Acyclic Recursion with Polymorphic Types and Underpecification
Roussanka Loukanova
2016
Abstract
The paper extends Moschovakis higher-order type theory of acyclic recursion by adding type polymorphism. We extend the type system of the theory to model parametric information that pertains to underspecified types. Different kinds of type polymorphism are presented via type variables and recursion constructs for alternative, disjunctive type assignments. Based on the new type system, we extend the reduction calculus of the theory of acyclic recursion. We motivate the type polymorphism with examples from English language.
References
- Barwise, J. (1981). Scenes and other situations. The Journal of Philosophy, 78:369-397.
- Cardelli, L. and Wegner, P. (1985). On understanding types, data abstraction, and polymorphism. ACM Computing Surveys (CSUR), 17(4):471-523.
- Copestake, A., Flickinger, D., Pollard, C., and Sag, I. (2005). Minimal recursion semantics: an introduction. Research on Language and Computation, 3:281-332.
- Gallin, D. (1975). Intensional and Higher-Order Modal Logic. North-Holland.
- Hurkens, A. J. C., McArthur, M., Moschovakis, Y. N., Moss, L. S., and Whitney, G. T. (1998). The logic of recursive equations. The Journal of Symbolic Logic, 63(2):451-478.
- Loukanova, R. (2010). Computational syntax-semantics interface. In Bel-Enguix, G. and Jiménez-L ópez, M. D., editors, Language as a Complex System: Interdisciplinary Approaches, pages 111-150. Cambridge Scholars Publishing.
- Loukanova, R. (2011a). From Montague's Rules of Quantification to Minimal Recursion Semantics and the Language of Acyclic Recursion. In Bel-Enguix, G., Dahl, V., and Jiménez-L ópez, M. D., editors, Biology, Computation and Linguistics - New Interdisciplinary Paradigms, volume 228 of Frontiers in Artificial Intelligence and Applications, pages 200-214. IOS Press, Amsterdam; Berlin; Tokyo; Washington, DC.
- Loukanova, R. (2011b). Modeling Context Information for Computational Semantics with the Language of Acyclic Recursion. In Pérez, J. B., Corchado, J. M., Moreno, M., Julián, V., Mathieu, P., Canada-Bago, J., Ortega, A., and Fernández-Caballero, A., editors, Highlights in Practical Applications of Agents and Multiagent Systems, volume 89 of Advances in Intelligent and Soft Computing. Springer, pages 265-274. Springer.
- Loukanova, R. (2011c). Reference, Co-reference and Antecedent-anaphora in the Type Theory of Acyclic Recursion. In Bel-Enguix, G. and Jiménez-L ópez, M. D., editors, Bio-Inspired Models for Natural and Formal Languages, pages 81-102. Cambridge Scholars Publishing.
- Loukanova, R. (2011d). Semantics with the Language of Acyclic Recursion in Constraint-Based Grammar. In Bel-Enguix, G. and Jiménez-L ópez, M. D., editors, Bio-Inspired Models for Natural and Formal Languages, pages 103-134. Cambridge Scholars Publishing.
- Loukanova, R. (2011e). Syntax-Semantics Interface for Lexical Inflection with the Language of Acyclic Recursion. In Bel-Enguix, G., Dahl, V., and JiménezL ópez, 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.
- Loukanova, R. (2012a). Algorithmic Semantics of Ambiguous Modifiers by the Type Theory of Acyclic Recursion. IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology, 3:117-121.
- Loukanova, R. (2012b). 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.
- Loukanova, R. (2013a). 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.
- Loukanova, R. (2013b). Algorithmic Semantics for Processing Pronominal Verbal Phrases. In Larsen, H. L., Martin-Bautista, M. J., Vila, M. A., Andreasen, T., and Christiansen, H., editors, Flexible Query Answering Systems, volume 8132 of Lecture Notes in Computer Science, pages 164-175. Springer Berlin Heidelberg.
- Loukanova, R. (2013c). A Predicative Operator and Underspecification by the Type Theory of Acyclic Recursion. In Duchier, D. and Parmentier, Y., editors, Constraint Solving and Language Processing, volume 8114 of Lecture Notes in Computer Science, pages 108-132. Springer Berlin Heidelberg.
- Loukanova, R. (2016). Specification of underspecified quantifiers via question-answering by the theory of acyclic recursion. In Andreasen, T., Christiansen, H., Kacprzyk, J., Larsen, H., Pasi, G., Pivert, O., De Tré, G., Vila, M. A., Yazici, A., and Zadroz?ny, S., editors, Flexible Query Answering Systems 2015, volume 400 of Advances in Intelligent Systems and Computing, pages 57-69. Springer International Publishing.
- Moschovakis, Y. N. (1989). The formal language of recursion. The Journal of Symbolic Logic, 54(04):1216- 1252.
- Moschovakis, Y. N. (1994). Sense and denotation as algorithm and value. In Oikkonen, J. and Vaananen, J., editors, Lecture Notes in Logic, number 2 in Lecture Notes in Logic, pages 210-249. Springer.
- 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.
- Muskens, R. (1995). Meaning and Partiality. Studies in Logic, Language and Information. CSLI Publications, Stanford, California.
- Thomason, R. H., editor (1974). Formal Philosophy: Selected Papers of Richard Montague. Yale University Press, New Haven, Connecticut.
- Van Lambalgen, M. and Hamm, F. (2004). The Proper Treatment Of Events. Explorations in Semantics. Wiley-Blackwell, Oxford.
- Villadsen, J. (2010). Nabla: A Linguistic System based on Type Theory, volume 3 of Foundations of Communication and Cognition (New Series). LIT Verlag M ünster-Hamburg-Berlin-Wien-London.
Paper Citation
in Harvard Style
Loukanova R. (2016). Acyclic Recursion with Polymorphic Types and Underpecification . In Proceedings of the 8th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, ISBN 978-989-758-172-4, pages 392-399. DOI: 10.5220/0005749003920399
in Bibtex Style
@conference{icaart16,
author={Roussanka Loukanova},
title={Acyclic Recursion with Polymorphic Types and Underpecification},
booktitle={Proceedings of the 8th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},
year={2016},
pages={392-399},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005749003920399},
isbn={978-989-758-172-4},
}
in EndNote Style
TY - CONF
JO - Proceedings of the 8th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,
TI - Acyclic Recursion with Polymorphic Types and Underpecification
SN - 978-989-758-172-4
AU - Loukanova R.
PY - 2016
SP - 392
EP - 399
DO - 10.5220/0005749003920399