11. For example, the three-valued logic A3 of Aukasiewicz can be axiomatized as: 12. Other types of digital signals can represent three-valued logic or higher valued logics. 13. Other types of digital signals can represent three-valued logic or higher valued logics . 14. Some many-valued logics may have incompatible definitions of equivalence and order ( entailment ). 15. He invented a popular shape analysis based on three-valued logic together with Tom Reps. 16. Multi-valued logics are intended to preserve the property of designationhood ( or being designated ). 17. T-norm fuzzy logics belong in broader classes of fuzzy logics and many-valued logics . 18. One of the early motivations for the study of many-valued logics has been precisely this issue. 19. This can lead to unexpected results, if users are not well versed in 3-value logic . 20. For an elementary introduction to the three-valued instantiation A 3, see three-valued logic .