Supplement to Preference Logic
Long descriptions for some figures in Preference Logic
Diagram A description
Commuting diagram where new proposition \(A\) is added in parallel to an existing base.
It consists of four vertices laid out in a square with arrows connecting some of them:
- upper left corner: \(\langle \mathscr{B}, < \rangle\) which has an arrow labeled \(\parallel A\) pointing to the vertice in the upper right corner and an unlabeled arrow pointing to the vertice in the lower left corner
- upper right corner: \(\langle \mathscr{B} \parallel A, < \rangle\) which has an unlabeled arrow pointing to the vertice in the lower right corner
- lower left corner: \(\langle W, \preceq \rangle\) which has an arrow labeled \(\sharp A\) pointing to the vertice in the lower right corner
- lower right corner: \(\langle W, \sharp A(\preceq) \rangle\)
Diagram B description
Commuting diagram where new proposition \(A\) is placed at the top of the priority graph.
It consists of four vertices laid out in a square with arrows connecting some of them:
- upper left: \(\langle \mathscr{B}, < \rangle\) which has an arrow labeled \(A; \mathscr{B}\) pointing to the vertice in the upper right corner and an unlabeled arrow pointing to the vertice in the lower left corner
- upper right: \(\langle A; \mathscr{B}, < \rangle\) which has an unlabeled arrow pointing to the vertice in the lower right corner
- lower left: \(\langle W, \preceq \rangle\) which has an arrow labeled \(\Uparrow A\) pointing to the vertice in the lower right corner
- lower right: \(\langle W, \Uparrow A(\preceq) \rangle\)