Can Adaptive Conjoint Analysis perform in a Preference Logic Framework?

Research on conjoint analysis/preference aggregation/social choice aggregation is performed by more than forty years by various communities. However, many proposed mathematical models understand preferences as irreflexive, transitive and statical relations while there is human psychology research work questioning these properties as being not enough motivated. This works propose to position the conjoint analysis inside a logical framework allowing for nontransitive and globally inconsistent preferences. Using a preference logics one can define a logic-based utility allowing to obtain an aggregate semantics of the collective choice.