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Introductions Fitting & Mendelsohn 1998
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  1. We Belong Together? A Plea for Modesty in Modal Plural Logic.Simon Hewitt - manuscript
    It is often assumed that pluralities are rigid, in the sense of having all and only their actual members necessarily. This assumption is operative in standard approaches to modal plural logic. I argue that a sceptical approach towards the assumption is warranted.
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  2. Modal Realism and the Meaning of 'Exist'.T. Parent - manuscript
    Here I first raise an argument purporting to show that Lewis’ Modal Realism ends up being entirely trivial. But although I reject this line, the argument reveals how difficult it is to interpret Lewis’ thesis that possibilia “exist.” Five natural interpretations are considered, yet upon reflection, none appear entirely adequate. On the three different “concretist” interpretations of ‘exist’, Modal Realism looks insufficient for genuine ontological commitment. Whereas, on the “multiverse” interpretation, Modal Realism acknowledges physical possibilities only--and worse, (assuming either axiom (...)
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  3. First Order Classical Modal Logic, Studia Logica, 84, 2, 171-210, 2006.Horacio Arlo-Costa & Eric Pacuit - manuscript
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  4. The Barcan Formulas and Necessary Existence: The View From Quarc.Hanoch Ben-Yami - forthcoming - Synthese:1-36.
    The Modal Predicate Calculus gives rise to issues surrounding the Barcan formulas, their converses, and necessary existence. I examine these issues by means of the Quantified Argument Calculus, a recently developed, powerful formal logic system. Quarc is closer in syntax and logical properties to Natural Language than is the Predicate Calculus, a fact that lends additional interest to this examination, as Quarc might offer a better representation of our modal concepts. The validity of the Barcan formulas and their converses is (...)
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  5. Now, Imagine an Actually Existing Unicorn: On Russellian Worries for Modal Meinongianism.Andreas de Jong - forthcoming - Axiomathes:1-16.
    Modal Meinongianism provides the semantics of sentences involving intentional verbs Priest (Towards Nonbeing, Oxford University Press, Oxford, 2016). To that end, Modal Meinongianism employs a pointed non-normal quantified modal logic model. Like earlier Meinongian views Modal Meinongianism has a characterisation principle (QCP), that claims that any condition whatsoever is satisfied by some object in some world. Recently, Everett (The nonexistent, Oxford University Press, Oxford, 2013, 169, p. 36) has proposed an argument against QCP that, if successful, gives rise to problems (...)
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  6. Binding Bound Variables in Epistemic Contexts.Brian Rabern - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy:1-31.
    Quine insisted that the satisfaction of an open modalised formula by an object depends on how that object is described. Kripke’s "objectual" interpretation of quantified modal logic, whereby variables are rigid, is commonly thought to avoid these Quinean worries. Yet there remain residual Quinean worries in the epistemic case. Theorists have recently been toying with assignment-shifting treatments of epistemic contexts. On such views an epistemic operator ends up binding all the variables in its scope. One might worry that this yields (...)
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  7. Themes From Barcan Marcus.Timothy Williamson - forthcoming - Lauener Library of Analytical Philosophy, Vol. 3.
  8. Self-Referential Theories.Samuel A. Alexander - 2020 - Journal of Symbolic Logic 85 (4):1687-1716.
    We study the structure of families of theories in the language of arithmetic extended to allow these families to refer to one another and to themselves. If a theory contains schemata expressing its own truth and expressing a specific Turing index for itself, and contains some other mild axioms, then that theory is untrue. We exhibit some families of true self-referential theories that barely avoid this forbidden pattern.
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  9. The Reduction of Necessity to Essence.Andreas Ditter - 2020 - Mind 129 (514):351-380.
    In `Essence and Modality', Kit Fine proposes that for a proposition to be metaphysically necessary is for it to be true in virtue of the nature of all objects whatsoever. Call this view Fine's Thesis. This paper is a study of Fine's Thesis in the context of Fine's logic of essence (LE). Fine himself has offered his most elaborate defense of the thesis in the context of LE. His defense rests on the widely shared assumption that metaphysical necessity obeys the (...)
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  10. A Patch to the Possibility Part of Gödel’s Ontological Proof.Johan E. Gustafsson - 2020 - Analysis 80 (2):229-240.
    Kurt Gödel’s version of the Ontological Proof derives rather than assumes the crucial Possibility Claim: the claim that it is possible that something God-like exists. Gödel’s derivation starts off with a proof of the Possible Instantiation of the Positive: the principle that, if a property is positive, it is possible that there exists something that has that property. I argue that Gödel’s proof of this principle relies on some implausible axiological assumptions but it can be patched so that it only (...)
