Authors
Claus-Peter Wirth
Title
[A New Indefinite Semantics for]

Hilbert's epsilon

[as an Operator of Indefinite Committed Choice]
In
Journal Version:
Cite as
Journal of Applied Logic 6 (2008), pp. 287-317
Permanent URL
http://dx.doi.org/10.1016/j.jal.2007.07.009
Bibtex Entry
bib.bib
Long Version:
SEKI-Report SR-2006-02
Bibtex Entry
Short version:
11th TABLEAU 2002, LNAI 2381, pp. 298-314, Springer.
Bibtex Entry.
Submitted version in .ps.gz; note that the editor has done some changes in the printed version which the author cannot condone. At least the editor has changed the small epsilon in the title to a capital epsilon, but maybe he garbled more than that. Give authors the control! (Vanevar Bush's WWW ideas would enable this.)
Copyright Owner
Journal Version:
Elsevier
Long Version:
SEKI
Short version:
Springer
Up-to-dateness
Yes!
Keywords
Hilbert's epsilon Operator, Logical Foundations, Theories of Truth and Validity, Formalized Mathematics, Human-Oriented Interactive Theorem Proving, Automated Theorem Proving, Formal Philosophy of Language, Computational Linguistics
Abstract
Paul Bernays and David Hilbert carefully avoided overspecification of Hilbert's epsilon-operator and axiomatized only what was relevant for their proof-theoretic investigations. Semantically, this left the epsilon-operator underspecified. In the meanwhile, there have been several suggestions for semantics of the epsilon as a choice operator. We propose a further one with the following features: We avoid overspecification (such as functionality), but admit indefinite choice, committed choice, and classical logics. Moreover, our semantics for the epsilon supports proof search optimally and is natural in the sense that it does not only mirror some cases of referential interpretation of indefinite articles in natural languages, but may also contribute to philosophy of language.
Review
Complete summary of anonymous review of a short version for TABLEAU 2002
Long Version Full paper