties from the component one-dimensional temporal logics to the resulting combined two-dimensional temporal logic. Three basic logical properties are analyzed, namely soundness, completeness, and decidability. Each combination method comprises three submethods that combine the languages, the inference systems, and the semantics of two one-dimensional temporal logic systems, generating (...)
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  7. Two-Dimensional Time.Michael Kowalik - manuscript
    Philosophical views about the logical structure of time are typically divided between proponents of A and B theories, based on McTaggart's A and B series. Drawing on Paul Ricoeur's hermeneutic phenomenology, I develop and defend McTaggart's thesis that the C series and the A series working together give a consistent description of temporal experience, provided that the two series are treated as distinct dimensions internal to time. In the proposed two-dimensional model, the C series expresses a nesting order (...)
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  8.  81
    ""Two-dimensional time: Macbeath's "time's square" and special relativity.Daniel King - 2004 - Synthese 139 (3):421 - 428.
    Murray MacBeath, in his essay ``Time's Square'', describes a fictitious scenariowhere various physical observations made by the participants would, he claims, invitethe interpretation that time for them is two-dimensional. In the present paper, however, Iargue that such observations come close to underdetermining the hypothesis of time's twodimensionality;for a rival hypothesis - that, under certain circumstances, the observationscan be explained in terms of the familiar time dilation effects predicted by special relativity- almost fits the evidence as well. That is, under (...)
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  9. On the Mosaic Method for Many-Dimensional Modal Logics: A Case Study Combining Tense and Modal Operators. [REVIEW]Carlos Caleiro, Luca Viganò & Marco Volpe - 2013 - Logica Universalis 7 (1):33-69.
    We present an extension of the mosaic method aimed at capturing many-dimensional modal logics. As a proof-of-concept, we define the method for logics arising from the combination of linear tense operators with an “orthogonal” S5-like modality. We show that the existence of a model for a given set of formulas is equivalent to the existence of a suitable set of partial models, called mosaics, and apply the technique not only in obtaining a proof of decidability and a proof of (...)
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  10.  1
    Ecstatic Temporality and Transcendence in Section 65 of Chapter III and Section 69 of Chapter IV in Relation to Ontological Movement in Section 74 of Chapter V in Division Two of Heidegger’s Being and Time (1927), Part I. [REVIEW]Rajesh Sampath - 2024 - Symposion: Theoretical and Applied Inquiries in Philosophy and Social Sciences 11 (1):49-76.
    This first article is part of a two-article series labeled Parts I and II. In Part I, we will attempt a close reading of Division Two of Heidegger’s greatest work, Being and Time (1927). We will execute a granular analysis of a few lines and phrases in section 65 in Chapter III, section 69 in Chapter IV, and sections 72 and 74 in Chapter V; those sections cover ‘primordial ecstatic, finite, unified, authentic temporality’ (Heidegger 1962, 380) and the ‘equiprimordiality of (...)
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  11. Two-dimensional modal logic.Krister Segerberg - 1973 - Journal of Philosophical Logic 2 (1):77 - 96.
  12. Actuality, Tableaux, and Two-Dimensional Modal Logics.Fabio Lampert - 2018 - Erkenntnis 83 (3):403-443.
    In this paper we present tableau methods for two-dimensional modal logics. Although models for such logics are well known, proof systems remain rather unexplored as most of their developments have been purely axiomatic. The logics herein considered contain first-order quantifiers with identity, and all the formulas in the language are doubly-indexed in the proof systems, with the upper indices intuitively representing the actual or reference worlds, and the lower indices representing worlds of evaluation—first and second dimensions, respectively. The tableaux (...)
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  13.  63
    Two-dimensional awareness logics.Hu Liu & Shier Ju - 2004 - Journal of Philosophical Logic 33 (5):481-495.
    Awareness logic is a type of belief logic in which an agent's beliefs are restricted to those sentences that the agent is aware of. Awareness logic is a successful way to circumvent the problem of omniscience so that actual belief is modelled in a reasonable way. In this paper, we suggest a new method modelling awareness and actual belief by using two-dimensional logics. We show that the two-dimensional logics are flexible tools. Different types of concepts (...)
