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On the structure of shared awareness
Author(s) -
Friedell Morris F.
Publication year - 1969
Publication title -
behavioral science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 45
eISSN - 1099-1743
pISSN - 0005-7940
DOI - 10.1002/bs.3830140105
Subject(s) - class (philosophy) , computer science , epistemology , stability (learning theory) , boolean algebra , algebra over a field , mathematics , sociology , artificial intelligence , pure mathematics , algorithm , philosophy , machine learning
Sentences of the form, “ A thinks B thinks ⃛,” arise in the analysis of game‐like situations and in the sociology of knowledge. These are modeled by a Boolean algebra with operators, where “ A believes x ,” is written Ax. Operators ∩ j=1 (∞ i , A i ) j representing complete consensus or “common opinion” are defined. Properties of these epistemic operators are derived from postulates. Sociological features of content, stability and change of shared awareness are discussed. Finally, the model is used to solve a class of 2‐person 0‐sum games in which the conventional requirements for mutual knowledge are relaxed.