MySQL doesn’t log queries anymore

Some time ago I updated my MySQL server to the v5.6:

SELECT VERSION();
5.6.30-0ubuntu0.14.04.1

Now the query logging isn't working though the configs in the /etc/mysql/my.cnf seem to be correct:

[mysqld]
general_log_file = /var/log/mysql/mysql.log
general_log      = 1
log              = /var/log/mysql-query.log # Added now, but it also hasn't helped.

The log files exist and are writable for the mysql user:

$ ls -lia /var/log/mysql | grep "mysql-query"
393371 -rwxrwxrwx  1 mysql adm   0 Jun  5 17:09 mysql-query.log
$ ls -lia /var/log | grep "mysql.log"
403924 -rwxrwxrwx  1 mysql adm   0 Jun  5 16:35 mysql.log

How to get MySQL logging queries again?

UPDATE

Additional information:

The error log displays some errors on (re-)starting the server.

2016-06-07 19:56:55 5861 [Note] /usr/sbin/mysqld: Normal shutdown

2016-06-07 19:56:55 5861 [Note] Giving 0 client threads a chance to die gracefully
2016-06-07 19:56:55 5861 [Note] Event Scheduler: Purging the queue. 0 events
2016-06-07 19:56:55 5861 [Note] Shutting down slave threads
2016-06-07 19:56:55 5861 [Note] Forcefully disconnecting 0 remaining clients
2016-06-07 19:56:55 5861 [Note] Binlog end
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'partition'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_SYS_DATAFILES'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_SYS_TABLESPACES'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_SYS_FOREIGN_COLS'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_SYS_FOREIGN'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_SYS_FIELDS'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_SYS_COLUMNS'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_SYS_INDEXES'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_SYS_TABLESTATS'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_SYS_TABLES'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_FT_INDEX_TABLE'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_FT_INDEX_CACHE'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_FT_CONFIG'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_FT_BEING_DELETED'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_FT_DELETED'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_FT_DEFAULT_STOPWORD'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_METRICS'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_BUFFER_POOL_STATS'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_BUFFER_PAGE_LRU'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_BUFFER_PAGE'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_CMP_PER_INDEX_RESET'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_CMP_PER_INDEX'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_CMPMEM_RESET'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_CMPMEM'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_CMP_RESET'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_CMP'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_LOCK_WAITS'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_LOCKS'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'INNODB_TRX'
2016-06-07 19:56:55 5861 [Note] Shutting down plugin 'InnoDB'
2016-06-07 19:56:55 5861 [Note] InnoDB: FTS optimize thread exiting.
2016-06-07 19:56:55 5861 [Note] InnoDB: Starting shutdown...
2016-06-07 19:56:57 5861 [Note] InnoDB: Shutdown completed; log sequence number 95410297
2016-06-07 19:56:57 5861 [Note] Shutting down plugin 'ARCHIVE'
2016-06-07 19:56:57 5861 [Note] Shutting down plugin 'PERFORMANCE_SCHEMA'
2016-06-07 19:56:57 5861 [Note] Shutting down plugin 'BLACKHOLE'
2016-06-07 19:56:57 5861 [Note] Shutting down plugin 'MEMORY'
2016-06-07 19:56:57 5861 [Note] Shutting down plugin 'MRG_MYISAM'
2016-06-07 19:56:57 5861 [Note] Shutting down plugin 'MyISAM'
2016-06-07 19:56:57 5861 [Note] Shutting down plugin 'CSV'
2016-06-07 19:56:57 5861 [Note] Shutting down plugin 'sha256_password'
2016-06-07 19:56:57 5861 [Note] Shutting down plugin 'mysql_old_password'
2016-06-07 19:56:57 5861 [Note] Shutting down plugin 'mysql_native_password'
2016-06-07 19:56:57 5861 [Note] Shutting down plugin 'binlog'
2016-06-07 19:56:57 5861 [Note] /usr/sbin/mysqld: Shutdown complete

