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  1. Maria Aloni (2005). Individual Concepts in Modal Predicate Logic. Journal of Philosophical Logic 34 (1):1 - 64.
    The article deals with the interpretation of propositional attitudes in the framework of modal predicate logic. The first part discusses the classical puzzles arising from the interplay between propositional attitudes, quantifiers and the notion of identity. After comparing different reactions to these puzzles it argues in favor of an analysis in which evaluations of de re attitudes may vary relative to the ways of identifying objects used in the context of use. The second part of the article gives this analysis (...)
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  2. Hajnal Andréka, István Németi & Johan van Benthem (1998). Modal Languages and Bounded Fragments of Predicate Logic. Journal of Philosophical Logic 27 (3):217-274.
    What precisely are fragments of classical first-order logic showing “modal” behaviour? Perhaps the most influential answer is that of Gabbay 1981, which identifies them with so-called “finite-variable fragments”, using only some fixed finite number of variables (free or bound). This view-point has been endorsed by many authors (cf. van Benthem 1991). We will investigate these fragments, and find that, illuminating and interesting though they are, they lack the required nice behaviour in our sense. (Several new negative results support this claim.) (...)
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  3. Horacio Arlo-Costa, First Order Extensions of Classical Systems of Modal Logic: The Role of Barcan Schemas.
    Horacio Arlo-Costa. First Order Extensions of Classical Systems of Modal Logic: The Role of Barcan Schemas.
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  4. Horacio Arlo-Costa & Eric Pacuit, First Order Classical Modal Logic, Studia Logica, 84, 2, 171-210, 2006.
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  5. Horacio Arlo-Costa & Eric Pacuit (2006). First-Order Classical Modal Logic. Studia Logica 84 (2):171 - 210.
    The paper focuses on extending to the first order case the semantical program for modalities first introduced by Dana Scott and Richard Montague. We focus on the study of neighborhood frames with constant domains and we offer in the first part of the paper a series of new completeness results for salient classical systems of first order modal logic. Among other results we show that it is possible to prove strong completeness results for normal systems without the Barcan Formula (like (...)
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  6. Horacio Arló-Costa & Eric Pacuit (2006). First-Order Classical Modal Logic. Studia Logica 84 (2):171 - 210.
    The paper focuses on extending to the first order case the semantical program for modalities first introduced by Dana Scott and Richard Montague. We focus on the study of neighborhood frames with constant domains and we offer in the first part of the paper a series of new completeness results for salient classical systems of first order modal logic. Among other results we show that it is possible to prove strong completeness results for normal systems without the Barcan Formula (like (...)
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  7. Steve Awodey & Kohei Kishida, Topology and Modality: The Topological Interpretation of First-Order Modal Logic.
    As McKinsey and Tarksi showed, the Stone representation theorem for Boolean algebras extends to algebras with operators to give topological semantics for (classical) propositional modal logic, in which the "necessity" operation is modeled by taking the interior of an arbitrary subset of a topological space. in this paper the topological interpretation is extended in a natural way to arbitrary theories of full first-order logic. The resulting system of S4 first-order modal logic is complete with respect to such topological semantics.
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  8. Steve Awody & K. Kishida (2008). Topology and Modality: The Topological Interpretation of First-Order Modal Logic. Review of Symbolic Logic 1 (2):146-166.
    As McKinsey and Tarski showed, the Stone representation theorem for Boolean algebras extends to algebras with operators to give topological semantics for (classical) propositional modal logic, in which the operation is modeled by taking the interior of an arbitrary subset of a topological space. In this article, the topological interpretation is extended in a natural way to arbitrary theories of full first-order logic. The resulting system of S4 first-order modal logic is complete with respect to such topological semantics.
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  9. Andrew Bacon (2013). Quantificational Logic and Empty Names. Philosophers' Imprint 13 (24).
    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 $\exists xt = x$; 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 (...)
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  10. Ruth Barcan Marcus (forthcoming). Possibiha and Possible Worlds. Grazer Philosophische Studien 25:107-133.
