Modal Sequents and Definability

We examine a certain modal consequence relation, and define the notion of validity of a modal sequent on a frame. We demonstrate that it is possible to define classes of frames. not definable by modal formulas, by modal sequents. Through the use of modal algebras and general frames, we obtain a characterization of modal sequent-definable classes of frames which are also first-order definable, and a sufficient condition for a class of frames to be definable by modal sequents. ACKNOWLEDGEMENTS AND DEDICATION First of all, I would like to thank my supervisor. Dr. Steve Thomason, for his support and guidance throughout the writing of this thesis. I would also like to thank Dr. Ray Jennings and the Institute for Applied Logic for supplying computing and typesetting resources. Finally, I would like to acknowledge the support that I received from NSERC during part of my time at SFU. This thesis is dedicated to my father and to the memory of my mother.