@ Arnak
Previously I have never had an issue viewing the contents of log files, whilst the self-defence module would preven't you from modifying the log file, I don't believe they should prevent just opening them.
What process are you using to open them for reading ?
Avast prefers the use of windows notepad and that is what the self-defence module may be objecting to.
That said, the log file is unlikely to provide the information you are seeking.
"I would like to see if there are any programs that have been stopped from working correctly."
By default the log only writes certain things, alerts and Hard errors, unless you are getting something like this for the affected program then it wouldn't appear in the log file.