Tense, Aspect and the Cognitive Representation of Time

This paper explores the relationshiDs between a computational meory of temporal representation (as developed by James Alien) and a Iormal linguiStiC theory Of tense (as developed by NorOert Hornstem) and aspect. It aims tO prowde exphcit answers to four lundamental Questions: (1) what ts the computational lustd~cat=on for me or=mmves of a hngu=stIc theory; (2) what ~s the computational explanation of the formal grammatical constraints; (3) what are the processing constraints ~ml3osed on the learnabdity and marKedness of these theoretical construCtS: and (4) what are the constramnts that a hnguist=c theory imposes or. representat¢ons. We show that one can effectively exploit (n~ ,nterface between the language faculty and the cognmve faculties by using hngu=stic constra,nts tO determine restrtcuons on tile cognitive representations and wce versa. Three mare results are cbtalned: (1) We derive an explanation of an oOserved grammabcal constrmnt on tense .. the Linear Order Constraint -from the re fo rmat ion mono ton ic i t y p roper t y of the constraint propagation algorithm of Allen's temPoral system: (2) We formulate a principle of mart~edness for the 13as=c tense structures Ioased on the computational efficiency of the temporal representations: and (3) We snow Allen's interval-Oased temporal System =s not arbitrary, bul it can be used to exolair, ;nctependently motwated lingulst~c constraints on tense and aspect interpretatmns. We also claim that the methodology of research developed in tins study -"cross-lever' investigation of independently motivated formal grammatical theory and computational moclets -. is a ¢owerful paradigm with which to attack representational problems =n oaslc cognitive domains, e.g.. space, t~me, c~u:~ality, etc. 1. Objectives and Main Results One malor effort m moclern hnguistlcs Is tO hmlt the class of possible grammars to those that are psychologically real. A grammar Is PSyChOlOgiCally/real if it ts (a) rea l izao le possessing a computational model that can reproduce certain psychological resource complexity measures, and (b) l ea rnab le . capable of Oemg acquired (at least, m principle) despite the poor quality of input linguistic data. A shift of eml3nasis from the pure characterization problem of grammar to the realization and leamability problems naturally bnnga linguistics closer tO AI work in na:ural language understanding Concerned wfth computational models of language use and language acquisit ion Computational study =Sm principle complementary tO more formal and aOstract grammatical theory. Each should contribute to the other. The purpose of this loader ~s to work Out an example of how formal grammatical meory and computational models can effectively constrain eacn diner s reoresematJons. In ~3artJcular, I seek to exolore four !undamental ~ssues: t. How ~s the cho=ce of onmmve structures m grammatical theory to be lustified? 2. What ~s the explanation of the rules and constramts that have to Oe stiI3ulated at the grammatical level? 3. HOw are these knowledge structures acau~red? 4. What are the theoretical constraints ~moosed by the grammar on the representational scheme of the computation theory? What I hope tO snow is that structures and prmcJoles that have to be sttoulatgG '~t the grammatical level fall out nalurally as consequences of the proDert=es of the algorithms and representations of the underlying comoutahonal model. In sO doing, I will also restnct the class of p lausmle computational models tO those that can exclam or incorporate the constraints =m;3osed by the formal grammatical theory. There are a numoer of requirements that must be met m order for such "cross.lever' study to succeed. First, there is a sizable collection of fzcts and data from the target domain to be explained. Second. there =s ,ndeDendent motwauon for the theory of grammar .. =t ~s empmca:ly adequate. And, third, the computational model =s also ,nrJeoendently motivated by ioemg sufhc=ently express=re and computatlonally efficient. With these considerations, I have chosen two domains: (1) tense and (2) aspect. Tense concerns the Chronological ordering Of situations with resnect tO some reference moment, usually the moment of s!3eech. Aspect =S the study of situation types and perspectives from which a particular situation can be viewed or evaluated (cf. Comrie75) The point of departure of this study is two papers: (1) for tl~e theory of tense, Hornstetn's "Towards a theory of Tense" (Homstem77) and (2) tor the cognitive theory of time. James Allen's "°Towarcls a General Theory ot Action and