[Prev][Next][Index][Thread]

Re: quantum logics

To: linear@cs.stanford.edu
Date: 09 Sep 92 17:01:22 PDT (Wed)

	Date: Wed, 9 Sep 92 09:55 BST
	From: Thomas Forster <T.Forster@pmms.cam.ac.uk>
	Does anybody know anything about sequent calculi for quantum logics?

There is a fleeting reference to sequent calculi on p.451 of M.L. Dalla
Chiara's survey article "Quantum Logic" in Vol. III of the Handbook of
Philosophical Logic.  She gives 12 rules for "a QL-calculus (in the
natural deduction style) which is a slight modification of a calculus
proposed by Goldblatt [J.Phil.Logic 1974, 19-35]", and proves its
soundness and completeness with respect to a Kripke semantics whose
relation is symmetric and irreflexive (QL: orthoframe; LL: web).

One algorithm for tracking down quantum logic topics is to look in the
index to Pavicic's recent "Bibliography on Quantum Logics and Related
Structures", Int.J.Theor.Physics 31:3373-461 (1992).  Following the
bibliography proper (1851 entries) is an index of all nontrivial words
appearing in the titles.  I looked in vain for sequent, calculus,
Gentzen, natural, and deduction.  Quantum logicians appear to hew to
the Birkhoff-von Neumann algebraic perspective and thus far seem to
have had little motivation to explore the world of sequent calculi.

So for this topic a better algorithm is apparently to look in survey
articles like Dalla Chiara's.

Some statistics on QL cited by Pavicic: 1851 papers in the
bibliography, involving 575 authors, only 112 of whom participated in
five or more papers (Pavicic infers that QL has a high turnover).
Average number of authors per paper: 1.3.

	Vaughan Pratt