A Segment is said to be "compatible" with some other Segment, if it can be played directly after that other Segment, without sounding awkward.
To test if a Segment A is compatible with a Segment B, select Segment B in the Source Tree View, and select Segment A in the Target Tree View. This will have Segment B (the "source" Segment) loaded to the left section, and Segment A (the "target" Segment) to the right section of the Playback Panel, where you can replay their transition to check how it sounds. In case the playback-buttons are disabled, check the path to your audio pool in the Project Property Panel.
To change the compatibility of a pair of Segments, see the instructions in the Target Tree View.
The default setting within psai is that any Segment is compatible with any other Segment, unless declared otherwise. Therefore their compatibilities will be indicated as "implicitly allowed". You can change this behavior for each Segment within the Segment Property Panel ("default compatibility as follower"). Changing this will result in "implicitly blocked" compatibility.
Compatibilities can not only be defined for single Segment transitions, but also for whole Groups or Themes. E.g. if you selected some Theme A in the Source Tree, and some other Theme B in the Target Tree, and set this transition to "blocked explicitly", this will disallow all transitions from any Segment within Theme A to any Segment in Theme B, along all Groups. Their transitions will be indicated as "blocked implicitly", as you defined the compatibility not on the same hierarchy level, but at least one level above. In practice it does not make a difference if a transition is blocked implicitly or explicitly - this transition will be forbidden during your game in any case. This distinction is just made to help in the authoring process.
Types of compatibility:
1. allowed implicitly (dark green)
This setting indicates that a transition from the selected source entity to the given target entity will be allowed. "Implicitly" indicates that this is either the default behavior, or the compatibility is inherited from the parent Group / Theme.
2. blocked implicitly (dark red)
This setting indicates that a transition from the selected source entity to the given target entity will be forbidden. "Implicitly" indicates that this is either the default behavior, or the compatibility is inherited from the parent Group / Theme.
3. allowed explicitly (light green)
This setting shows that a transition from the selected source entity to the given target entity was manually / explicitly allowed. This transition will stay allowed, independently from the compatibility of the parent Groups / Themes.
4. blocked explicitly (light red)
This setting shows that a transition from the selected source entity to the given target entity was manually and explicitly blocked. This transition will stay forbidden, independently from the compatibility of the parent Groups / Themes.
5. impossible transition (white square with black X)
Psai's playback rules imply that Segment transitions will never occur at runtime. E.g. if there is a Segment that is only usable at the end of a certain Theme, this will never be followed directly by some other Segment that is only usable to end some other Theme or Group. Impossible Transitions like this are indicated by an X-Icon.