In Defense of the Simplest Quantified Modal Logic

Linsky, Bernard; Zalta, Edward N.

doi:10.2307/2214181

Cited by 134 publications

(72 citation statements)

References 38 publications

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“…(A3) makes an assumption explicit that is typically taken for granted in modal logics whose languages are too coarse to make the distinction between sentence and predicate modifier uses of modal operators. 9 In systems that have the resources to represent the difference, (A3) 8 For a defense of necessitarianism, see, e.g., Linsky and Zalta (1994) and Williamson (2002), however.…”

Section: Scope Limitationsmentioning

confidence: 99%

Defining Global Supervenience

Steinberg

2013

Erkenn

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Section: Scope Limitationsmentioning

confidence: 99%

Defining Global Supervenience

Steinberg

2013

Erkenn

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“…Simplest second-order quantified S5 modal logic (Linsky and Zalta 1994), including 1st and 2nd order Barcan formulas (i.e., fixed domains) Logic of Encoding: 3xF → 2xF …”

Section: Relation Variables and Constants: Fmentioning

confidence: 99%

Steps Toward a Computational Metaphysics

Fitelson

Zalta

2007

J Philos Logic

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In this paper, the authors describe their initial investigations in computational metaphysics. Our method is to implement axiomatic metaphysics in an automated reasoning system. In this paper, we describe what we have discovered when the theory of abstract objects is implemented in prover9 (a first-order automated reasoning system which is the successor to otter). After reviewing the second-order, axiomatic theory of abstract objects, we show (1) how to represent a fragment of that theory in prover9's firstorder syntax, and (2) how prover9 then finds proofs of interesting theorems of metaphysics, such as that every possible world is maximal. We conclude the paper by discussing some issues for further research.

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“…A salient feature of the standard first order models of modalities is that for those models the constancy of domains requires the validity of both the BF and the CBF (see [22] for a nice proof of this fact). Many philosophers have seen the possibilist approach as the only one tenable (see for example, [18], [41], [50]), and as a matter of fact the possibilist approach is the one that seems natural in many of the epistemic and computational applications that characterize the wave of recent research in modal logic (see, for example, the brief section devoted to this issue in [21]). Nevertheless, while the possibilist approach seems reasonable on its own, the logical systems that adopt the Barcan Formulas and predicate logic rules for the quantifiers might be seen as too strong for many applications.…”

Section: Models For First Order Modalitiesmentioning

confidence: 99%

First-Order Classical Modal Logic

Arló-Costa

Pacuit

2006

Stud Logica

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Abstract.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 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 FOL + K) in terms of neighborhood frames with constant domains. The first order models we present permit the study of many epistemic modalities recently proposed in computer science as well as the development of adequate models for monadic operators of high probability. Models of this type are either difficult of impossible to build in terms of relational Kripkean semantics.We conclude by introducing general first order neighborhood frames and we offer a general completeness result in terms of them which circumvents some well-known problems of propositional and first order neighborhood semantics (mainly the fact that many classical modal logics are incomplete with respect to an unmodified version of neighborhood frames). We argue that the semantical program that thus arises surpasses both in expressivity and adequacy the standard Kripkean approach, even when it comes to the study of first order normal systems.

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In Defense of the Simplest Quantified Modal Logic

Cited by 134 publications

References 38 publications

Defining Global Supervenience

Defining Global Supervenience

Steps Toward a Computational Metaphysics

First-Order Classical Modal Logic

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