States on Polyadic Heyting Algebras
Dumitru Daniel Drăgulici
This paper concerns the algebraic logic associated to probabilistic models of intuitionistic predicate calculus. We consider Bosbach’s style states on polyadic Heyting algebras, define the polyadic states, the weak polyadic states, the state models and the weak state models of the states. The main result of this paper asserts that any state defined on a Heyting subalgebra of a polyadic Heyting algebra has a weak state model. This theorem has as consequence that any intuitionistic probability has a weak probabilistic model.
Keywords: Polyadic state, polyadic Heyting algebra, intuitionistic probability, intuitionistic predicate logic
AMS classification (2010): 03G15, 06D20, 03B20, 03C90