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Intensional models for first degree formulas1

Published online by Cambridge University Press:  12 March 2014

Nuel D. Belnap Jr
Nuel D. Belnap Jr*
Affiliation:
University of Pittsburgh
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Extract

In Anderson and Belnap [8] there was developed a semantics for first degree entailments (fde), i.e., entailments A → B between formulas A and B involving only truth-functions (defined in terms of “or” and “not”) and quantifiers. The key ideas were (i) the notion of a frame ⟨P, FIP, I⟩, where P is a set of (intensional) propositions closed under negation and multiple disjunction, I is a domain of individuals, and FIP is the set of functions from I into P; and (ii) the semantic relation of cons (consequence), as obtaining between a set of propositions taken conjunctively, and a set taken disjunctively; and (iii) the notion of an atomic frame, i.e., a frame generated by a set of propositions X closed under negation, such that for any disjoint subclasses Y and Z of X, Y does not bear cons to Z.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 32 , Issue 1 , June 1967 , pp. 1 - 22
Copyright
Copyright © Association for Symbolic Logic 1967

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Footnotes

1

This research was supported in part by National Science Foundation Grant GS-190 (History & Philosophy of Science). I wish to thank J. Barwise for his considerable assistance in the early stages of this research, and P. Woodruff and M. Dunn for reading later drafts.

References

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