aspects, (2) in the definition of aspect operations, such as initiative, terminative, progressive, perfective, etc., and also (3) in the definition of adding time adverbials. This paper reviews the semantic problems with respect to aspect, and presents a consistent mechanism of aspect interpretation in order to settle all these semantic puzzles at once. For the sake of logical clarity, we construct a formal language, Lt, where every meaningful formula is a pair of a meaningful sentence and its aspect. The syntax of Lt describes the phenomenology of aspect shifts. The semantics of Lt defines temporal interpretation for all the meaningful sentences of Lt, with assuming the temporal interpretations of three inherent aspects, state, achievement, and activity. The proposed aspect interpretation gives a reasonable account for aspect shifts, and solves the imperfective paradox by asssuming the time structure to be backwards linear." />


A Study of Aspect Calculus

Kazuo HASHIMOTO  Tohru ASAMI  Seiichi YAMAMOTO  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E75-A   No.3   pp.436-450
Publication Date: 1992/03/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Foundations of Artificial Intelligence and Knowledge Processing
Keyword: 
aspect,  tense,  temporal logic,  formal semantics,  

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Summary: 
Since Vendler classified aspect into four categories, state, achievement, activity, and accomplishment, much effort has been made to define the notion of aspect logically. It is commonly agreed that aspect represents the general temporal characteristics of events and states. However, there still remains a considerable amount of disagreement about its formal treatment. One of the major problems is that the aspect of a sentence shifts by certain types of sentence construction. For instance, adding time adverbials to a sentence modifies the original aspect, taking the progressive form of the verb changes the aspect, and so on. These phenomena are known as the aspect shifts. The other is the problem known as the imperfective paradox. The imperfective paradox is a problem of the truth definition of the progressives. The truth condition of the progressive form of the sentence is defined at an internal subinterval of the temporal range of the corresponding non-progressive sentence. If the truth condition of the progressive form of the sentence is defined using the truth condition of the non-progressive form of the sentence, there are logical contradictions of truth definition in a sentence such as "Max was building a house, but he never built it". These problems cause much confusion (1) in the truth definition of aspects, (2) in the definition of aspect operations, such as initiative, terminative, progressive, perfective, etc., and also (3) in the definition of adding time adverbials. This paper reviews the semantic problems with respect to aspect, and presents a consistent mechanism of aspect interpretation in order to settle all these semantic puzzles at once. For the sake of logical clarity, we construct a formal language, Lt, where every meaningful formula is a pair of a meaningful sentence and its aspect. The syntax of Lt describes the phenomenology of aspect shifts. The semantics of Lt defines temporal interpretation for all the meaningful sentences of Lt, with assuming the temporal interpretations of three inherent aspects, state, achievement, and activity. The proposed aspect interpretation gives a reasonable account for aspect shifts, and solves the imperfective paradox by asssuming the time structure to be backwards linear.