Babalog-1
Probably not Turing complete.

Enter ? to go into query mode, and | to go back into rule mode.
|- (this is a comment)
|- BABA IS YOU
|- FLAG IS WIN
|- FLAG IS BABA (gives quality BABA)
|- KEKE IS MOVE
|- KEKE MIMIC BABA (copies qualities of BABA)
|- SKULL IS DEFEAT
|- ALL IS OPEN
|- ME IS NOT OPEN
|- ALL FEELING DEFEAT IS SAFE
|- ALL FEELING SHUT IS NOT OPEN
|- DOOR IS SHUT
|- SKULL FEELING OPEN IS SINK
|- ?
?- BABA
IS YOU
IS OPEN (from ALL)
?- FLAG
IS WIN
IS BABA
IS OPEN (from ALL)
?- KEKE
IS MOVE
IS YOU (from BABA)
IS OPEN (from ALL)
?- SKULL
IS DEFEAT
IS OPEN (from ALL)
IS SAFE (because FEELING DEFEAT from ALL)
IS SINK (because FEELING OPEN from SKULL)
?- ME
[s]IS OPEN[/s] (from ALL)
IS NOT OPEN
?- DOOR
[s]IS OPEN[/s] (from ALL)
IS NOT OPEN (because FEELING SHUT from ALL)
IS SHUT
?- IS YOU
BABA
KEKE
?- IS OPEN
BABA
FLAG
KEKE
SKULL
?- MIMIC BABA
KEKE
?- .?
(insert help here)
?- .??
[b]Information about Babalog-1[/b]

[b]Special nouns[/b]
[b]ALL[/b]: encapsulates all names (for every name X, X MIMIC ALL)

[b]Operators[/b]
[b]IS[/b]: assigns a quality to a name
[b]MIMIC[/b]: copies all qualities assigned to a name
[b]FEELING[/b]: applies a rule only when the specified quality is assigned to a name
[b]NOT[/b]: falsifies the following phrase (ex. NOT WIN falsifies WIN, NOT NOT WIN falsifies NOT WIN)
?- .X

GROUPs and a lot of other additions I don't currently know would be a thing in Babalog-2 to make it less... terrible.