Skip to main content
Article thumbnail
Location of Repository

A Realistic (Non-Associative) Logic And a Possible Explanations of 7±2 Law

By Raúl Trejo, Vladik Kreinovich, I.R. Goodman, Jesus Martinez, Reginaldo Gonzalez and Sistemas De Informacion


When we know the subjective probabilities (degrees of belief) p1 and p2 of two statements S1 and S2 , and we have no information about the relationship between these statements, then the probability of S1 &S2 can take any value from the interval [max(p1 + p2 \Gamma 1; 0); min(p1 ; p2 )]. If we must select a single number from this interval, the natural idea is to take its midpoint. The corresponding "and" operation p1 & p2 def = (1=2) \Delta (max(p1 +p2 \Gamma 1; 0)+min(p1 ; p2)) is not associative. However, since the largest possible non-associativity degree j(a & b) & c \Gamma a & (b & c)j is equal to 1/9, this non-associativity is negligible if the realistic "granular" degree of belief have granules of width 1=9. This may explain why humans are most comfortable with 9 items to choose from (the famous "7 plus minus 2" law). We also show that the use of interval computations can simplify the (rather complicated) proofs. 1 1 In Expert Systems, We Need Estimates for the Degree of..

Year: 2000
OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • (external link)
  • (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.