Temporal reasoning constitutes one of the main topics within the field of Artificial Intelligence. Particularly interesting are interval-based methods, in which time intervals are treated as basic ontological objects, in opposite to point-based methods, where time-points are considered as basic. The former approach is more expressive and seems to be more appropriate for such applications as natural language analysis or real time processes verification. My research concerns the classical interval-based logic, namely Halpern-Shoham logic (HS). In particular, my investigation continues recently proposed search for well-behaved - i.e., expressive enough for practical applications and of low computational complexity - HS fragments obtained by imposing syntactical restrictions on the usage of propositional connectives in their languages.