Abstract
The objective of this paper is to give formal semantics to aspects, independent of individual natural languages. Recent aspect theories explain that aspects are different ways of viewing the common event structure. However, the theories are still informal and not expressed in precise logical formalisms, and in addition, aspectual terms are different from one theory to another. We first survey those theories and give a united view to terms. Thereafter, we propose to adopt arrow logic for the representation of aspect, where we regard arrows as the fundamental temporal extent, instead of conventional time points or intervals. We show that the logic could tersely represent various aspects in regard to the relations between the event structure and its references. We also formalize the rules for aspectual shifts from temporally infinite forms to aspectual forms, in logical inferences. Therefore, we not only represent the static representation of aspects, but also show the dynamic processes from an event ontology to aspects.