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  11. Modal Fragmentalism.Samuele Iaquinto - 2020 - The Philosophical Quarterly 70 (280):570-587.
    In this paper, I will argue that there is a version of possibilism—inspired by the modal analogue of Kit Fine’s fragmentalism—that can be combined with a weakening of actualism. The reasons for analysing this view, which I call Modal Fragmentalism, are twofold. Firstly, it can enrich our understanding of the actualism/possibilism divide, by showing that, at least in principle, the adoption of possibilia does not correspond to an outright rejection of the actualist intuitions. Secondly, and more specifically, it can enrich (...)
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  12. A First-Order Modal Theodicy: God, Evil, and Religious Determinism.Gesiel Borges da Silva & Fábio Bertato - 2019 - South American Journal of Logic 5 (1):49-80.
    Edward Nieznanski developed in 2007 and 2008 two different systems in formal logic which deal with the problem of evil. Particularly, his aim is to refute a version of the logical problem of evil associated with a form of religious determinism. In this paper, we revisit his first system to give a more suitable form to it, reformulating it in first-order modal logic. The new resulting system, called N1, has much of the original basic structure, and many axioms, definitions, and (...)
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  13. A Note on Algebraic Semantics for $Mathsf{S5}$ with Propositional Quantifiers.Wesley H. Holliday - 2019 - Notre Dame Journal of Formal Logic 60 (2):311-332.
    In two of the earliest papers on extending modal logic with propositional quantifiers, R. A. Bull and K. Fine studied a modal logic S5Π extending S5 with axioms and rules for propositional quantification. Surprisingly, there seems to have been no proof in the literature of the completeness of S5Π with respect to its most natural algebraic semantics, with propositional quantifiers interpreted by meets and joins over all elements in a complete Boolean algebra. In this note, we give such a proof. (...)
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  14. A Note on Algebraic Semantics for S5 with Propositional Quantifiers.Wesley H. Holliday - 2019 - Notre Dame Journal of Formal Logic 60 (2):311-332.
    In two of the earliest papers on extending modal logic with propositional quantifiers, R. A. Bull and K. Fine studied a modal logic S5Π extending S5 with axioms and rules for propositional quantification. Surprisingly, there seems to have been no proof in the literature of the completeness of S5Π with respect to its most natural algebraic semantics, with propositional quantifiers interpreted by meets and joins over all elements in a complete Boolean algebra. In this note, we give such a proof. (...)
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  15. Explicitní/implicitní přesvědčení a derivační systémy [Explicit/Implicit Belief and Derivation Systems].Jiri Raclavsky & Ivo Pezlar - 2019 - Filosoficky Casopis 67 (1): 89-120.
    The problem of hyperintensional contexts, and the problem of logical omniscience, shows the severe limitation of possible-worlds semantics which is employed also in standard epistemic logic. As a solution, we deploy here hyperintensional semantics according to which the meaning of an expression is an abstract structured algorithm, namely Tichý's construction. Constructions determine the denotata of expressions. Propositional attitudes are modelled as attitudes towards constructions of truth values. Such a model of belief is, of course, inferentially restrictive. We therefore also propose (...)
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  16. Partial Semantics for Quantified Modal Logic.Eric Johannesson - 2018 - Journal of Philosophical Logic 47 (6):1049-1060.
    When it comes to Kripke-style semantics for quantified modal logic, there’s a choice to be made concerning the interpretation of the quantifiers. The simple approach is to let quantifiers range over all possible objects, not just objects existing in the world of evaluation, and use a special predicate to make claims about existence. This is the constant domain approach. The more complicated approach is to assign a domain of objects to each world. This is the varying domain approach. Assuming that (...)
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  17. On the Expressive Power of First-Order Modal Logic with Two-Dimensional Operators.Alexander 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 are often justified (...)
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  18. 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 modulate (...)
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  19. Existential Import and Relations of Categorical and Modal Categorical Statements.Jiri Raclavsky - 2018 - Logic and Logical Philosophy 27 (3): 271-300.
    I examine the familiar quadruple of categorical statements “Every F is/is not G.”, “Some F is/is not G.” as well as the quadruple of their modal versions “Necessarily, every F is/is not G.”, “Possibly, some F is/is not G.”. I focus on their existential import and its impact on the resulting Squares of Opposition. Though my construal of existential import follows modern approach, I add some extra details which are enabled by framing my definition of existential import within expressively rich (...)
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  20. Logic: The Basics (2nd Edition).Jc Beall & Shay A. Logan - 2017 - Routledge.
