Quick completeness proofs for some logics of conditionals.

Burgess, John P.

doi:10.1305/ndjfl/1093883341

Cited by 111 publications

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“…Theorem 3.1 (Burgess 1981). For any finite set Γ of formulas and formula ϕ, the following are equivalent:…”

Section: Counterfactualsmentioning

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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“…Theorem 3.1 (Burgess 1981). For any finite set Γ of formulas and formula ϕ, the following are equivalent:…”

Section: Counterfactualsmentioning

confidence: 99%

Axiomatization in the Meaning Sciences

Holliday¹,

Icard²

2018

The Science of Meaning

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“…A-world that is checked for the truth of C. In [Lewis, 1973] and [Burgess, 1981], that second option is chosen, and a semantics without the limit assumption is axiomatized. Interestingly enough, Burgess proves that CL and its extensions have the finite model property.…”

Section: ]) Another Possibility Is To Complicate the Definition Of Amentioning

confidence: 99%

“…It is known that CK + (ID) + (CA) + (ASC) is an alternative axiomatization of CL (see e.g. [Burgess, 1981]). It has been proved in [Burgess, 1981, Katsuno and Satoh, 1995, Crocco, 1993 that CL axiomatizes the valid formulas of the sublanguage FOR C without the update operator.…”

Section: Theorem 42 the Following Can Be Derived In Uclmentioning

confidence: 99%

“…[Burgess, 1981]). It has been proved in [Burgess, 1981, Katsuno and Satoh, 1995, Crocco, 1993 that CL axiomatizes the valid formulas of the sublanguage FOR C without the update operator. [Katsuno and Satoh, 1995] [Nute, 1980, Nute, 1984, Crocco, 1993.…”

Section: Theorem 42 the Following Can Be Derived In Uclmentioning

confidence: 99%

“…Such semantics have been studied in [Burgess, 1981] as generalisations of Lewis' sphere systems [Lewis, 1973]. They have been taken up in [Katsuno and Satoh, 1995, Nejdl, 1991, Arló Costa and Shapiro, 1992.…”

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confidence: 99%

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Logics for Belief Base Updating

Herzig

1998

Belief Change

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Indicative Conditionals

Rooij¹,

Schulz²

2020

The Wiley Blackwell Companion to Semantics

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In this chapter on indicative conditionals, we focus on two central challenges that any analysis of indicative conditionals must meet, instead of writing (yet another) general overview. The first is the challenge of accounting for the non‐monotonic inference pattern that conditionals in general display. The second is that of accounting for the interaction with probability claims (and adverbs of quantification in general) and the related triviality results.

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Quick completeness proofs for some logics of conditionals.

Cited by 111 publications

References 0 publications

Axiomatization in the Meaning Sciences

Axiomatization in the Meaning Sciences

Logics for Belief Base Updating

Indicative Conditionals

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