Every line comes with two pieces of free information: its walls. The first clue in the list cannot start before the left edge and the last cannot end past the right edge, so anything that happens near a wall is unusually easy to interpret. Edge logic is the habit of checking the borders of the grid first, where deductions are cheapest.
The classic pattern is a filled cell touching the edge. If a line starts with clue 3 and its very first cell is filled, there is no room for doubt: that cell belongs to the first run, the run is anchored to the wall, and it extends exactly three cells — followed by a mandatory empty cell.
The same reasoning works from the right with the last clue, and the two directions do not interfere — work both ends of every line. On the top and bottom rows of the grid, edge logic is often the very first foothold, because those rows constrain the first and last cells of every column at once.
The deeper insight is that walls are wherever you make them. A proven-empty cell behaves exactly like a grid edge: no run can cross it. That means the stretch between two X marks (or between an X and a real wall) is a miniature line in its own right, and every edge technique applies inside it. If a clue is confined to a five-cell segment, treat that segment as a width-5 line: apply the overlap formula there, anchor runs against the X walls there, cross off its dead ends there.
This composes naturally with simple spaces (which manufactures the walls) and splitting (which decides which clue lives in which segment). Late in a hard puzzle, nearly every move is edge logic inside some small segment — the grid has effectively dissolved into dozens of tiny lines, each one or two deductions from done.