Abstrakt
In this paper, a nonstandard semantic framework for intuitionistic logic is introduced and its relation to Kripke semantics is studied. The main peculiarity of the framework is that it allows for information states that support a disjunction without supporting any of its disjuncts.
The semantic structures of the framework are called information models and they consist of a join-semilattice with a zero element and a valuation assigning to every atomic formula an ideal in the algebraic structure. A method will be described that transforms any Kripke model into an equivalent information model and any information model into an equivalent Kripke model.
It will also be shown how to extend the framework to the case of first-order logic.