zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Quantitative research of generalized tautologies in n-valued propositional logic L n * . (Chinese) Zbl 1212.03011
Summary: By means of the infinite product of evenly distributed probability spaces, the proportion of the class of valuations which satisfies v(A)ζ (or v(A)>ζ, where ζ[0,1]) in the set of all valuations is considered. The concepts of ζ-truth degree and ζ + -truth degree in the n-valued R 0 -propositional logic system L n * are introduced in order to double-grade the concept of tautology. Also, the theories of σ-(ζ-tautology) and σ-(ζ + -tautology) are defined. Moreover, relationships between ζ-truth degrees (ζ + -truth degrees) and generalized tautologies together with the graded generalized tautologies are discussed and the general reference rules endowed with ζ-truth degrees are proved.
03B50Many-valued logic
03B48Probability logic; inductive logic
03B52Fuzzy logic; logic of vagueness