# Quantified Modal Logic

Edited by Sasa Buvac
 Introductions Fitting & Mendelsohn 1998
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1. Fast-Collapsing Theories.Samuel 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.
2. 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.
3. Individual Concepts in Modal Predicate Logic.Maria Aloni - 2005 - 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 (...)
4. Repairing the Interpolation Theorem in Quantified Modal Logic.Carlos Areces, Patrick Blackburn & Maarten Marx - 2003 - Annals of Pure and Applied Logic 124 (1-3):287-299.
Quantified hybrid logic is quantified modal logic extended with apparatus for naming states and asserting that a formula is true at a named state. While interpolation and Beth's definability theorem fail in a number of well-known quantified modal logics , their counterparts in quantified hybrid logic have these properties. These are special cases of the main result of the paper: the quantified hybrid logic of any class of frames definable in the bounded fragment of first-order logic has the interpolation property, (...)
5. Horacio Arlo-Costa. First Order Extensions of Classical Systems of Modal Logic: The Role of Barcan Schemas.
6. First-Order Classical Modal Logic.Horacio Arló-Costa & Eric Pacuit - 2006 - 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 (...)
7. Topology and Modality: The Topological Interpretation of First-Order Modal Logic.Steve Awody & K. Kishida - 2008 - 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.
8. Quantificational Logic and Empty Names.Andrew Bacon - 2013 - 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 ∃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 (...)
9. Labelled Modal Logics: Quantifiers. [REVIEW]David Basin, Seán Matthews & Luca Viganò - 1998 - 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. (...)
10. 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 (...)
11. 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 (...)
12. Quantified Modal Logic and the Plural De Re.Phillip Bricker - 1989 - 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 (...)
13. Modalities and Quantification.Rudolf Carnap - 1946 - Journal of Symbolic Logic 11 (2):33-64.
14. Reduction to First Degree in Quantificational S5.Michael J. Carroll - 1979 - 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.
15. Some Reflections on Quantified Epistemic Logic.Robert C. Coburn - 1972 - Canadian Journal of Philosophy 2 (2):233 - 247.
16. Modality, Quantification, and Many Vlach-Operators.Fabrice Correia - 2007 - 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 (...)
17. A Unified Completeness Theorem for Quantified Modal Logics.Giovanna Corsi - 2002 - 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 (...)
18. Quantified Modal Logics of Positive Rational Numbers and Some Related Systems.Giovanna Corsi - 1993 - Notre Dame Journal of Formal Logic 34 (2):263-283.
19. Quantified Modal Logic With Rigid Terms.Giovanna Corsi - 1988 - Mathematical Logic Quarterly 34 (3):251-259.
20. Quantified Modal Logic With Rigid Terms.Giovanna Corsi - 1988 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 34 (3):251-259.
21. Quantified Modal Logic.Horacio Costa - 2010 - Journal of the Indian Council of Philosophical Research 27 (2).
The chapter is divided in two parts. The first part gives an introduction to issues in quantified modal logic . We provide an overview of recent work in QML and we presuppose the use of a relational semantics. We discuss models for constant domains, increasing domains and varying domains and present axiomatizations for the corresponding logics. We also discuss philosophical issues related to the interpretation of the quantifiers, terms and identity and we present a first-order quantified intensional logic. A crucial (...)
22. First Order Extensions of Classical Systems of Modal Logic; the Role of the Barcan Schemas.Horacio Arló Costa - 2002 - 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).
23. Physical theories and possible worlds.M. J. Cresswell - 1973 - Logique Et Analyse 16 (63):495.
Formalized physical theories are not, as a rule, stated in intensional languages. Yet in talking about them we often treat them as if they were. We say for instance: 'Consider what would happen if instead of p's being true q were. In such a case r would be likely.' If we say this sort of thing, p, q and r appear to stand for the meanings of sentences of the theory, but meanings in some intensional sense. Now it is very (...)
24. 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 (...)
