Should the properties of constraint monotonicity and foundedness be mandatory requirements that every answer set and world view semantics must satisfy? This question is challenging and has incurred a debate in answer set programming (ASP). In this paper we address the question by introducing natural logic programs whose expected answer sets and world views violate these properties and thus may be viewed as counter-examples to these requirements. Specifically we use instances of the generalized strategic companies problem for ASP benchmark competitions as concrete examples to demonstrate that the requirements of constraint monotonicity and foundedness may exclude expected answer sets for some simple disjunctive programs and world views for some epistemic specifications. In conclusion these properties should not be mandatory conditions for an answer set and world view semantics in general.