The Linguistic Association of Korea Journal, 21(1). 155-184. Deixis is a phenomenon that has been studied from many different perspectives, and there are several issues in the debate on the meaning of it. Adopting the cognitive perspective of relevance theory, this paper applies the fundamental distinction between ‘conceptual’ and ‘procedural’ linguistic meanings to the question of how a variety of uses of proximal demonstrative in explained. It is proposed that proximal demonstratives ‘this’ in English and ‘I’ in Korean encode both pro-conceptual and prodcedural information which has a fundmantally pragmatic effect on interpretation as part of relevance-theoretic comprehension procedure. The procedural meaning encoded by proximal demonstratives intreucts the hearer to pay attention to the intended referent which is mist salient in the given context, while the pro-conceptual meaning of distance encoded by these demonstratives has to be contextually specified and directs the hearer`s attention to the intended referent which is located as proximal on the distance scale. When the information encoded in the proximal demonstratives is superfluous during the phase of referent assignment, the extra effort required to process this information is justified by yielding an adequate ranges of additional inferential effects. An important implication of this study is that it offers a unified account of the spatio-temporal, discourse-deictic, anaphoric, and emotional uses of proximal demonstratives in terms of the relevance-theoretic notion of pro-conceptual and procedural meanings.