The logical representation of extensive games

Given an extensive formG, we associate with every choice an atomic sentence and with every information set a set of well-formed formulas (wffs) of prepositional calculus. The set of such wffs is denoted by Γ(G). Using the so-called topological semantics for propositional calculus (which differs from the standard one based on truth tables), we show that the extensive form yields a topological model of Γ(G), that is, every wff in Γ(G), is “true in G”. We also show that, within the standard truth-table semantics for propositional calculus, there is a one-to-one and onto correspondence between the set of plays ofG and the set of valuations that satisfy all the wffs in Γ(G).