PS2 era left a great bunch of games and Sony could bring part of those titles to PS4. Some evidences have emerged on the internet about this topic.
1. Siren appeared on a PS4 profile published on Reddit.
2. Ape Escape 2, Dark Cloud 2 and Twisted Metal: Black were rated for PS4 in Europe.
3. Sid Shuman from PS blog confirmed that these titles will be available on PS4 (PS Store) with Trophies support. Sony did not make official this information.
Therefore, Sony is likely preparing a selected collection of PS2 titles for PS4.