Talk:Stratification (mathematics)

New Foundations

I changed the section heading from 'New Foundations' to 'Set theory' in the hopes that it would be clearer at first glance that we're talking about 'set theory' of which NF is one axiomatization. Zero sharp 15:06, 20 August 2007 (UTC)

Stratified Negation

Question. I am mostly self taught when it comes to the formal logics, and I've found propositional and first order predicate logic fairly intuitive. I am trying to understand stratification as it applies to negation in the bodies of HORNSAT rules. Looking at the 'In mathematical logic' section, the need for stratification in clauses with negated atoms is understandable, yet I can not find any definition (here or elsewhere) that explains what the stratification number (S) represents or how it is derived. This is an issue that seems to impact more than just Wikipedia's explanation of the topic, giving me the impression that the implicit stratification number of a predicate is something that students would grasp out of context. However, with multiple definitions I've read, the definition of the stratification number itself and the manner in witch it is supplied are never explicitly stated, only that a rule head must be greater than or equal to (unless negated, then just greater than) than all of the atoms in the body. Is this number related to the concept of safe horn clause rules (no free variables in the head that are not also refrenced in the body)? In regards to the article, is this something that needs to be explained more clearly? C4Cypher (talk) 15:23, 26 November 2012 (UTC)

Looking at class notes for Knowledge Representation at Imperial College, London I realize that the definition I'm looking for is recursive. S(P)=0 would represent a clause without negation, S(P)=1 would only allow negation of predicates in the body where S(P)=0, or to put it another way, you cannot negate a predicate in a rule's body unless there exists a rule with that predicate in the head. Is this correct? C4Cypher (talk) 15:47, 26 November 2012 (UTC)

Stratification in field arithmetic

There is a further definition of P-stratification, for various properties P: a P-stratification of a constructible set A is a partition of A into a finite collection of constructible sets each having property P. See Fried, Michael D.; Jarden, Moshe (2008). Field arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. Vol. 11 (3rd ed.). Springer-Verlag. p. 424. ISBN 978-3-540-77269-9. Zbl 1145.12001. Deltahedron (talk) 17:07, 22 June 2014 (UTC)