    Logic: the Basics is an accessible introduction to the core philosophy topic of standard logic. Focussing on traditional Classical Logic the book deals with topics such as mathematical preliminaries, propositional logic, monadic quantified logic, polyadic quantified logic, and English and standard ‘symbolic transitions’. With exercises and sample answers throughout this thoroughly revised new edition not only comprehensively covers the core topics at introductory level but also gives the reader an idea of how they can take their knowledge further and the (...)
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  21. Strongly Millian Second-Order Modal Logics.Bruno Jacinto - 2017 - Review of Symbolic Logic (3):1-58.
    The most common first- and second-order modal logics either have as theorems every instance of the Barcan and Converse Barcan formulae and of their second-order analogues, or else fail to capture the actual truth of every theorem of classical first- and second-order logic. In this paper we characterise and motivate sound and complete first- and second-order modal logics that successfully capture the actual truth of every theorem of classical first- and second-order logic and yet do not possess controversial instances of (...)
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  22. The Modal Argument Against Nominal Description Theory.Jiri Raclavsky - 2017 - Kriterion - Journal of Philosophy 31 (1):77-100.
    The paper examines Loar’s and Bach’s defence of Nominal Description Theory against Kripkean Modal Argument (MA). Using formal tools of hyperintensional logic, I discriminate three kinds of nominal description which are possible substitutes for a proper name, thus considering various readings of the MA. On its natural understanding, the MA is valid – contrary to what Loar and Bach say. On the other hand, the soundness of the MA remains doubtful, as pointed out already by Loar and Bach.
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  23. Two Standard and Two Modal Squares of Opposition.Jiri Raclavsky - 2017 - In The Square of Opposition: A Cornerstone of Thought. 93413 Cham, Německo: pp. 119-142.
    In this study, we examine modern reading of the Square of Opposition by means of Tichý's Transparent intensional logic. Explicit use of possible world semantics helps us to sharply discriminate between standard and modal readings of categorial statements. We thus get two basic versions of the Square, whereas the Modal Square has not been fully introduced in the contemporary debate yet. Some properties ascribed by mediaeval logicians to the Square require a shift from its Standard to Modal version. Not inevitably, (...)
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  24. Objects and Modalities.Tero Tulenheimo - 2017 - Springer Verlag.
    This book develops a novel generalization of possible world semantics, called ‘world line semantics’, which recognizes worlds and links between world-bound objects (world lines) as mutually independent aspects of modal semantics. Addressing a wide range of questions vital for contemporary debates in logic and philosophy of language and offering new tools for theoretical linguistics and knowledge representation, the book proposes a radically new paradigm in modal semantics. This framework is motivated philosophically, viewing a structure of world lines as a precondition (...)
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  25. Modal Logic and Contingentism: A Comment on Timothy Williamsons Modal Logic as Metaphysics.Louis deRosset - 2016 - Analysis 76 (2):155-172.
    Necessitists hold that, necessarily, everything is such that, necessarily, something is identical to it. Timothy Williamson has posed a number of challenges to contingentism, the negation of necessitism. One such challenge is an argument that necessitists can more wholeheartedly embrace possible worlds semantics than can contingentists. If this charge is correct, then necessitists, but not contingentists, can unproblematically exploit the technical successes of possible worlds semantics. I will argue, however, that the charge is incorrect: contingentists can embrace possible worlds semantics (...)
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  26. First-Order Modal Logic in the Necessary Framework of Objects.Peter Fritz - 2016 - Canadian Journal of Philosophy 46 (4-5):584-609.
    I consider the first-order modal logic which counts as valid those sentences which are true on every interpretation of the non-logical constants. Based on the assumptions that it is necessary what individuals there are and that it is necessary which propositions are necessary, Timothy Williamson has tentatively suggested an argument for the claim that this logic is determined by a possible world structure consisting of an infinite set of individuals and an infinite set of worlds. He notes that only the (...)
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  27. Higher-Order Contingentism, Part 1: Closure and Generation.Peter Fritz & Jeremy Goodman - 2016 - Journal of Philosophical Logic 45 (6):645-695.
    This paper is a study of higher-order contingentism – the view, roughly, that it is contingent what properties and propositions there are. We explore the motivations for this view and various ways in which it might be developed, synthesizing and expanding on work by Kit Fine, Robert Stalnaker, and Timothy Williamson. Special attention is paid to the question of whether the view makes sense by its own lights, or whether articulating the view requires drawing distinctions among possibilities that, according to (...)
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  28. The Problem of Cross-World Predication.Alexander Kocurek - 2016 - Journal of Philosophical Logic 45 (6):697-742.
