Comment 3 for bug 1603286

Thank you for taking the time to report this bug and helping to make Ubuntu better. The relevant dpkg terminal log says:

touch: cannot touch '/boot/initrd.img-4.4.0-31-generic.new': Read-only file system

So your /boot partition mounted from /dev/sda1 was read-only. CurrentDmesg.txt shows:

[ 81.268414] sd 1:0:0:0: [sda] 124735488 512-byte logical blocks: (63.9 GB/59.5 GiB)
[ 81.287023] sda: sda1 sda2 sda3
[ 82.689255] EXT4-fs (sda2): mounting ext2 file system using the ext4 subsystem
[ 82.708006] EXT4-fs (sda2): warning: mounting unchecked fs, running e2fsck is recommended
[ 82.727344] EXT4-fs (sda2): mounted filesystem without journal. Opts: (null)
[ 82.734136] FAT-fs (sda1): Volume was not properly unmounted. Some data may be corrupt. Please run fsck.

So running fsck and mounting /boot read-write should solve the issue. Feel free to continue to report any other bugs you may find.