160607 19:56:57 mysqld_safe mysqld from pid file /var/run/mysqld/mysqld.pid ended
160607 19:56:58 mysqld_safe Starting mysqld daemon with databases from /var/lib/mysql
2016-06-07 19:56:58 0 [Warning] TIMESTAMP with implicit DEFAULT value is deprecated. Please use --explicit_defaults_for_timestamp server option (see documentation for more details).
2016-06-07 19:56:58 0 [Note] /usr/sbin/mysqld (mysqld 5.6.30-0ubuntu0.14.04.1) starting as process 6430 ...
2016-06-07 19:56:58 6430 [Warning] Buffered warning: Changed limits: max_open_files: 1024 (requested 5000)

2016-06-07 19:56:58 6430 [Warning] Buffered warning: Changed limits: table_open_cache: 431 (requested 2000)

2016-06-07 19:56:58 6430 [Note] Plugin 'FEDERATED' is disabled.
2016-06-07 19:56:58 6430 [ERROR] Function 'innodb' already exists
2016-06-07 19:56:58 6430 [Warning] Couldn't load plugin named 'innodb' with soname 'ha_innodb.so'.
2016-06-07 19:56:58 6430 [ERROR] Function 'federated' already exists
2016-06-07 19:56:58 6430 [Warning] Couldn't load plugin named 'federated' with soname 'ha_federated.so'.
2016-06-07 19:56:58 6430 [ERROR] Function 'blackhole' already exists
2016-06-07 19:56:58 6430 [Warning] Couldn't load plugin named 'blackhole' with soname 'ha_blackhole.so'.
2016-06-07 19:56:58 6430 [ERROR] Function 'archive' already exists
2016-06-07 19:56:58 6430 [Warning] Couldn't load plugin named 'archive' with soname 'ha_archive.so'.
2016-06-07 19:56:58 6430 [Note] InnoDB: Using atomics to ref count buffer pool pages
2016-06-07 19:56:58 6430 [Note] InnoDB: The InnoDB memory heap is disabled
2016-06-07 19:56:58 6430 [Note] InnoDB: Mutexes and rw_locks use GCC atomic builtins
2016-06-07 19:56:58 6430 [Note] InnoDB: Memory barrier is not used
2016-06-07 19:56:58 6430 [Note] InnoDB: Compressed tables use zlib 1.2.8
2016-06-07 19:56:58 6430 [Note] InnoDB: Using Linux native AIO
2016-06-07 19:56:58 6430 [Note] InnoDB: Using CPU crc32 instructions
2016-06-07 19:56:58 6430 [Note] InnoDB: Initializing buffer pool, size = 128.0M
2016-06-07 19:56:58 6430 [Note] InnoDB: Completed initialization of buffer pool
2016-06-07 19:56:58 6430 [Note] InnoDB: Highest supported file format is Barracuda.
2016-06-07 19:56:58 6430 [Note] InnoDB: 128 rollback segment(s) are active.
2016-06-07 19:56:58 6430 [Note] InnoDB: Waiting for purge to start
2016-06-07 19:56:58 6430 [Note] InnoDB: 5.6.30 started; log sequence number 95410297
2016-06-07 19:56:58 6430 [Note] Server hostname (bind-address): '*'; port: 3306
2016-06-07 19:56:58 6430 [Note] IPv6 is available.
2016-06-07 19:56:58 6430 [Note]   - '::' resolves to '::';
2016-06-07 19:56:58 6430 [Note] Server socket created on IP: '::'.
2016-06-07 19:56:58 6430 [Note] Event Scheduler: Loaded 0 events
2016-06-07 19:56:58 6430 [Note] /usr/sbin/mysqld: ready for connections.
Version: '5.6.30-0ubuntu0.14.04.1'  socket: '/var/run/mysqld/mysqld.sock'  port: 3306  (Ubuntu)

Maybe it relates somehow to the issue.