Minds and Machines

, Volume 9, Issue 1, pp 81–103 | Cite as

Event, State, And Process In Arrow Logic

  • Satoshi Tojo


Artificial agents, which are embedded in a virtual world, need to interpret a sequence of commands given to them adequately, considering the temporal structure for each command. In this paper, we start with the semantics of natural language and classify the temporal structures of various eventualities into such aspectual classes as action, process, and event. In order to formalize these temporal structures, we adopt Arrow Logic. This logic specifies the domain for the valuation of a sentence as an arrow. We can connect, or give order to, arrows by defining inter-arrow operations, and can give different views for sentences. Thereafter we formalize the rules of aspectual shifts in situated inference, in the style of a logic programming language. Thus, we not only describe the static representation of temporal features, but also show the dynamic process to deduce how each eventuality is viewed. The rules are applied to the information flow through the sequence of commands; therefore, we consider how the temporal structure of a command affects the succeeding commands.

Aspect Arrow Logic Situated Inference 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Allen, J. F. 1984, Towards a general theory of action and time. Artificial Intelligence, 23: 123–154.Google Scholar
  2. Barwise, J. 1991, The Situation in Logic. CSLI Lecture Notes 17.Google Scholar
  3. Binnick, R. I. 1991, Time and the Verb. Oxford University Press, 1991.Google Scholar
  4. Blackburn, P. Gardent, C. and de Rijke, M. 1996, On rich ontologies on tense and aspect. In J. Seligman and D. Westerstahl, ed., Logic, Language, and Computation, vol. 1. CSLI, Stanford UniversityGoogle Scholar
  5. Comrie, B. 1976, Aspect. Cambridge University Press.Google Scholar
  6. Cooper, R. 1985, Aspectual classes in situation semantics. Technical Report CSLI–84–14C, Center for the Study of Language and Information.Google Scholar
  7. Cooper, R. Tense and discourse location in situation semantics. Linguistics and Philosophy, 9(1): 17–36, February 1986.Google Scholar
  8. Devlin, K. 1991, Logic and Information. Cambridge University Press.Google Scholar
  9. Dowty, D. 1979, Word Meaning and Montague Grammar. D. Reidel.Google Scholar
  10. Glasbey, S. 1996, Towards a channel-theoretic account of the progressive. In J. Seligman and D. Westerstahl, (eds), Logic, Language, and Computation, vol. 1. CSLI, Stanford University.Google Scholar
  11. Gunji, T. 1992, A Proto-Lexical Analysis of Temporal Properties of Japanese Verbs. In B. S. Park, (ed.), Linguistics Studies on Natural Language, pages 197–217. Hanshin Publishing, December.Google Scholar
  12. Kamp, H. 1979, Events, Instants, and Temporal References, pages 376–417. SpringerVerlag. in Semantics from Different Points of View.Google Scholar
  13. Kamp, H. and Reyle, U. 1993, From Discourse to Logic. Kluwer Academic Publisher's.Google Scholar
  14. Landman, F. 1991, Structures for Semantics. Kluwer Academic Press.Google Scholar
  15. McDermott, D.V. 1982), A temporal logic for reasoning about processes and plans. Cognitive Science, 6: 101–155.Google Scholar
  16. Moens, M. and Steedman, M. 1988, Temporal ontology and temporal reference. Computational Linguistics, 14(2): 15–28.Google Scholar
  17. Parsons, T. 1990, Events in the Semantics of English. MIT press.Google Scholar
  18. Partee, B. H. 1984, Nominal and temporal anaphora. Linguistics and Philosophy, 7: 243–286.CrossRefGoogle Scholar
  19. Reichenbach, H. 1947, Elements of Symbolic Logic. University of California Press, Berkeley.Google Scholar
  20. Shoham, Y. 1988, Reasoning about Change. The MIT Press.Google Scholar
  21. ter Meulen, A. G. B. 1995, Representing Time in Natural Language. The MIT Press, Cambridge, MA.Google Scholar
  22. Terenziani, P. 1993, Integrating linguistic and pragmatic temporal information innatural language understanding: the case of when sentences. In Proc. of 13th International Joint Conference on Artificial Intelligence, vol. 2, pages 1304–1309.Google Scholar
  23. Tojo, S. and Nitta, K. 1997, Similarity of legal cases: From temporal relations of affairs. Artificial Intelligence and Law, 5: 161–176.Google Scholar
  24. Tojo, S. and Wong, S. 1996, A legal reasoning system based on situation theory. In J. Seligman and D. Westerstahl, editors, Logic, Language, and Computation, vol. 1. CSLI, Stanford University.Google Scholar
  25. van Benthem, J. 1994, A Note on Dynamic Arrow Logic, pages 15–29. The MIT Press.Google Scholar
  26. Vendler, Z. 1967, Verbs and times. Philosophical Review, 66: 143–60.Google Scholar
  27. Yokota, K., Tsuda, H., Morita, Y., Tojo, S. and Yasukawa, H. 1993, Specific features of a deductive object-oriented database language Quixote. In Proc. of the work-shop on combining declarative and object-oriented databases, ACM SIGMOD, Washington, D.C. Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Satoshi Tojo
    • 1
  1. 1.Japan Advanced Institute of Science and TechnologyTatsunokuchi, IshikawaJapan e-mail

Personalised recommendations