1. A dialogue speech recognition system comprising: a speech recognition unit that receives a speech signal of each speaker in a dialog among a plurality of speakers and turn information indicating whether a speaker having generated the speech signal has turn to speak or indicating a probability that the speaker has turn to speak and performs speech recognition for the speech signal, wherein the speech recognition unit at least includes: an acoustic likelihood computation unit that provides a likelihood of occurrence of an input speech signal from a given phoneme sequence; a linguistic likelihood computation unit that provides a likelihood of occurrence of a given word sequence; and a maximum likelihood candidate search unit that provides a word sequence with a maximum likelihood of occurrence from a speech signal by using the likelihoods provided by the acoustic likelihood computation unit and the linguistic likelihood computation unit, and the linguistic likelihood computation unit provides different linguistic likelihoods when a speaker having generated a speech signal input to the speech recognition unit has the turn to speak and when not.