Restricted Computations and Parameters in Type-Theory of Acyclic Recursion
Abstract The paper extends the formal language and the reduction calculus of Moschovakis type-theory of recursion, by adding a restrictor operator on terms with predicative restrictions. Terms with restrictions over memory variables formalise inductive algorithms with generalised, restricted parameters. The extended type-theory of restricted recursion (TTRR) provides computations for algorithmic semantics of mathematical expressions and definite descriptors, in formal and natural languages. The reduction calculi of TTRR provides a mathematical foundation of the work of compilers for reducing recursive programs to iterative ones. The type-theory of acyclic recursion (TTAR) has a special importance to syntax-semantics interfaces in computational grammars.
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Gallin, D., 1975. Intensional and Higher-Order Modal Logic: With Applications to Montague Semantics. North-Holland Publishing Company, Amsterdam and Oxford, and American Elsevier Publishing Company. ISBN 0 7204 0360 X.
Henkin, L., 1950. Completeness in the Theory of Types. Journal of Symbolic Logic, 15(2):81–91.
Loukanova, R., 1991. Situation Semantical Analysis of Natural Language. Ph.D. thesis, Faculty of Mechanics and Mathematics, Moscow State University (MGU), Moscow. (in Russian).
Loukanova, R., 2001. Russellian and Strawsonian Definite Descriptions in Situation Semantics. In Gelbukh, A., editor, Computational Linguistics and Intelligent Text Processing. CICLing 2001, volume 2004 of Lecture Notes in Computer Science, pages 69–79. Springer, Berlin, Heidelberg. ISBN 978-3-540-44686-6.
Loukanova, R., 2002. Quantification and Intensionality in Situation Semantics. In Gelbukh, A., editor, Computational Linguistics and Intelligent Text Processing. CICLing 2002, volume 2276 of Lecture Notes in Computer Science, pages 32–45. Springer, Berlin, Heidelberg. ISBN 978-3-540-45715-2.
Loukanova, R., 2011a. Reference, Co-reference and Antecedent-anaphora in the Type Theory of Acyclic Recursion. In Bel-Enguix, G. and Jiménez-López, M. D., editors, Bio-Inspired Models for Natural and Formal Languages, pages 81–102. Cambridge Scholars Publishing.
Loukanova, R., 2011b. 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.
Loukanova, R., 2011c. 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, 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.
Loukanova, R., 2012a. Algorithmic Semantics of Ambiguous Modifiers by the Type Theory of Acyclic Recursion. In Web Intelligence and Intelligent Agent Technology, IEEE/WIC/ACM International Conference, volume 3, pages 117–121. IEEE Computer Society, Los Alamitos, CA, USA.
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., 2014. Situation Theory, Situated Information, and Situated Agents. In Nguyen, N. T., Kowalczyk, R., Fred, A., and Joaquim, F., editors, Transactions on Computational Collective Intelligence XVII, volume 8790 of Lecture Notes in Computer Science, pages 145–170. Springer, Berlin, Heidelberg.
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. ISSN 2255-2863.
Loukanova, R., 2017. Typed Theory of Situated Information and its Application to Syntax-Semantics of Human Language. In Christiansen, H., Jiménez-López, M. D., Loukanova, R., and Moss, L. S., editors, Partiality and Underspecification in Information, Languages, and Knowledge, pages 151–188. Cambridge Scholars Publishing.
Loukanova, R., 2019a. Computational Syntax-Semantics Interface with Type-Theory of Acyclic Recursion for Underspecified Semantics. In Osswald, R., Retoré, C., and Sutton, P., editors, IWCS 2019 Workshop on Computing Semantics with Types, Frames and Related Structures. Proceedings of the Workshop, pages 37–48. The Association for Computational Linguistics (ACL), Gothenburg, Sweden.
Loukanova, R., 2019b. Gamma-Reduction in Type Theory of Acyclic Recursion. Fundamenta Informaticae, 170(4):367–411. ISSN 0169-2968 (P) 1875-8681 (E).
Loukanova, R., 2019c. Gamma-Star Canonical Forms in the Type-Theory of Acyclic Algorithms. In van den Herik, J. and Rocha, A. P., editors, Agents and Artificial Intelligence, pages 383–407. Springer International Publishing, Cham.
Loukanova, R., 2020a. Algorithmic Eta-Reduction in Type-Theory of Acyclic Recursion. In Rocha, A., Steels, L., and van den Herik, J., editors, Proceedings of the 12th International Conference on Agents and Artificial Intelligence (ICAART 2020), volume 2, pages 1003–1010. INSTICC, CITEPRESS – Science and Technology Publications, Lda. ISBN 978-989-758-395-7.
