LogMiner operational information (as opposed to redo data) is contained in the following views. You can use SQL to query them as you would any other view.
V$LOGMNR_DICTIONARY
Shows information about a LogMiner dictionary file that was created using the STORE_IN_FLAT_FILE option to DBMS_LOGMNR.START_LOGMNR. The information shown includes information about the database from which the LogMiner dictionary was created.
V$LOGMNR_LOGS
Shows information about specified redo log files, as described in "Querying V$LOGMNR_LOGS".
V$LOGMNR_PARAMETERS
Shows information about optional LogMiner parameters, including starting and ending system change numbers (SCNs) and starting and ending times.
V$DATABASE, DBA_LOG_GROUPS, ALL_LOG_GROUPS, USER_LOG_GROUPS, DBA_LOG_GROUP_COLUMNS, ALL_LOG_GROUP_COLUMNS, USER_LOG_GROUP_COLUMNS
Shows information about the current settings for supplemental logging, as described in "Querying Views for Supplemental Logging Settings".