Resource title

The common knowledge of formula exclusion

Resource image

image for OpenScout resource :: The common knowledge of formula exclusion

Resource description

A multi-partition with evaluations is defined by two sets S and X, a collection P1, . . . ,Pn of partitions of S and a function : S ! {0, 1}X. To each partition Pj corresponds a person j who cannot distinguish between any two points belonging to the same member of Pj but can distinguish between different members of Pj . A cell of a multi-partition is a minimal subset C such that for all j the properties P 2 Pj and P \ C 6= ; imply that P C. Construct a sequence R0,R1, . . . of partitions of S by R0 = { −1(a) | a 2 {0, 1}X} and x and y belong to the same member of Ri if and only if x and y belong to the same member of Ri−1 and for every person i the members Px and Py of Pj containing x and y respectively intersect the same members of Ri−1. Let R1 be the limit of the Ri, namely x and y belong to the same member of R1 if and only if x and y belong to the same member of Ri for every i. For any set X and number n of persons there is a canonical multi-partition with evaluations defined on a set such that from any multi-partition with evaluations (using the same X and n) there is a canonical map to with the property that x and y are mapped to the same point of if and only if x and y share the same member of R1. We define a cell of to be surjective if every multi-partition with evaluations that maps to it does so surjectively. A cell of a multi-partition with evaluations has finite fanout if every P 2 Pj in the cell has finitely many elements. All cells of with finite fanout are surjective, but the converse does not hold.

Resource author

Resource publisher

Resource publish date

Resource language

en

Resource content type

Resource resource URL

http://eprints.lse.ac.uk/13793/

Resource license