 Restall (1996) along with Mares (1996) work out this connection as follows. Restall assumes that channels are amongst the information sites (Mares does not). Instead of information sites, common terminology speaks of information states. Information states may be incomplete and/or inconsistent, indeed they may be sub-propositional entirely (as will be the case below when we look at fine-grained information-based semantics for natural languages based on informationalised versions of the Lambek Calculi). In Kripke/frame semantics terms, we have ternary information frame \(\mathbf{F}:\langle S, \sqsubseteq, R\rangle\), where \(S\) is a set of information states, \(\sqsubseteq\) is a partial order on \(S\), and \(R\) is a ternary accessibility relation on members of \(S\). An information model is an information frame \(\mathbf{F}\) along with an evaluation/supports relation \(\Vdash\) between members of \(S\) and types/propositions \(\phi, \psi\ldots\). How exactly we read \(x\Vdash\phi\) is going to depend on what sort of information state \(x\) happens to be, and what type of thing \(\phi\) is. The simplest case will be when \(x\) is a situation and \(\phi\) is a proposition. In this case we may read \(x\Vdash\phi\) as \(\phi\) is true at \(x\). Given this much,  (12)  is translated as follows: