  Shapleys impossibility result indicates that the two-person bargaining
problem has no non-trivial ordinal solution with the traditional game-theoretic
bargaining model. Although the result is no longer true for bargaining problems
with more than two agents, none of the well known bargaining solutions are
ordinal. Searching for meaningful ordinal solutions, especially for the
bilateral bargaining problem, has been a challenging issue in bargaining theory
for more than three decades. This paper proposes a logic-based ordinal solution
to the bilateral bargaining problem. We argue that if a bargaining problem is
modeled in terms of the logical relation of players physical negotiation items,
a meaningful bargaining solution can be constructed based on the ordinal
structure of bargainers preferences. We represent bargainers demands in
propositional logic and bargainers preferences over their demands in total
preorder. We show that the solution satisfies most desirable logical
properties, such as individual rationality (logical version), consistency,
collective rationality as well as a few typical game-theoretic properties, such
as weak Pareto optimality and contraction invariance. In addition, if all
players demand sets are logically closed, the solution satisfies a fixed-point
condition, which says that the outcome of a negotiation is the result of mutual
belief revision. Finally, we define various decision problems in relation to
our bargaining model and study their computational complexity.
