we use ASP.NET with C# and based on open source projects/articles I passed through, I found many properties were including a logic but when I did so the team-le
A common answer applies here: It Depends.
Generally, it is not a good idea to implement business logic in getters and setters. If your object is a simple DTO (data transfer object) this would violate Single Responsibility.
However, state-tracking logic and other housekeeping is often found in properties. For example, Entity Framework 4 self-tracking entities have state management logic in every primitive property setter to allow for tracking.
An alternative to logic in properties is Aspect-Oriented Programming (AOP.) Using AOP, you can "inject" logic between objects and the hosting process. Access to objects can be "intercepted" and handled conditionally.