    While standard first-order modal logic is quite powerful, it cannot express even very simple sentences like “I could have been taller than I actually am” or “Everyone could have been smarter than they actually are”. These are examples of cross-world predication, whereby objects in one world are related to objects in another world. Extending first-order modal logic to allow for cross-world predication in a motivated way has proven to be notoriously difficult. In this paper, I argue that the standard accounts (...)
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  29. Modal Science.Timothy Williamson - 2016 - Canadian Journal of Philosophy 46 (4-5):453-492.
    This paper explains and defends the idea that metaphysical necessity is the strongest kind of objective necessity. Plausible closure conditions on the family of objective modalities are shown to entail that the logic of metaphysical necessity is S5. Evidence is provided that some objective modalities are studied in the natural sciences. In particular, the modal assumptions implicit in physical applications of dynamical systems theory are made explicit by using such systems to define models of a modal temporal logic. Those assumptions (...)
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  30. Reply to Bacon, Hawthorne and Uzquiano.Timothy Williamson - 2016 - Canadian Journal of Philosophy 46 (4-5):542-547.
  31. Reply to Fine.Timothy Williamson - 2016 - Canadian Journal of Philosophy 46 (4-5):571-583.
  32. Reply to Fritz.Timothy Williamson - 2016 - Canadian Journal of Philosophy 46 (4-5):610-612.
  33. Reply to Goodman.Timothy Williamson - 2016 - Canadian Journal of Philosophy 46 (4-5):640-653.
  34. Reply to Linnebo.Timothy Williamson - 2016 - Canadian Journal of Philosophy 46 (4-5):677-682.
  35. Reply to Stalnaker.Timothy Williamson - 2016 - Canadian Journal of Philosophy 46 (4-5):727-734.
  36. Williamson on Modality.Juhani Yli-Vakkuri & Mark McCullagh - 2016 - Canadian Journal of Philosophy 46 (4-5):453-851.
    This special issue of the Canadian Journal of Philosophy is dedicated to Timothy Williamson's work on modality. It consists of a new paper by Williamson followed by papers on Williamson's work on modality, with each followed by a reply by Williamson. -/- Contributors: Andrew Bacon, Kit Fine, Peter Fritz, Jeremy Goodman, John Hawthorne, Øystein Linnebo, Ted Sider, Robert Stalnaker, Meghan Sullivan, Gabriel Uzquiano, Barbara Vetter, Timothy Williamson, Juhani Yli-Vakkuri.
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  37. Ontology of Sentential Moods.Berislav Žarnić - 2016 - In Myśli o języku, nauce i wartościach. Seria druga. Profesorowi Jackowi Juliuszowi Jadackiemu w siedemdziesiątą rocznicę urodzin. pp. 323-339.
    In this paper ontological implications of the Barcan formula and its converse will be discussed at the conceptual and technical level. The thesis that will be defended is that sentential moods are not ontologically neutral since the rejection of ontological implications of Barcan formula and its converse is a condition of a possibility of the imperative mood. The paper is divided into four sections. In the first section a systematization of semantical systems of quantified modal logic is introduced for the (...)
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  38. Ockhamism and Quantified Modal Logic.Andrea Iacona - 2015 - Logique Et Analyse 58:353-370.
    This paper outlines a formal account of tensed sentences that is consistent with Ockhamism, a view according to which future contingents are either true or false. The account outlined substantively differs from the attempts that have been made so far to provide a formal apparatus for such a view in terms of some expressly modified version of branching time semantics. The system on which it is based is the simplest quantified modal logic.
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  39. Gödel's "Slingshot" Argument and His Onto-Theological System.Srećko Kovač & Kordula Świętorzecka - 2015 - In Kordula Świętorzecka (ed.), Gödel's Ontological Argument: History, Modifications, and Controversies. Semper. pp. 123-162.
  40. Logic, Essence, and Modality — Review of Bob Hale's Necessary Beings. [REVIEW]Christopher Menzel - 2015 - Philosophia Mathematica 23 (3):407-428.
    Bob Hale’s distinguished record of research places him among the most important and influential contemporary analytic metaphysicians. In his deep, wide ranging, yet highly readable book Necessary Beings, Hale draws upon, but substantially integrates and extends, a good deal his past research to produce a sustained and richly textured essay on — as promised in the subtitle — ontology, modality, and the relations between them. I’ve set myself two tasks in this review: first, to provide a reasonably thorough (if not (...)
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  41. Barcan Formulas in Second-Order Modal Logic.Timothy Williamson - 2015 - In Michael Frauchiger (ed.), Themes From Barcan Marcus. Ontos Verlag. pp. 51-74.