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  14.  87
    Deontic Tense Logic With Historical Necessity, Frame Constants, and a Solution to the Epistemic Obligation Paradox.Lennart Åqvist - 2014 - Theoria 80 (4):319-349.
    In an earlier paper by the author, Åqvist , I presented an approach to the logic of historical necessity, or inevitability, in the sense of a “two-dimensional” combination of tense and modal logic for worlds, or histories, with the same time order, known as T × W logic. Distinctive features of that approach were, apart from its two-dimensionality, its being based on discrete and finite time, and its use of so-called systematic frame constants in order to (...)
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  15.  94
    Non-finitely axiomatisable two-dimensional modal logics.Agi Kurucz & Sérgio Marcelino - 2012 - Journal of Symbolic Logic 77 (3):970-986.
    We show the first examples of recursively enumerable (even decidable) two-dimensional products of finitely axiomatisable modal logics that are not finitely axiomatisable. In particular, we show that any axiomatisation of some bimodal logics that are determined by classes of product frames with linearly ordered first components must be infinite in two senses: It should contain infinitely many propositional variables, and formulas of arbitrarily large modal nesting-depth.
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  16.  8
    Branching Time Structures and Points of View.Margarita Vázquez Campos - 2015 - In Temporal Points of View: Subjective and Objective Aspects. Cham: Springer. pp. 183-195.
    In this paper I analyze the temporal structures that are appropriate to study the notion of point of view. When we analyze the points of view and their structure, it seems clear that we must take into account the time t in which a point of view is attributed to a subject. A two-dimensional temporal logic which combines a modal dimension for possibilities and a temporal one for the flow of time, offers a clear view (...)
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  17.  83
    A cut-free sequent system for two-dimensional modal logic, and why it matters.Greg Restall - 2012 - Annals of Pure and Applied Logic 163 (11):1611-1623.
    The two-dimensional modal logic of Davies and Humberstone [3] is an important aid to our understanding the relationship between actuality, necessity and a priori knowability. I show how a cut-free hypersequent calculus for 2D modal logic not only captures the logic precisely, but may be used to address issues in the epistemology and metaphysics of our modal concepts. I will explain how the use of our concepts motivates the inference rules of the sequent calculus, and then (...)
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  18. A logic for epistemic two-dimensional semantics.Peter Fritz - 2013 - Synthese 190 (10):1753-1770.
    Epistemic two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. While this theory is usually presented in an informal manner, I take some steps in formalizing it in this paper. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, and apriority that captures the relevant ideas of epistemic two-dimensional semantics. (...)
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  19.  51
    A two-dimensional logic for diagonalization and the a priori.Melissa Fusco - 2020 - Synthese 198 (9):8307-8322.
    Two-dimensional semantics, which can represent the distinction between a priority and necessity, has wielded considerable influence in the philosophy of language. In this paper, I axiomatize the dagger operator of Stalnaker’s “Assertion” in the formal context of two-dimensional modal logic. The language contains modalities of actuality, necessity, and a priority, but is also able to represent diagonalization, a conceptually important operation in a variety of contexts, including models of the relative a priori and a posteriori often appealed (...)
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  20.  46
    Two Temporal Logics of Contingency.Matteo Pascucci - 2015 - Australasian Journal of Logic 12 (2):121-134.
    This work concerns the use of operators for past and future contingency in Priorean temporal logic. We will develop a system named C_t, whose language includes a propositional constant and prove that (I) C_t is complete with respect to a certain class of general frames and (II) the usual operators for past and future necessity are definable in such system. Furthermore, we will introduce the extension C_t(lin) that can be interpreted on linear and transitive general frames. The theoretical (...)
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  21.  50
    Modal logics of domains on the real plane.V. B. Shehtman - 1983 - Studia Logica 42 (1):63-80.
    This paper concerns modal logics appearing from the temporal ordering of domains in two-dimensional Minkowski spacetime. As R. Goldblatt has proved recently, the logic of the whole plane isS4.2. We consider closed or open convex polygons and closed or open domains bounded by simple differentiable curves; this leads to the logics:S4,S4.1,S4.2 orS4.1.2.
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  22.  15
    Two dimensional Standard Deontic Logic [including a detailed analysis of the 1985 Jones–Pörn deontic logic system].M. de Boer, D. Gabbay, X. Parent & M. Slavkova - 2012 - Synthese 187 (2):623-660.
