Bipolar qualitative/quantitative models for cognitive modeling and multiagent decision analysis

NPN (negative-positive-neutral) calculi, a family of eight qualitative-quantitative models for bipolar cognitive modeling and decision analysis, are introduced and analyzed. It is proved that NPN logic, NPN fuzzy logic, NPN algebra, NPN relational model, and NPN linear algebra provide six new strict (quantitative) structures after the usual 4-valued model. It is observed that there is no clear-cut between qualitative and quantitative models; the more levels of specifications the closer is a qualitative model towards a quantitative model; and any qualitative model may fail without deeper levels of specifications. Based on these observations, eight different models are positioned on a qualitative-quantitative spectrum. Cognitive modeling and multiagent decision analysis using different models are illustrated and compared