Universally free logic and standard quantification theory

Robert K. Meyer; Karel Lambert

doi:10.2307/2270048

Universally free logic and standard quantification theory

Journal of Symbolic Logic ◽

10.2307/2270048 ◽

1968 ◽

Vol 33 (1) ◽

pp. 8-26 ◽

Cited By ~ 26

Author(s):

Robert K. Meyer ◽

Karel Lambert

Keyword(s):

Free Logic ◽

Van Fraassen ◽

Quantification Theory

Interest has steadily increased among logicians and philosophers in versions of quantification theory which meet the following criteria: (1) no existence assumptions are made with respect to individual constants, and (2) theorems are valid in every domain including the empty domain. Logics meeting the former of these criteria are called free logics by Lambert and have been investigated in a series of papers by him and by van Fraassen, and by Leblanc and Thomason.1Although it is natural to impose (2) in the presence of (1), the criteria are independent.2 Hence we baptize logics which meet both criteria universally free.

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Nonstandard theories of quantification and identity

Journal of Symbolic Logic ◽

10.2307/2270518 ◽

1970 ◽

Vol 35 (2) ◽

pp. 267-294 ◽

Cited By ~ 6

Author(s):

A. Trew

Keyword(s):

Predicate Logic ◽

Type A ◽

The Other ◽

Standard System ◽

Free Logic ◽

Quantification Theory ◽

Singular Terms ◽

Free Variables

In this paper a number of nonstandard systems of predicate logic with or without identity, are translated with subsystems of applied standard system of predicate logic with identity. There are nonstandard theories of quantification which, following [16], are described as inclusive systems; their theorems are valid in all domains, including the empty domain. Theories of quantification which allow for the substitution of denotationless terms for free variables, are described, following [21], as systems of free logic; they are said to be free of the requirement that all singular terms must have denotations. Free logics and inclusive logics may each be of the other type. A nonstandard theory of identity, described, following [12] as a theory of nonreflexive identity, may be combined with a standard or with a nonstandard theory of quantification. Another kind of nonstandard system of predicate logic examined is a nonstandard version of a system of monadic predicate logic in which a distinction is made between sentence and predicate negation, and which is nonstandard in the sense that the laws relating sentence and predicate negation diverge from the standard ones. In the systems examined, this is combined with an inclusive quantification theory.

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On supervaluations in free logic

Journal of Symbolic Logic ◽

10.2307/2274148 ◽

1984 ◽

Vol 49 (3) ◽

pp. 943-950 ◽

Cited By ~ 12

Author(s):

Peter W. Woodruff

Keyword(s):

Semantic Analysis ◽

Arbitrary Element ◽

Free Logic ◽

Atomic Sentence ◽

Van Fraassen ◽

Open Formula ◽

Truth Value ◽

Image Position ◽

Axiomatic Systems ◽

Arbitrary Fashion

The concepts “classical valuation” and “supervaluation” were introduced by van Fraassen around 1966, to provide a semantic analysis of the then extant axiomatic systems of free logic. Consider an atomic sentenceand a “partial” model which fails to interpret c. Then (1) has no truth value in , nor doesWhile the valuelessness of (1) was found intuitively acceptable, that of (2) was not. Indeed, (2) and all other tautologies are theorems of free logic.Van Fraassen found a way to accommodate both intuitions. He interprets the unproblematic atomic sentences as usual, while “interpreting” those like (1) by simply assigning them a truth-value in arbitrary fashion. Then a truth-value for every sentence can be defined in the usual way; the result van Fraassen calls a “classical valuation” of the language. The arbitrary element in any given classical valuation is then eliminated by passage to the “supervaluation” over , which agrees with the classical valuations where they agree among themselves, and otherwise is undefined. In the supervaluation over , (1) is valueless but (2) true (since true on all classical valuations), as was required.There is a slight, but crucial oversimplification in the preceding account. Evaluation of the sentencerequires prior evaluation of the open formulaBut here mere assignment of truth-value is not enough; a whole set must be arbitrarily assigned as extension. The quantification over classical valuations involved in passage to the supervaluation thus involves an implicit quantification over subsets of the domain of : supervaluations are second order.

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Modern Quantification Theory

10.1007/978-981-16-2470-4 ◽

2021 ◽

Author(s):

Shizuhiko Nishisato ◽

Eric J. Beh ◽

Rosaria Lombardo ◽

Jose G. Clavel

Keyword(s):

Quantification Theory

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Study on the Attractiveness Factors of Online Courses

Education Sciences ◽

10.3390/educsci9020128 ◽

2019 ◽

Vol 9 (2) ◽

pp. 128 ◽

Cited By ~ 2

Author(s):

Jia-Xuan Han ◽

Min-Yuan Ma

Keyword(s):

Online Teaching ◽

Online Courses ◽

Rapid Development ◽

Grid Method ◽

Type I ◽

Digital Learning ◽

Key Factors ◽

Quantification Theory ◽

Global Trend ◽

Education Industry

With the rapid development of online courses, digital learning has become a global trend. In this context, this study analyzed the high intake population of online courses for online affective cognition, and explored what the user’s attraction factors for online courses are. The key factors that affect consumers’ usage of online courses and the weights of impact relations are presented, aiming to provide guidance for future improvement of online courses. This study was conducted through the evaluation grid method of Miryoku engineering. In order to make the charm factors more accurate and representative, this study summarized the charm elements using the Kawakita Jiro (KJ) method, and then quantified the factors in the form of a questionnaire. Through the statistical analysis of the questionnaire and quantification theory type I, the correlation between the charm feeling and the online course as well as the weight of each item (original evaluation item) and category (specific evaluation item) were calculated. Through the research and discussion on the charm factors of online teaching, the results analyzed and integrated in this paper could give more substantive suggestions and help to the education industry.

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