25. Logic for Contigent Beings.Harry Deutsch - 1994 - Journal of Philosophical Research 19:273-329.
One of the logical problems with which Arthur Prior struggled is the problem of finding, in Prior’s own phrase, a “logic for contingent beings.” The difficulty is that from minimal modal principles and classical quantification theory, it appears to follow immediately that every possible object is a necessary existent. The historical development of quantified modal logic (QML) can be viewed as a series of attempts---due variously to Kripke, Prior, Montague, and the fee-logicians---to solve this problem. In this paper, I review (...)
26. Divine Command Theory and the Semantics of Quantified Modal Logic.David Efird - 2009 - In Yujin Nagasawa & Erik J. Wielenberg (eds.), New Waves in Philosophy of Religion. Palgrave-Macmillan. pp. 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.
27. The Permutation Principle in Quantificational Logic.Kit Fine - 1983 - Journal of Philosophical Logic 12 (1):33 - 37.
28. First-Order Modal Theories III — Facts.Kit Fine - 1982 - Synthese 53 (1):43-122.
29. Model Theory for Modal Logic—Part III Existence and Predication.Kit Fine - 1981 - Journal of Philosophical Logic 10 (3):293 - 307.
30. First-Order Modal Theories I--Sets.Kit Fine - 1981 - Noûs 15 (2):177-205.
31. First-Order Modal Theories. II: Propositions.Kit Fine - 1980 - 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.
32. Failures of the Interpolation Lemma in Quantified Modal Logic.Kit Fine - 1979 - Journal of Symbolic Logic 44 (2):201-206.
33. ModelTtheory for Modal Logic. Part I — The de Re/de Dicto Distinction.Kit Fine - 1978 - Journal of Philosophical Logic 7 (1):125 - 156.
34. Model Theory for Modal Logic—Part II The Elimination of de Re Modality.Kit Fine - 1978 - Journal of Philosophical Logic 7 (1):277 - 306.
35. Properties, Propositions and Sets.Kit Fine - 1977 - Journal of Philosophical Logic 6 (1):135 - 191.
36. 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.
37. Interpolation for First Order S5.Melvin Fitting - 2002 - 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.
38. First Order Modal Logic.Melvin Fitting & Richard Mendelsohn - 2001 - Studia Logica 68 (2):287-289.
39. First-Order Modal Logic.Melvin Fitting & Richard L. Mendelsohn - 1998 - Kluwer Academic Publishers.
40. 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 (...)
41. Modal Ontology and Generalized Quantifiers.Peter Fritz - 2013 - 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 (...)
42. 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 (...)
43. Unifying Quantified Modal Logic.James W. Garson - 2005 - Journal of Philosophical Logic 34 (5-6):621-649.
Quantified modal logic 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 work (...)
44. Quantified Modal Logic, Dynamic Semantics and S 5.Paul Gochet Et Eric Gillet - 1999 - Dialectica 53 (3-4):243–251.
45. Review: Melvin Fitting, Richard L. Mendelsohn, First-Order Modal Logic. [REVIEW]Roderic A. Girle - 2002 - Bulletin of Symbolic Logic 8 (3):429-431.
46. Quantified Modal Logic, Dynamic Semantics and S 5.Paul Gochet & Eric Gillet - 1999 - Dialectica 53 (3‐4):243-251.
47. The Logic of Common Nouns: An Investigation in Quantified Modal Logic.Anil Gupta - 1980 - Yale University Press.
48. Expressive Completeness in Modal Language.Allen Hazen - 1976 - 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 (...)
49. Modalising Plurals.Simon Hewitt - 2012 - Journal of Philosophical Logic 41 (5):853-875.
There has been very little discussion of the appropriate principles to govern a modal logic of plurals. What debate there has been has accepted a principle I call (Necinc); informally if this is one of those then, necessarily: this is one of those. On this basis Williamson has criticised the Boolosian plural interpretation of monadic second-order logic. I argue against (Necinc), noting that it isn't a theorem of any logic resulting from adding modal axioms to the plural logic PFO+, and (...)
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