Notre Dame Journal of Formal Logic

An Intensional Schrödinger Logic

Décio Krause and Newton C. A. da Costa

Abstract

We investigate the higher-order modal logic $S_{\omega}I$, which is a variant of the system $S_{\omega}$ presented in our previous work. A semantics for that system, founded on the theory of quasi sets, is outlined. We show how such a semantics, motivated by the very intuitive base of Schrödinger logics, provides an alternative way to formalize some intensional concepts and features which have been used in recent discussions on the logical foundations of quantum mechanics; for example, that some terms like 'electron' have no precise reference and that 'identical' particles cannot be named unambiguously. In the last section, we sketch a classical semantics for quasi set theory.

Article information

Source
Notre Dame J. Formal Logic Volume 38, Number 2 (1997), 179-194.

Dates
First available in Project Euclid: 12 December 2002

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1039724886

Mathematical Reviews number (MathSciNet)
MR1489409

Digital Object Identifier
doi:10.1305/ndjfl/1039724886

Zentralblatt MATH identifier
0901.03024

Subjects
Primary: 03B60: Other nonclassical logic
Secondary: 03B15: Higher-order logic and type theory 03B30: Foundations of classical theories (including reverse mathematics) [See also 03F35] 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}

Citation

da Costa, Newton C. A.; Krause, Décio. An Intensional Schrödinger Logic. Notre Dame Journal of Formal Logic 38 (1997), no. 2, 179--194. doi:10.1305/ndjfl/1039724886. http://projecteuclid.org/euclid.ndjfl/1039724886.


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