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Handbook of Philosophical Logic pp 53–131Cite as

Alternatives to Standard First-Order Semantics

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Part of the book series: Handbook of Philosophical Logic ((HALO,volume 2))

Abstract

Alternatives to standard semantics are legion, some even antedating standard semantics. I shall study several here, among them: substitutional semantics, truth-value semantics, and probabilistic semantics. All three interpret the quantifiers substitutionally, i.e. all three rate a universal (an existential) quantification true if, and only if, every one (at least one) of its substitution instances is true.1 As a result, the first, which retains models, retains only those which are to be called Henkin models. The other two dispense with models entirely, truth-value semantics using instead truth-value assignments (or equivalents thereof to be called truth-value functions) and probabilistic semantics using probability functions. So reference, central to standard semantics, is no concern at all of truth-value and probabilistic semantics; and truth, also central to standard semantics, is but a marginal concern of probabilistic semantics.

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Authors and Affiliations

  1. Temple University, USA

    Hugues Leblanc

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  1. Hugues Leblanc
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  1. King’s College, London, USA

    D. M. Gabbay

  2. Centrum für Informations- und Sprachverarbeitung, Ludwig-Maximilians-Universität München, Germany

    F. Guenthner

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Leblanc, H. (2001). Alternatives to Standard First-Order Semantics. In: Gabbay, D.M., Guenthner, F. (eds) Handbook of Philosophical Logic. Handbook of Philosophical Logic, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0452-6_2

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  • DOI: https://doi.org/10.1007/978-94-017-0452-6_2

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