    Four questions are raised about the semantics of Quantified Modal Logic (QML). Does QML admit possible objects, i.e. possibilia? Is it plausible to admit them? Can sense be made of such objects? Is QML committed to the existence of possibilia?The conclusions are that QML, generalized as in Kripke, would seem to accommodate possibilia, but they are rejected on philosophical and semantical grounds. Things must be encounterable, directly nameable and a part of the actual order before they may plausibly enter into (...)
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  11. David Basin, Seán Matthews & Luca Viganò (1998). Labelled Modal Logics: Quantifiers. [REVIEW] Journal of Logic, Language and Information 7 (3):237-263.
    In previous work we gave an approach, based on labelled natural deduction, for formalizing proof systems for a large class of propositional modal logics that includes K, D, T, B, S4, S4.2, KD45, and S5. Here we extend this approach to quantified modal logics, providing formalizations for logics with varying, increasing, decreasing, or constant domains. The result is modular with respect to both properties of the accessibility relation in the Kripke frame and the way domains of individuals change between worlds. (...)
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  12. Hanoch Ben-Yami (forthcoming). The Quantified Argument Calculus. Review of Symbolic Logic:1-27.
    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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  13. Phillip Bricker (1989). Quantified Modal Logic and the Plural De Re. Midwest Studies in Philosophy 14 (1):372-394.
    Modal sentences of the form "every F might be G" and "some F must be G" have a threefold ambiguity. in addition to the familiar readings "de dicto" and "de re", there is a third reading on which they are examples of the "plural de re": they attribute a modal property to the F's plurally in a way that cannot in general be reduced to an attribution of modal properties to the individual F's. The plural "de re" readings of modal (...)
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  14. Rudolf Carnap (1946). Modalities and Quantification. Journal of Symbolic Logic 11 (2):33-64.
  15. Michael J. Carroll (1979). Reduction to First Degree in Quantificational S5. Journal of Symbolic Logic 44 (2):207-214.
    It is shown that the modally first-degree formulas of quantificational S5 constitute a reduction class. This is done by defining prenex normal forms for quantificational S5, and then showing that for any formula A there is a formula B in prenex normal form, such that B is modally first-degree and is provable if and only if A is provable.
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  16. Fabrice Correia (2007). Modality, Quantification, and Many Vlach-Operators. Journal of Philosophical Logic 36 (4):473 - 488.
    Consider two standard quantified modal languages A and P whose vocabularies comprise the identity predicate and the existence predicate, each endowed with a standard S5 Kripke semantics where the models have a distinguished actual world, which differ only in that the quantifiers of A are actualist while those of P are possibilist. Is it possible to enrich these languages in the same manner, in a non-trivial way, so that the two resulting languages are equally expressive-i.e., so that for each sentence (...)
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  17. Giovanna Corsi (2002). A Unified Completeness Theorem for Quantified Modal Logics. Journal of Symbolic Logic 67 (4):1483-1510.
    A general strategy for proving completeness theorems for quantified modal logics is provided. Starting from free quantified modal logic K, with or without identity, extensions obtained either by adding the principle of universal instantiation or the converse of the Barcan formula or the Barcan formula are considered and proved complete in a uniform way. Completeness theorems are also shown for systems with the extended Barcan rule as well as for some quantified extensions of the modal logic B. The incompleteness of (...)
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  18. Giovanna Corsi (1993). Quantified Modal Logics of Positive Rational Numbers and Some Related Systems. Notre Dame Journal of Formal Logic 34 (2):263-283.
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  19. Horacio Arló Costa (2002). First Order Extensions of Classical Systems of Modal Logic; the Role of the Barcan Schemas. Studia Logica 71 (1):87-118.
    The paper studies first order extensions of classical systems of modal logic (see (Chellas, 1980, part III)). We focus on the role of the Barcan formulas. It is shown that these formulas correspond to fundamental properties of neighborhood frames. The results have interesting applications in epistemic logic. In particular we suggest that the proposed models can be used in order to study monadic operators of probability (Kyburg, 1990) and likelihood (Halpern-Rabin, 1987).