Loukanova, R., 2020b. Type-Theory of Acyclic Algorithms for Models of Consecutive Binding of Functional Neuro-Receptors. In Grabowski, A., Loukanova, R., and Schwarzweller, C., editors, AI Aspects in Reasoning, Languages, and Computation, volume 889, pages 1–48. Springer International Publishing, Cham. ISBN 978-3-030-41425-2.
Loukanova, R., 2021. Type-Theory of Parametric Algorithms with Restricted Computations. In Dong, Y., Herrera-Viedma, E., Matsui, K., Omatsu, S., González Briones, A., and Rodríguez González, S., editors, Distributed Computing and Artificial Intelligence, 17th International Conference, pages 321–331. Springer International Publishing, Cham. ISBN 978-3-030-53036-5.
Loukanova, R., to appear. Eta-Reduction in Type-Theory of Acyclic Recursion.
Ludlow, P., 2021. Descriptions. In Zalta, E. N., editor, The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University, Fall 2021 edition.
Moschovakis, Y. N., 1989. The formal language of recursion. Journal of Symbolic Logic, 54(4):1216–1252.
Moschovakis, Y. N., 1993. Sense and denotation as algorithm and value. In Oikkonen, J. and Väänänen, J., editors, Logic Colloquium ’90: ASL Summer Meeting in Helsinki, volume Volume 2 of Lecture Notes in Logic, pages 210–249. Springer-Verlag, Berlin.
Moschovakis, Y. N., 1997. The logic of functional recursion. In Dalla Chiara, M. L., Doets, K., Mundici, D., and van Benthem, J., editors, Logic and Scientific Methods, volume 259, pages 179–207. Springer, Dordrecht.
Moschovakis, Y. N., 2006. A Logical Calculus of Meaning and Synonymy. Linguistics and Philosophy, 29(1):27–89. ISSN 1573-0549.
Mostowski, A., 1957. On a generalization of quantifiers. Fundamenta Mathematicae, 1(44):12–36.
Russell, B., 1905. On Denoting. Mind, 14(56):479–493. ISSN 00264423, 14602113.
Strawson, P. F., 1950. On Referring. Mind, 59(235):320–344. ISSN 00264423, 14602113.
Thomason, R. H., editor, 1974. Formal Philosophy: Selected Papers of Richard Montague. Yale University Press, New Haven, Connecticut.
Henkin, L., 1950. Completeness in the Theory of Types. Journal of Symbolic Logic, 15(2):81–91.
Loukanova, R., 1991. Situation Semantical Analysis of Natural Language. Ph.D. thesis, Faculty of Mechanics and Mathematics, Moscow State University (MGU), Moscow. (in Russian).
Loukanova, R., 2001. Russellian and Strawsonian Definite Descriptions in Situation Semantics. In Gelbukh, A., editor, Computational Linguistics and Intelligent Text Processing. CICLing 2001, volume 2004 of Lecture Notes in Computer Science, pages 69–79. Springer, Berlin, Heidelberg. ISBN 978-3-540-44686-6.
Loukanova, R., 2002. Quantification and Intensionality in Situation Semantics. In Gelbukh, A., editor, Computational Linguistics and Intelligent Text Processing. CICLing 2002, volume 2276 of Lecture Notes in Computer Science, pages 32–45. Springer, Berlin, Heidelberg. ISBN 978-3-540-45715-2.
Loukanova, R., 2011a. Reference, Co-reference and Antecedent-anaphora in the Type Theory of Acyclic Recursion. In Bel-Enguix, G. and Jiménez-López, M. D., editors, Bio-Inspired Models for Natural and Formal Languages, pages 81–102. Cambridge Scholars Publishing.
Loukanova, R., 2011b. 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.
Loukanova, R., 2011c. 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, 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.
Loukanova, R., 2012a. Algorithmic Semantics of Ambiguous Modifiers by the Type Theory of Acyclic Recursion. In Web Intelligence and Intelligent Agent Technology, IEEE/WIC/ACM International Conference, volume 3, pages 117–121. IEEE Computer Society, Los Alamitos, CA, USA.
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., 2014. Situation Theory, Situated Information, and Situated Agents. In Nguyen, N. T., Kowalczyk, R., Fred, A., and Joaquim, F., editors, Transactions on Computational Collective Intelligence XVII, volume 8790 of Lecture Notes in Computer Science, pages 145–170. Springer, Berlin, Heidelberg.
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. ISSN 2255-2863.