    Second-order logic and modal logic are both, separately, major topics of philosophical discussion. Although both have been criticized by Quine and others, increasingly many philosophers find their strictures uncompelling, and regard both branches of logic as valuable resources for the articulation and investigation of significant issues in logical metaphysics and elsewhere. One might therefore expect some combination of the two sorts of logic to constitute a natural and more comprehensive background logic for metaphysics. So it is somewhat surprising to find (...)
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  42. A Machine That Knows Its Own Code.Samuel A. Alexander - 2014 - Studia Logica 102 (3):567-576.
    We construct a machine that knows its own code, at the price of not knowing its own factivity.
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  43. The Quantified Argument Calculus.Hanoch Ben-Yami - 2014 - Review of Symbolic Logic 7 (1):120-146.
    I develop a formal logic in which quantified arguments occur in argument positions of predicates. This logic also incorporates negative predication, anaphora and converse relation terms, namely, additional syntactic features of natural language. In these and additional respects, it represents the logic of natural language more adequately than does any version of Frege’s Predicate Calculus. I first introduce the system’s main ideas and familiarize it by means of translations of natural language sentences. I then develop a formal system built on (...)
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  44. Roles, Rigidity, and Quantification in Epistemic Logic.Wesley H. Holliday & John Perry - 2014 - In Alexandru Baltag & Sonja Smets (eds.), Johan van Benthem on Logic and Information Dynamics. Springer. pp. 591-629.
    Epistemic modal predicate logic raises conceptual problems not faced in the case of alethic modal predicate logic : Frege’s “Hesperus-Phosphorus” problem—how to make sense of ascribing to agents ignorance of necessarily true identity statements—and the related “Hintikka-Kripke” problem—how to set up a logical system combining epistemic and alethic modalities, as well as others problems, such as Quine’s “Double Vision” problem and problems of self-knowledge. In this paper, we lay out a philosophical approach to epistemic predicate logic, implemented formally in Melvin (...)
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  45. Quantified Modal Logic on the Rational Line.Philip Kremer - 2014 - Review of Symbolic Logic 7 (3):439-454.
  46. Modal Validity and the Dispensability of the Actuality Operator.Vittorio Morato - 2014 - In Michal Dancak & Vit Punochar (eds.), The Logica Yearbook 2013. London, UK:
    In this paper, I claim that two ways of defining validity for modal languages (“real-world” and “general” validity), corresponding to distinction between a correct and an incorrect way of defining modal valid- ity, correspond instead to two substantive ways of conceiving modal truth. At the same time, I claim that the major logical manifestation of the real- world/general validity distinction in modal propositional languages with the actuality operator should not be taken seriously, but simply as a by-product of the way (...)
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  47. Validity and Actuality.Vittorio Morato - 2014 - Logique Et Analyse 227:379-405.
    The notion of validity for modal languages could be defined in two slightly different ways. The first is the original definition given by S. Kripke, for which a formula φ of a modal language L is valid if and only if it is true in every actual world of every interpretation of L. The second is the definition that has become standard in most textbook presentations of modal logic, for which a formula φ of L is valid if and only (...)
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  48. Fast-Collapsing Theories.Samuel A. Alexander - 2013 - Studia Logica (1):1-21.
    Reinhardt’s conjecture, a formalization of the statement that a truthful knowing machine can know its own truthfulness and mechanicalness, was proved by Carlson using sophisticated structural results about the ordinals and transfinite induction just beyond the first epsilon number. We prove a weaker version of the conjecture, by elementary methods and transfinite induction up to a smaller ordinal.
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  49. Quantificational Logic and Empty Names.Andrew Bacon - 2013 - Philosophers' Imprint 13.
    The result of combining classical quantificational logic with modal logic proves necessitism – the claim that necessarily everything is necessarily identical to something. This problem is reflected in the purely quantificational theory by theorems such as ∃x t=x; it is a theorem, for example, that something is identical to Timothy Williamson. The standard way to avoid these consequences is to weaken the theory of quantification to a certain kind of free logic. However, it has often been noted that in order (...)
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  50. Quantified Multimodal Logics in Simple Type Theory.Christoph Benzmüller & Lawrence C. Paulson - 2013 - Logica Universalis 7 (1):7-20.
    We present an embedding of quantified multimodal logics into simple type theory and prove its soundness and completeness. A correspondence between QKπ models for quantified multimodal logics and Henkin models is established and exploited. Our embedding supports the application of off-the-shelf higher-order theorem provers for reasoning within and about quantified multimodal logics. Moreover, it provides a starting point for further logic embeddings and their combinations in simple type theory.
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