A coalgebraic view on positive modal logic

Positive modal logic is the restriction of the modal local consequence relation defined by the class of all Kripke models to the propositional negation-free modal language. The class of positive modal algebras is the one canonically associated with PML according to the theory of the algebrization of logics (Lecture Notes in Logic, Springer, Berlin, 1996). A Priestley-style duality is established between the category of positive modal algebras and the category of K+-spaces in (J. IGPL 7 (6) (1999) 683). In this paper, we establish a categorical equivalence between the category K+ of K+-spaces and the category Coalg(V) of coalgebras of a suitable endofunctor V on the category of Priestley spaces. (C) 2004 Elsevier B.V. All rights reserved.