Loukanova, R., 2017. Typed Theory of Situated Information and its Application to Syntax-Semantics of Human Language. In Christiansen, H., Jiménez-López, M. D., Loukanova, R., and Moss, L. S., editors, Partiality and Underspecification in Information, Languages, and Knowledge, pages 151–188. Cambridge Scholars Publishing.
Loukanova, R., 2019a. Computational Syntax-Semantics Interface with Type-Theory of Acyclic Recursion for Underspecified Semantics. In Osswald, R., Retoré, C., and Sutton, P., editors, IWCS 2019 Workshop on Computing Semantics with Types, Frames and Related Structures. Proceedings of the Workshop, pages 37–48. The Association for Computational Linguistics (ACL), Gothenburg, Sweden.
Loukanova, R., 2019b. Gamma-Reduction in Type Theory of Acyclic Recursion. Fundamenta Informaticae, 170(4):367–411. ISSN 0169-2968 (P) 1875-8681 (E).
Loukanova, R., 2019c. Gamma-Star Canonical Forms in the Type-Theory of Acyclic Algorithms. In van den Herik, J. and Rocha, A. P., editors, Agents and Artificial Intelligence, pages 383–407. Springer International Publishing, Cham.
Loukanova, R., 2020a. Algorithmic Eta-Reduction in Type-Theory of Acyclic Recursion. In Rocha, A., Steels, L., and van den Herik, J., editors, Proceedings of the 12th International Conference on Agents and Artificial Intelligence (ICAART 2020), volume 2, pages 1003–1010. INSTICC, CITEPRESS – Science and Technology Publications, Lda. ISBN 978-989-758-395-7.
Loukanova, R., 2020b. Type-Theory of Acyclic Algorithms for Models of Consecutive Binding of Functional Neuro-Receptors. In Grabowski, A., Loukanova, R., and Schwarzweller, C., editors, AI Aspects in Reasoning, Languages, and Computation, volume 889, pages 1–48. Springer International Publishing, Cham. ISBN 978-3-030-41425-2.
Loukanova, R., 2021. Type-Theory of Parametric Algorithms with Restricted Computations. In Dong, Y., Herrera-Viedma, E., Matsui, K., Omatsu, S., González Briones, A., and Rodríguez González, S., editors, Distributed Computing and Artificial Intelligence, 17th International Conference, pages 321–331. Springer International Publishing, Cham. ISBN 978-3-030-53036-5.
Loukanova, R., to appear. Eta-Reduction in Type-Theory of Acyclic Recursion.
Ludlow, P., 2021. Descriptions. In Zalta, E. N., editor, The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University, Fall 2021 edition.
Moschovakis, Y. N., 1989. The formal language of recursion. Journal of Symbolic Logic, 54(4):1216–1252.
Moschovakis, Y. N., 1993. Sense and denotation as algorithm and value. In Oikkonen, J. and Väänänen, J., editors, Logic Colloquium ’90: ASL Summer Meeting in Helsinki, volume Volume 2 of Lecture Notes in Logic, pages 210–249. Springer-Verlag, Berlin.
Moschovakis, Y. N., 1997. The logic of functional recursion. In Dalla Chiara, M. L., Doets, K., Mundici, D., and van Benthem, J., editors, Logic and Scientific Methods, volume 259, pages 179–207. Springer, Dordrecht.
Moschovakis, Y. N., 2006. A Logical Calculus of Meaning and Synonymy. Linguistics and Philosophy, 29(1):27–89. ISSN 1573-0549.
Mostowski, A., 1957. On a generalization of quantifiers. Fundamenta Mathematicae, 1(44):12–36.
Russell, B., 1905. On Denoting. Mind, 14(56):479–493. ISSN 00264423, 14602113.
Strawson, P. F., 1950. On Referring. Mind, 59(235):320–344. ISSN 00264423, 14602113.
Thomason, R. H., editor, 1974. Formal Philosophy: Selected Papers of Richard Montague. Yale University Press, New Haven, Connecticut.
Loukanova, R. (2023). Restricted Computations and Parameters in Type-Theory of Acyclic Recursion. ADCAIJ: Advances in Distributed Computing and Artificial Intelligence Journal, 12(1), e29081. https://doi.org/10.14201/adcaij.29081
Most read articles by the same author(s)
- Roussanka Loukanova, Relationships between Specified and Underspecified Quantification by the Theory of Acyclic Recursion , ADCAIJ: Advances in Distributed Computing and Artificial Intelligence Journal: Vol. 5 No. 4 (2016)
- Roussanka Loukanova, Eta-Reduction in Type-Theory of Acyclic Recursion , ADCAIJ: Advances in Distributed Computing and Artificial Intelligence Journal: Vol. 12 (2023)
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