10 Higher order modal logic

Muskens, Reinhard

doi:10.1016/s1570-2464(07)80013-9

Cited by 17 publications

(13 citation statements)

References 36 publications

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“…Exceptions include projects that are directly responding to these earlier proposals: e.g., there have been a number of axiomatizations of alternatives to Montague-Gallin intensional type theory by Fitting, Muskens, Zalta, and others (see Muskens 2007 for a review); and there is work on completeness theorems for fragments of counterfactual conditional logics that differ from the LewisStalnaker style account (e.g., Galles and Pearl 1998, Briggs 2012, Halpern 2013. To be sure, questions of completeness can be raised any time one has specified a model-theoretic interpretation of a well-defined class of expressions.…”

Section: Completeness In Semanticsmentioning

confidence: 99%

Axiomatization in the Meaning Sciences

Holliday¹,

Icard²

2018

The Science of Meaning

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While much of semantic theorizing is based on intuitions about logical phenomena associated with linguistic constructions-phenomena such as consistency and entailment-it is rare to see axiomatic treatments of linguistic fragments. Given a fragment interpreted in some class of formally specified models, it is often possible to ask for a characterization of the reasoning patterns validated by the class of models. Axiomatizations provide such a characterization, often in a perspicuous and efficient manner.In this paper, we highlight some of the benefits of providing axiomatizations for the purpose of semantic theorizing. We illustrate some of these benefits using three examples from the study of modality.

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Section: Completeness In Semanticsmentioning

confidence: 99%

Axiomatization in the Meaning Sciences

Holliday¹,

Icard²

2018

The Science of Meaning

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“…Muskens [26] develops a higher-order quantified modal logic, MTT (modal type theory), which deserves credit for cleaning up IL, partly by letting predication be nonextensional in a sense even stronger than that available in ML ν . MTT prides itself on two features orthogonal to the concerns of CIFOL: (1) It is what we may call "hyperintensional" in that it is suitable for epistemic and doxastic modalities as well as possibility and necessity.…”

Section: A Brief Overview Of Other Systemsmentioning

confidence: 99%

“…26 In a strictly parallel fashion, the natural type of an intensional operator would be the type of functions from individual intensions into individual intensions (intensions in, intensions out). The official type, however, as promised in Section 3.1.2, must have the form → X, and so we use the transpose instead:…”

Section: Operator Constants Predicate Constants Complex Terms Predmentioning

confidence: 99%

“…26 The overwhelmingly common (but regrettable) choice of standard first-order quantified modal logics is to let the type of the intension of a predicate constant be → (D → 2), or, equivalently, → ℘ (D), thereby forcing all predicates to be extensional as a matter of logic. This choice severely reduces the expressive power of any such quantified modal logic.…”

Section: Operator Constants Predicate Constants Complex Terms Predmentioning

confidence: 99%

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CIFOL: Case-Intensional First Order Logic

Belnap

Müller

2013

J Philos Logic

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This is part I of a two-part essay introducing case-intensional first order logic (CIFOL), an easy-to-use, uniform, powerful, and useful combination of firstorder logic with modal logic resulting from philosophical and technical modifications of Bressan's General interpreted modal calculus (Yale University Press 1972). CIFOL starts with a set of cases; each expression has an extension in each case and an intension, which is the function from the cases to the respective case-relative extensions. Predication is intensional; identity is extensional. Definite descriptions are context-independent terms, and lambda-predicates and -operators can be introduced without constraints. These logical resources allow one to define, within CIFOL, important properties of properties, viz., extensionality (whether the property applies, depends only on an extension in one case) and absoluteness, Bressan's chief innovation that allows tracing an individual across cases without recourse to any notion of "rigid designation" or "trans-world identity." Thereby CIFOL abstains from incorporating any metaphysical principles into the quantificational machinery, unlike extant frameworks of quantified modal logic. We claim that this neutrality makes CIFOL a useful tool for discussing both metaphysical and scientific arguments involving modality and quantification, and we illustrate by discussing in diagrammatic detail a number of such arguments involving the extensional identification of individuals

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“…Full details of the logic can be found in [16]. Other useful references on modal higher-order logic include [10,17] and on higher-order logic include [15,[18][19][20][21][22]. For a highly readable account of the advantages of working in higher-order logic rather than first-order, we strongly recommend [23].…”

Section: Logicmentioning

confidence: 99%

Declarative programming for agent applications

Lloyd

2010

Auton Agent Multi-Agent Syst

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This paper introduces the execution model of a declarative programming language intended for agent applications. Features supported by the language include functional and logic programming idioms, higher-order functions, modal computation, probabilistic computation, and some theorem-proving capabilities. The need for these features is motivated and examples are given to illustrate the central ideas.

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10 Higher order modal logic

Cited by 17 publications

References 36 publications

Axiomatization in the Meaning Sciences

Axiomatization in the Meaning Sciences

CIFOL: Case-Intensional First Order Logic

Declarative programming for agent applications

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