    This paper offers a two dimensional variation of Standard Deontic Logic SDL, which we call 2SDL. Using 2SDL we can show that we can overcome many of the difficulties that SDL has in representing linguistic sets of Contrary-to-Duties (known as paradoxes) including the Chisholm, Ross, Good Samaritan and Forrester paradoxes. We note that many dimensional logics have been around since 1947, and so 2SDL could have been presented already in the 1970s. Better late than never! As a (...)
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  23.  62
    A Two-Dimensional Logic for Two Paradoxes of Deontic Modality.Melissa Fusco & Alexander W. Kocurek - 2022 - Review of Symbolic Logic 15 (4):991-1022.
    In this paper, we axiomatize the deontic logic in Fusco (2015), which uses a Stalnaker-inspired account of diagonal acceptance and a two-dimensional account of disjunction to treat Ross’s Paradox and the Puzzle of Free Choice Permission. On this account, disjunction-involving validities are a priori rather than necessary. We show how to axiomatize two-dimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as one-dimensional projections of more general two-dimensional rules. These completeness results (...)
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  24. Modal Logics for Integral Spacetime.John F. Phillips - 1999 - Dissertation, The University of Wisconsin - Madison
    The main project of this dissertation is to analyze various temporal conceptions of modality for discrete n-dimensional spacetime. The first chapter contains an introduction to the problem and known results. Chapter 2 consists of a study of logics which are analogues of the so-called 'logic of today and tomorrow' and 'logic of tomorrow' investigated by Segerberg and others. We consider the analogues of these successor logics for 2-dimensional integral spacetime. We provide axiomatizations in monomodal and (...)
     
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  25.  49
    Questions in Two-Dimensional Logic.Thom van Gessel - 2022 - Review of Symbolic Logic 15 (4):859-879.
    Since Kripke, philosophers have distinguished a priori true statements from necessarily true ones. A statement is a priori true if its truth can be established before experience, and necessarily true if it could not have been false according to logical or metaphysical laws. This distinction can be captured formally using two-dimensional semantics. There is a natural way to extend the notions of apriority and necessity so they can also apply to questions. Questions either can or cannot be resolved before (...)
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  26. A Statement of Temporal Realism.Two Essays on Temporal Realism - 1996 - In Brian Jack Copeland (ed.), Logic and reality: essays on the legacy of Arthur Prior. New York: Oxford University Press.
     
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  27.  68
    Arthur Prior and ‘Now’.Patrick Blackburn & Klaus Frovin Jørgensen - 2016 - Synthese 193 (11).
    On the 4th of December 1967, Hans Kamp sent his UCLA seminar notes on the logic of ‘now’ to Arthur N. Prior. Kamp’s two-dimensional analysis stimulated Prior to an intense burst of creativity in which he sought to integrate Kamp’s work into tense logic using a one-dimensional approach. Prior’s search led him through the work of Castañeda, and back to his own work on hybrid logic: the first made temporal reference philosophically respectable, the second (...)
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  28. Two-Dimensional Semantics.Manuel García-Carpintero & Josep Macià (eds.) - 2006 - New York: Oxford: Clarendon Press.
    Two-dimensional semantics is a framework that helps us better understand some of the most fundamental issues in philosophy: those having to do with the relationship between the meaning of words, the way the world is, and our knowledge of the meaning of words. This selection of new essays by some of the world's leading authorities in this field sheds fresh light both on foundational issues regarding two-dimensional semantics and on its specific applications. Contributors: Richard Breheny, Alex Byrne, David (...)
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  29. Two-dimensional adventures.Lloyd Humberstone - 2004 - Philosophical Studies 118 (1-2):17--65.
    This paper recalls some applications of two-dimensional modal logic from the 1980s, including work on the logic of Actually and on a somewhat idealized version of the indicative/subjunctive distinction, as well as on absolute and relative necessity. There is some discussion of reactions this material has aroused in commentators since. We also survey related work by Leslie Tharp from roughly the same period.
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  30.  60
    Two Technical Images: Blockchain and High-Frequency Trading.Diego Viana - 2018 - Philosophy and Technology (1):77-102.
