We give a uniform presentation of representation and decidability results related to the Kripke-style semantics of several nonclassical logics. We show that a general representation theorem (which has as particular instances the representation theorems as algebras of sets for Boolean algebras, distributive lattices and semilattices) extends in a natural way to several classes of operators and allows to establish a relationship between algebraic and Kripke-style models. We illustrate the ideas on several examples. We conclude by showing how the Kripkestyle models thus obtained can be used (if rst-order axiomatizable) for automated theorem proving by resolution for some non-classical logics.

3.97> v m (ph) = 1, p.51. Newbasax def = (Basaxnf Ax6; Ax3;AxE g)[f Ax6 00 ; Ax6 01 ; Ax3 0 ; AxE 0 g = f Ax1;Ax2;Ax3 0 ; Ax4;Ax5;Ax6 00 ; Ax6 01 ; AxE 0 g (cf. p.191), where: Ax6 00 (8m; k 2 Obs) wm [tr m (k)] Rng(w k ), p.190. Intuitively, observer k sees all those events which are seen by another observer m on k's life-line. Ax6 01 (8m; k