I'm not a linguist, so this is just my opinion. (どなたか別の方にもご回答頂けましたら幸いです。) "は" has a function of "differentiation" or "contrast". In your example, "本はあります" indicates that you don't have something else, which is "辞書". EX) 私はスポーツを見るのは好きです。 So I understand that she/he likes to WATCH sports, but she/he probably does not like to PLAY sports. EX) 私はスポーツを見るのが好きです。 This is just a self introduction, and she/he just like to watch sports and does not mean anything else. I hope it helps :)

Hi Christine, I wrote a blog post about it here http://www.japaneserabbit.com/#!は-or-が/c218b/561ad7130cf2c3576e58661a Hope it helps.

Naoki's answer is correct. In addition to that, I want to answer you. ※I am a linguist.（^-^） But I do not understand your question. Are you asking us whether 本はありますが、辞書はありません could be changed to 本がありますが、辞書がありません or 本がありますが、辞書はありません? Why did you write 本がありません．．．?