This paper attempts at an integrated approach to the various semantic properties of English demon- stratives this and that. According to previous scholars, a demonstrative has very diverse functions-spatial and temporal relations with the speaker, discourse deixis, the speaker`s psychological and emotional expressions. This study reviews two representative approaches in order to see whether there are unified principles that can account for all those cases. First, the seman- tic/pragmatic approach tries to find the meanings of the demonstratives this and that from their basic semantic features, proximal/distal from the speaker, and second, the cognitive approach accounts for their meanings in consideration of the possibility of the hearer`s cognitive processing. This paper discusses the merits and limitations of those two approaches, and proposes the following approach as an alternative: the proximal/distal demonstratives this and that are related with the speaker`s and hearer`s projection of focus onto the referent.

This paper takes a hybrid approach, combining the time and causality frame approaches to examine the interchangeability between should and must, which are epistemic modal auxiliary verbs that indicate logical inference and deduction. It is argued that only must is used when deduction is temporally situated at the present or in the past and directed from consequences to causes, but only should is used when the same process is situated in the future and directed from causes to consequences. The paper also shows either should or must are used in the remaining two types of cases-that is, those in which the process of deduction regards future situations and moves from effects to causes, and those in which deduction regards present or past situations and moves from causes to effects.