    The article examines two digital phenomena linked to money and finance, which are the bitcoin and high-frequency trading, through the lens of Vilém Flusser’s concept of technical image. Flusser’s theory highlights three aspects of technical images: they are engendered by the act of organizing particles, are produced by people who operate devices through keys, and are mediated by code, which is linear and pertains to the era of written text, which Flusser conflates with the notion of history. In this article, (...)
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  31. A conjectured axiomatization of two-dimensional Reichenbachian tense logic.Lennart Åqvist - 1977 - Uppsala: [Filosofiska föreningen och Filosofiska institutionen, Uppsala universitet].
     
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  32.  27
    A Two Dimensional Tense-modal Sortal Logic.Max A. Freund - 2007 - Journal of Philosophical Logic 36 (5):571-598.
    We consider a formal language whose logical syntax involves both modal and tense propositional operators, as well as sortal quantifiers, sortal identities and (second order) quantifiers over sortals. We construct an intensional semantics for the language and characterize a formal logical system which we prove to be sound and complete with respect to the semantics. Conceptualism is the philosophical background of the semantic system.
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  33.  27
    A Note on Axiomatisations of Two-Dimensional Modal Logics.Agi Kurucz - 2013 - In Kamal Lodaya (ed.), Logic and Its Applications. Springer. pp. 27--33.
  34. Some Free Thinking about Time.Two Essays on Temporal Realism - 1996 - In Brian Jack Copeland (ed.), Logic and reality: essays on the legacy of Arthur Prior. New York: Oxford University Press.
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  35. Completeness results for some two-dimensional logics of actuality.David R. Gilbert & Edwin D. Mares - 2012 - Review of Symbolic Logic 5 (2):239-258.
    We provide a Hilbert-style axiomatization of the logic of , as well as a two-dimensional semantics with respect to which our logics are sound and complete. Our completeness results are quite general, pertaining to all such actuality logics that extend a normal and canonical modal basis. We also show that our logics have the strong finite model property and permit straightforward first-order extensions.
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  36. The logic of historical necessity as founded on two-dimensional modal tense logic.Lennart Åqvist - 1999 - Journal of Philosophical Logic 28 (4):329-369.
    We consider a version of so called T x W logic for historical necessity in the sense of R.H. Thomason (1984), which is somewhat special in three respects: (i) it is explicitly based on two-dimensional modal logic in the sense of Segerberg (1973); (ii) for reasons of applicability to interesting fields of philosophical logic, it conceives of time as being discrete and finite in the sense of having a beginning and an end; and (iii) it utilizes (...)
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  37.  43
    Temporal Logic: Mathematical Foundations and Computational Aspects.Dov M. Gabbay, Ian Hodkinson & Mark A. Reynolds - 1994 - Oxford University Press on Demand.
    This much-needed book provides a thorough account of temporal logic, one of the most important areas of logic in computer science today. The book begins with a solid introduction to semantical and axiomatic approaches to temporal logic. It goes on to cover predicate temporal logic, meta-languages, general theories of axiomatization, many dimensional systems, propositional quantifiers, expressive power, Henkin dimension, temporalization of other logics, and decidability results. With its inclusion of cutting-edge results and (...)
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  38. On the expressive power of first-order modal logic with two-dimensional operators.Alexander W. Kocurek - 2018 - Synthese 195 (10):4373-4417.
    Many authors have noted that there are types of English modal sentences cannot be formalized in the language of basic first-order modal logic. Some widely discussed examples include “There could have been things other than there actually are” and “Everyone who is actually rich could have been poor.” In response to this lack of expressive power, many authors have discussed extensions of first-order modal logic with two-dimensional operators. But claims about the relative expressive power of these extensions (...)
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  39. The Foundations of Two-Dimensional Semantics.David J. Chalmers - 2006 - In Manuel García-Carpintero & Josep Macià (eds.), Two-Dimensional Semantics. New York: Oxford: Clarendon Press. pp. 55-140.
    Why is two-dimensional semantics important? One can think of it as the most recent act in a drama involving three of the central concepts of philosophy: meaning, reason, and modality. First, Kant linked reason and modality, by suggesting that what is necessary is knowable a priori, and vice versa. Second, Frege linked reason and meaning, by proposing an aspect of meaning (sense) that is constitutively tied to cognitive signi?cance. Third, Carnap linked meaning and modality, by proposing an aspect of (...)
