An essay in natural modal logic

A generalized inclusion (g.i.) frame consists of a set of points (or "worlds") W and an assignment of a binary relation Rw on W to each point w in W. generalized inclusion frames whose Rw are partial orders are called comparison frames. Conditional logics of various comparative notions, for example, Lewis's V-logic of comparative possibility and utilitarian accounts of conditional obligation, model the dyadic modal operator > on comparison frames according to (what amounts to) the following truth condition: oc>13"holds at w" if every point in the truth set of a bears Rw to some point where holds. In this essay I provide a relational frame theory which embraces both accessibility semantics and g.i. semantics as special cases. This goal is achieved via a philosophically significant generalization of universal strict implication which does not assume accessibility as a primitive. Within this very general setting, I provide the first axiomatization of the dyadic modal logic corresponding to the class of all g.i. frames. Various correspondences between dyadic logics and first order definable subclasses of the class of g.i. frames are established. Finally, some general model constructions are developed which allow uniform completeness proofs for important sublogics of Lewis' V.

Name thesis:degree_name

Doctor of Philosophy - PhD

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Philosophy

Grantor dc:publisher

University of British Columbia

Year dc:date

1992

Author dc:creator

• Apostoli, Peter J.

Statement dc:rights

• For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.

Language dc:language

eng

Handle dc:identifier

http://hdl.handle.net/2429/2277

OAI identifier oai:identifier

oai:circle.library.ubc.ca:2429/2277