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The Influence of the Test Operator on the Expressive Powers of PDL-Like Logics

Berman and Paterson proved that Test-Free PDL is weaker than PDL. As the description logics ALCtrans and ALCreg are, respectively, variants of Test-Free PDL and PDL, there is a concept of ALCreg that is not equivalent to any concept of ALCtrans. Generalizing this, we show that there is a concept of ALCreg that is not equivalent to any concept of the logic that extends ALCtrans with inverse roles, nominals, qualified number restrictions, the universal role and local reflexivity of roles. We also provide some results for the case with RBoxes and TBoxes. One of them states that tests can be eliminated from TBoxes of the deterministic Horn fragment of ALCreg.