The Logical Modalities and Their Semantics

Abstract

<p>This thesis is an interpretation of the logical modalities with the formulation of a suitable semantics. The system devised, QS4.3*, is based on the modal system S4.3, with the defining axiom, ם]םpםכq] vם]םqםכp], and the addition of quantifiers. The "accessibility relation" for the system is reflexive, transitive and anti-symmetric which defines a partial-ordering of possible partial worlds, rather than of the usual possible worlds. The need for a partial-ordering allows for a fuller interpretation of truth in all/some possible partial worlds with respect to states-of-affairs and sub-states-of-affairs. This is possible with a restricted meaning of the possible world as a possible partial world.</p>