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  40.  32
    Two-Dimensional Tableaux.David Gilbert - 2016 - Australasian Journal of Logic 13 (7).
    We present two-dimensional tableau systems for the actuality, fixedly, and up-arrow operators. All systems are proved sound and complete with respect to a two-dimensional semantics. In addition, a decision procedure for the actuality logics is discussed.
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  41. Epistemic Two-Dimensional Semantics.David J. Chalmers - 2004 - Philosophical Studies 118 (1-2):153-226.
  42. Two-dimensional semantics and the articulation problem.Diego Marconi - 2005 - Synthese 143 (3):321-49.
    . David Chalmerss version of two-dimensional semantics is an attempt at setting up a unified semantic framework that would vindicate both the Fregean and the Kripkean semantic intuitions. I claim that there are three acceptable ways of carrying out such a project, and that Chalmerss theory does not coherently fit any of the three patterns. I suggest that the theory may be seen as pointing to the possibility of a double reading for many linguistic expressions (a double reading which, (...)
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  43. Reference, contingency, and the two-dimensional framework.Martin Davies - 2004 - Philosophical Studies 118 (1-2):83-131.
    I review and reconsider some of the themes of ‘Two notions of necessity’ (Davies and Humberstone, 1980) and attempt to reach a deeper understanding and appreciation of Gareth Evans’s reflections (in ‘Reference and contingency’, 1979) on both modality and reference. My aim is to plot the relationships between the notions of necessity that Humberstone and I characterised in terms of operators in two-dimensional modal logic, the notions of superficial and deep necessity that Evans himself described, and the epistemic (...)
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  44. A Note on the Modal and Temporal Logics for N -Dimensional Spacetime.John F. Phillips - 1998 - Notre Dame Journal of Formal Logic 39 (4):545-553.
    We generalize an observation made by Goldblatt in "Diodorean modality in Minkowski spacetime" by proving that each -dimensional integral spacetime frame equipped with Robb's irreflexive `after' relation determines a unique temporal logic. Our main result is that, unlike -dimensional spacetime where, as Goldblatt has shown, the Diodorean modal logic is the same for each frame , in the case of -dimensional integral spacetime, the frame determines a unique Diodorean modal logic.
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  45.  67
    Presupposition and two-dimensional logic.Merrie Bergmann - 1981 - Journal of Philosophical Logic 10 (1):27 - 53.
  46.  15
    Defeasible linear temporal logic.Anasse Chafik, Fahima Cheikh-Alili, Jean-François Condotta & Ivan Varzinczak - 2023 - Journal of Applied Non-Classical Logics 33 (1):1-51.
    After the seminal work of Kraus, Lehmann and Magidor (formally known as the KLM approach) on conditionals and preferential models, many aspects of defeasibility in more complex formalisms have been studied in recent years. Examples of these aspects are the notion of typicality in description logic and defeasible necessity in modal logic. We discuss a new aspect of defeasibility that can be expressed in the case of temporal logic, which is the normality in an execution. In (...)
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  47.  90
    Many-dimensional modal logics: theory and applications.Dov M. Gabbay (ed.) - 2003 - Boston: Elsevier North Holland.
    Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects. To (...)
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  48. Plausibility Revision in Higher-Order Logic With an Application in Two-Dimensional Semantics.Erich Rast - 2010 - In Arrazola Xabier & Maria Ponte (eds.), LogKCA-10 - Proceedings of the Second ILCLI International Workshop on Logic and Philosophy of Knowledge. ILCLI.
    In this article, a qualitative notion of subjective plausibility and its revision based on a preorder relation are implemented in higher-order logic. This notion of plausibility is used for modeling pragmatic aspects of communication on top of traditional two-dimensional semantic representations.
     
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  49. Matrices and Modalities: On the Logic of Two-Dimensional Semantics.Peter Fritz - manuscript
    Two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. Usually, this theory is presented in an informal manner. In this thesis, I take first steps in formalizing it, and use the formalization to present some considerations in favor of two-dimensional semantics. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, (...)
     
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  50.  49
    A conjectured axiomatization of two-dimensional Reichenbachian tense logic.Lennart Åqvist - 1979 - Journal of Philosophical Logic 8 (1):1 - 45.
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