Value Coalition Logic: A Typed Assignment-Based Reconstruction of Coalition Logic

We introduce Value Coalition Logic, a typed assignment-based reconstruction of classical coalition logic. The strategic semantics is unchanged: coalitional ability is still interpreted by the standard one-step game-form clause. The change is at the atomic level. Instead of flat propositional valuations, states carry total assignments of values to finitely typed variables. As a result, exhaustivity and mutual exclusion of alternative values are built into the semantics, rather than imposed as external coherence constraints. We prove that, over each fixed finite typed signature, Value Coalition Logic is truth-equivalent to propositional coalition logic over coherent valuations. This correspondence yields a sound and complete Hilbert-style axiomatisation obtained by adding finite-domain value-coherence axioms to the standard axioms of coalition logic. The main contribution is structural. Projecting ordinary coalitional ability onto a single value domain yields quotient game forms, projected effectivity families, and strategic value-range hypergraphs. These structures support set-valued strategic exclusion, transversal polarity for disjoint coalitions, exact boundary duality between the empty and grand coalitions, and a measure of residual value indeterminacy. Thus the logic is conservative in its strategic modality, but exposes value-level invariants that are hidden in flat propositional encodings.