1. A language model learning system, comprising: a language model storage device for storing a language model used for speech recognition; a recognizing device which performs speech recognition on learning speech data stored in advance by using the language model stored in the language model storage device, and outputs a recognition result; a reliability degree computing device for computing reliability degrees of respective word strings in the recognition result; a language model parameter updating device which updates a parameter of the language model stored in the language model storage device based on the reliability degrees of the respective word strings computed by the reliability degree computing device; and a word string number counting device which computes a number of all the word strings within the learning text data corresponding to the learning speech data and computes appearing number of the respective word strings, wherein the reliability degree computing device computes posteriori probability of the respective word strings based on the recognition result as the reliability degrees of the corresponding word strings, the posteriori probability of the respective word strings are obtained from forward probability and backward probability that relate to an order of appearance of words computed based on the recognition result, the language model parameter updating device computes appearance frequencies of the respective words from the number of all the word strings computed by the word string number counting device and the appearing number of the respective word strings, and updates the parameter of the language model stored in the language model storage device based on the appearance frequencies of the respective word strings and the reliability degrees of the respective word strings computed by the reliability degree computing device, and provided that the appearing number of the word string ω j in the learning text data is N j , a total number of word strings having the same word number as ω j contained in the learning text data is R, the reliability degree of the word string ω j when observation time series O r is observed in the recognition result is p(ω j |O r ), a constant is D, and the value of the language model before update is p j , the language model parameter updating device computes parameter p j of the language model corresponding to the word string ω j according to Expression 1 and updates the parameter to a computed value P j = N j - ∑ r ⁢ p ⁡ ( ω j ❘ O r ) + Dp j R - ∑ j ⁢ ∑ r ⁢ p ⁡ ( ω j ❘ O r ) + D ⁢ ⁢ ∑ r ⁢ : ⁢ ⁢ Sum ⁢ ⁢ of ⁢ ⁢ learning ⁢ ⁢ speech ⁢ ⁢ data ⁢ ⁢ numbers ⁢ ⁢ ∑ j ⁢ : ⁢ ⁢ Sum ⁢ ⁢ of ⁢ ⁢ all ⁢ ⁢ word ⁢ ⁢ strings. [ Expression ⁢ ⁢ 1 ]