Thesis announcement
Ville Nurmi <ville.v.nurmi-pxSi+dnQzZMxHbG02/[email protected]> Sat, 12 Sep 2009 11:48:20 +0300 (EEST)
| Newsgroups | gmane.science.mathematics.frogs |
|---|---|
| Message-ID | <[email protected]> |
Dear all, I wish to announce my doctoral thesis "Dependence Logic: Investigations into Higher-Order Semantics Defined on Teams". It is available as PDF here: http://urn.fi/URN:ISBN:978-952-10-5679-6 The thesis is about a new logic called dependence logic. The relevance of the thesis to the Frogs mailing list is in Chapter 6, "Axiomatising Fragments of FOD", where I try to provide a complete proof system for a fragment of dependence logic. I use calculus of structures for classical propositional logic and enforce it with what I call a "flow condition"; The atomic flows of two distinct atom occurrences in the premise must not connect anywhere in the derivation. The flow condition is needed because contraction is not a sound inference rule in the fragment I investigated. The flow condition limits the use of contraction. I did not manage to complete the proof of completeness of this proof system for the fragment. Also, I'm not actively in research any more because I have changed jobs. Therefore, I'd be happy if this (or any other) open question from the thesis is investigated and even proved or falsified by anyone. Best regards, Ville Nurmi University of Helsinki PS I'm not on the Frogs mailing list. Possible questions about this subject can be sent to me at ville.v.nurmi(at)helsinki.fi