Relationships between Specified and Underspecified Quantification by the Theory of Acyclic Recursion


The paper introduces a technique for representing quantifier relations that can have different scope order depending on context. The technique is demonstrated by classes of terms denoting relations, where each of the arguments of a relation term is bound by a different quantifier. We represent a formalization of linking quantifiers with the corresponding argument slots that they bind, across lambda-abstractions and reduction steps. The purpose of the technique is to represent underspecified order of quantification, in the absence of a context and corresponding information about the order. Furthermore, it is used to represent subclasses of larger classes of relations depending on order of quantification or specific relations.
  • Referencias
  • Cómo citar
  • Del mismo autor
  • Métricas
Copestake, A., Flickinger, D., Pollard, C., and Sag, I., 2005. Minimal recursion semantics: an introduction. Research on Language and Computation, 3:281–332. doi:DOI10.1007/s11168-006-6327-9.

CSLI LinGO, Oct 2016 (last accessed). CSLI Linguistic Grammars Online (LinGO) Lab at Stanford University.

DELPH-IN, Oct 2016 (last accessed). Deep Linguistic Processing with HPSG (DELPH-IN).

Gallin, D., 1975. Intensional and Higher-Order Modal Logic. North-Holland.
Loukanova, R., 2002. Generalized Quantification in Situation Semantics. In Gelbukh, A., editor, Computational Linguistics and Intelligent Text Processing, volume 2276 of Lecture Notes in Computer Science, pages 46–57. Springer Berlin / Heidelberg. ISBN 3-540-43219-1. doi:10.1007/3-540-45715-1_4.

Loukanova, R., 2011a. Semantics with the Language of Acyclic Recursion in Constraint-Based Grammar. In Bel-Enguix, G. and Jiménez-López, M. D., editors, Bio-Inspired Models for Natural and Formal Languages,
pages 103–134. Cambridge Scholars Publishing. ISBN (10): 1-4438-2725-8, (13): 978-1-4438-2725-6.

Loukanova, R., 2011b. Syntax-Semantics Interface for Lexical Inflection with the Language of Acyclic Recursion. In Bel-Enguix, G., Dahl, V., and Jiménez-López, M. D., editors, Biology, Computation and Linguistics — New Interdisciplinary Paradigms, volume 228 of Frontiers in Artificial Intelligence and Applications, pages 215–236. IOS Press, Amsterdam; Berlin; Tokyo; Washington, DC. ISBN 978-1-60750-761-1 (print), 978-1-60750-762-8 (online).

Loukanova, R., 2012. Semantic Information with Type Theory of Acyclic Recursion. In Huang, R., Ghorbani, A. A., Pasi, G., Yamaguchi, T., Yen, N. Y., and Jin, B., editors, Active Media Technology - 8th International Conference, AMT 2012, Macau, China, December 4-7, 2012. Proceedings, volume 7669 of Lecture Notes in Computer Science, pages 387–398. Springer. ISBN 978-3-642-35235-5.

Loukanova, R., 2013. Algorithmic Granularity with Constraints. In Imamura, K., Usui, S., Shirao, T., Kasamatsu, T., Schwabe, L., and Zhong, N., editors, Brain and Health Informatics, volume 8211 of Lecture Notes in Computer Science, pages 399–408. Springer International Publishing. ISBN 978-3-319-02752-4. doi: 10.1007/978-3-319-02753-1_40.

Loukanova, R., 2017. Reduction in Type Theory of Acyclic Recursion. (to appear).

Loukanova, R. and Jiménez-López, M. D., 2012. On the Syntax-Semantics Interface of Argument Marking Prepositional Phrases. In Pérez, J. B., Sánchez, M. A., Mathieu, P., Rodríguez, J. M. C., Adam, E., Ortega, A., Moreno, M. N., Navarro, E., Hirsch, B., Lopes-Cardoso, H., and Julián, V., editors, Highlights on Practical Applications of Agents and Multi-Agent Systems, volume 156 of Advances in Intelligent and Soft Computing, pages 53–60. Springer Berlin / Heidelberg. ISBN 978-3-642-28761-9.

Montague, R., 1973. The proper treatment of quantification in ordinary English. In Hintikka, J., Moravcsik, J., and Suppes, P., editors, Approaches to Natural Language, pages 221–242. D. Reidel Publishing Co., Dordrecht, Holland. Reprinted in (Thomason, 1974, pp. 247–270).

Montague, R., 1988. The proper treatment of quantification in ordinary English. In Philosophy, Language, and Artificial Intelligence, pages 141–162. Springer.

Moschovakis, Y. N., 1989. The formal language of recursion. The Journal of Symbolic Logic, 54(04):1216–1252.

Moschovakis, Y. N., 1997. The logic of functional recursion. In Logic and Scientific Methods, pages 179–207. Kluwer Academic Publishers. Springer.

Moschovakis, Y. N., 2006. A logical calculus of meaning and synonymy. Linguistics and Philosophy, 29:27–89.

Thomason, R. H., editor, 1974. Formal Philosophy: Selected Papers of Richard Montague. Yale University Press, New Haven, Connecticut.
Loukanova, R. (2016). Relationships between Specified and Underspecified Quantification by the Theory of Acyclic Recursion. ADCAIJ: Advances in Distributed Computing and Artificial Intelligence Journal, 5(4), 19–42.


Download data is not yet available.

Author Biography

Roussanka Loukanova

Stockholm University, Sweden
Department of Mathematics, Ph.D., Researcher