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  20. David Efird (2009). Divine Command Theory and the Semantics of Quantified Modal Logic. In Yujin Nagasawa & Erik J. Wielenberg (eds.), New Waves in Philosophy of Religion. Palgrave Macmillan. 91.
    I offer a series of axiomatic formalizations of Divine Command Theory motivated by certain methodological considerations. Given these considerations, I present what I take to be the best axiomatization of Divine Command Theory, an axiomatization which requires a non-standardsemantics for quantified modal logic.
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  21. Kit Fine (1983). The Permutation Principle in Quantificational Logic. Journal of Philosophical Logic 12 (1):33 - 37.
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  22. Kit Fine (1982). First-Order Modal Theories III — Facts. Synthese 53 (1):43-122.
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  23. Kit Fine (1981). First-Order Modal Theories I--Sets. Noûs 15 (2):177-205.
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  24. Kit Fine (1981). Model Theory for Modal Logic—Part III Existence and Predication. Journal of Philosophical Logic 10 (3):293 - 307.
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  25. Kit Fine (1980). First-Order Modal Theories. Studia Logica 39 (2-3):159 - 202.
    This paper is part of a general programme of developing and investigating particular first-order modal theories. In the paper, a modal theory of propositions is constructed under the assumption that there are genuinely singular propositions, ie. ones that contain individuals as constituents. Various results on decidability, axiomatizability and definability are established.
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  26. Kit Fine (1979). Failures of the Interpolation Lemma in Quantified Modal Logic. Journal of Symbolic Logic 44 (2):201-206.
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  27. Kit Fine (1978). Model Theory for Modal Logic Part I—the de Re/de Dicto Distinction. Journal of Philosophical Logic 7 (1):125 - 156.
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  28. Kit Fine (1978). Model Theory for Modal Logic—Part II the Elimination of de Re Modality. Journal of Philosophical Logic 7 (1):277 - 306.
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  29. Kit Fine (1977). Properties, Propositions and Sets. Journal of Philosophical Logic 6 (1):135 - 191.
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  30. Melvin Fitting, On Quantified Modal Logic.
    Propositional modal logic is a standard tool in many disciplines, but first-order modal logic is not. There are several reasons for this, including multiplicity of versions and inadequate syntax. In this paper we sketch a syntax and semantics for a natural, well-behaved version of first-order modal logic, and show it copes easily with several familiar difficulties. And we provide tableau proof rules to go with the semantics, rules that are, at least in principle, automatable.
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  31. Melvin Fitting (2002). Interpolation for First Order S5. Journal of Symbolic Logic 67 (2):621-634.
    An interpolation theorem holds for many standard modal logics, but first order S5 is a prominent example of a logic for which it fails. In this paper it is shown that a first order S5 interpolation theorem can be proved provided the logic is extended to contain propositional quantifiers. A proper statement of the result involves some subtleties, but this is the essence of it.
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  32. Peter Fritz (2013). Modal Ontology and Generalized Quantifiers. Journal of Philosophical Logic 42 (4):643-678.
    Timothy Williamson has argued that in the debate on modal ontology, the familiar distinction between actualism and possibilism should be replaced by a distinction between positions he calls contingentism and necessitism. He has also argued in favor of necessitism, using results on quantified modal logic with plurally interpreted second-order quantifiers showing that necessitists can draw distinctions contingentists cannot draw. Some of these results are similar to well-known results on the relative expressivity of quantified modal logics with so-called inner and outer (...)
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  33. James W. Garson (2005). Unifying Quantified Modal Logic. Journal of Philosophical Logic 34 (5/6):621 - 649.
    Quantified modal logic (QML) has reputation for complexity. Completeness results for the various systems appear piecemeal. Different tactics are used for different systems, and success of a given method seems sensitive to many factors, including the specific combination of choices made for the quantifiers, terms, identity, and the strength of the underlying propositional modal logic. The lack of a unified framework in which to view QMLs and their completeness properties puts pressure on those who develop, apply, and teach QML to (...)
