aleks jakulin btyqaeaslfdsfriuniljsi dear lotfi attempt tackle concrete examples mention probability theory differentiate probability possibility case point let x number passengers car know car fivepassenger sedan understanding possible squeeze five passengers car probability x 3 probability x 6 assuming theta parameters distribution observed observable 5passenger sedans possibility defined purely ppx6theta 0 course could give different name fundamentally stay within context probability theory probability theory differentiate imprecision uncertainty would handle following simple problema problem similar stated earlier message usually takes hour drive home airport left house l0 morning time would arrive airport want ptime_at_airporttime_at_home 10 constraints one constraints example time_at_airporttime_at_home normal1 hour sigma sigma corresponds would construct bayesian model following problem box contains balls various sizes perceptions 20 balls box b small c several times many small balls large balls probability ball drawn random neither large small perceptions interpreted constraints help define probability distribution sizes set balls number balls techniques maximum entropy used transform constraints probability distributions bayesian constraints vague therefore also probability distribution uncertain problems arise primarily due translating words parameters distributions whats quantitative meaning x 20 balls variance one could assume number gets rounded 20 meaning x 07uniform152503uniform195205 could acquire matching x actual x obtain probability distribution several people definition small large function range sizes smallest largest perhaps small balls defined ones smaller x large ones larger compute proportion smalllarge distribution quantitative meaning example smalllarge uniform0810 constraint distribution problem one probability problem lies conversion qualitative natural language expressions quantitative probability distributions address building probabilistic model connects concrete meaning linguistic expression best regards aleks jakulin department statistics columbia university thu 07 aug 2008 065254 0500 uai fuzzy logic probability