We study partiality in propositional logics containing formulas with either unde ned or over-de ned truth-values. Unde ned values are created by adding a four-place connective W termed transjunction to complete models which, together with the usual Boolean connectives is shown to be functionally complete for all partial functions. Transjunction is seen to be motivated from a game-theoretic perspective, emerging from a two-stage extensive form semantic game of imperfect information between two players. This game-theoretic approach yields an interpretation where partiality is generated as a property of non-determinacy of games. Over-de ned values are produced by adding a weak, contradictory negation or, alternatively, by relaxing the assumption that games are strictly competitive. In general, particular forms of extensive imperfect information games give rise to a generalised propositional logic where various forms of informational dependencies and independencies of connectives can be studied.

The purpose of this paper is to explore the extent in which the idea of using negotiation games in tandem with the theory of semantic games is relevant to the concept of meaning in logical semantics. The need for such negotiations is argued to arise when some formulas are logically non-coherent, which in turn may take place because of conflicts between the players playing the associated non-strictly competitive semantic language-games on these formulas.