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  34. Paul Gochet Et Eric Gillet (1999). Quantified Modal Logic, Dynamic Semantics and S 5. Dialectica 53 (3-4):243–251.
  35. Roderic A. Girle (2002). Review: Melvin Fitting, Richard L. Mendelsohn, First-Order Modal Logic. [REVIEW] Bulletin of Symbolic Logic 8 (3):429-431.
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  36. Anil Gupta (1980). The Logic of Common Nouns: An Investigation in Quantified Modal Logic. Yale University Press.
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  37. Allen Hazen (1976). Expressive Completeness in Modal Language. Journal of Philosophical Logic 5 (1):25--46.
    The logics of the modal operators and of the quantifiers show striking analogies. The analogies are so extensive that, when a special class of entities (possible worlds) is postulated, natural and non-arbitrary translation procedures can be defined from the language with the modal operators into a purely quantificational one, under which the necessity and possibility operators translate into universal and existential quantifiers. In view of this I would be willing to classify the modal operators as ‘disguised’ quantifiers, and I think (...)
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  38. Harold T. Hodes (1984). Axioms for Actuality. Journal of Philosophical Logic 13 (1):27 - 34.
  39. Harold T. Hodes (1984). On Modal Logics Which Enrich First-Order S. Journal of Philosophical Logic 13 (4):423 - 454.
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  40. Harold T. Hodes (1984). Some Theorems on the Expressive Limitations of Modal Languages. Journal of Philosophical Logic 13 (1):13 - 26.
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  41. Wesley H. Holliday & John Perry (forthcoming). Roles, Rigidity, and Quantification in Epistemic Logic. In Alexandru Baltag & Sonja Smets (eds.), Trends in Logic, Outstanding Contributions: Johan F. A. K. van Benthem on Logical and Informational Dynamics. Springer.
    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 Fitting’s (...)
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  42. Andrea Iacona (forthcoming). Ockhamism and Quantified Modal Logic. Logique Et Analyse.
    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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  43. Andrea Iacona (2007). Not Everything is Possible. Logic Journal of the IGPL 15.
    This paper makes a point about the interpretation of the simplest quantified modal logic, that is, quantified modal logic with a single domain. It is commonly assumed that the domain in question is to be understood as the set of all possibile objects. The point of the paper is that this assumption is misguided.
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  44. Thomas Jager (1982). An Actualistic Semantics for Quantified Modal Logic. Notre Dame Journal of Formal Logic 23 (3):335-349.
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  45. Srećko Kovač (2009). First-Order Belief and Paraconsistency. Logic and Logical Philosophy 18 (2):127-143.
    A first-order logic of belief with identity is proposed, primarily to give an account of possible de re contradictory beliefs, which sometimes occur as consequences of de dicto non-contradictory beliefs. A model has two separate, though interconnected domains: the domain of objects and the domain of appearances. The satisfaction of atomic formulas is defined by a particular S-accessibility relation between worlds. Identity is non-classical, and is conceived as an equivalence relation having the classical identity relation as a subset. A tableau (...)
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  46. Saul A. Kripke (1963). Semantical Considerations on Modal Logic. Acta Philosophica Fennica 16 (1963):83-94.
  47. Henrik Lagerlund, Sten Lindström & Rysiek Sliwinski (eds.) (2006). Modality Matters: Twenty-Five Essays in Honour of Krister Segerberg. Uppsala Philosophical Studies 53.
  48. David Lewis (1993). Counterpart Theory, Quantified Modal Logic, and Extra Argument Places. Analysis 53 (2):69-71.
  49. David K. Lewis (1968). Counterpart Theory and Quantified Modal Logic. Journal of Philosophy 65 (5):113-126.
  50. Sten Lindström (2006). On the Proper Treatment of Quantification in Contexts of Logical and Metaphysical Modalities. In Henrik Lagerlund, Sten Lindström & Rysiek Sliwinski (eds.), Modality Matters: Twenty-Five Essays in Honour of Krister Segerberg. Uppsala Philosophical Studies 53.
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