Linguistics and Philosophy

, Volume 38, Issue 6, pp 521–576 | Cite as

Against ellipsis: arguments for the direct licensing of ‘noncanonical’ coordinations

  • Yusuke KubotaEmail author
  • Robert Levine
Research Article


Categorial grammar is well-known for its elegant analysis of coordination enabled by the flexible notion of constituency it entertains. However, to date, no systematic study exists that examines whether this analysis has any obvious empirical advantage over alternative analyses of nonconstituent coordination available in phrase structure-based theories of syntax. This paper attempts precisely such a comparison. We compare the direct constituent coordination analysis of non-canonical coordinations (right-node raising, dependent cluster coordination and Gapping) in categorial grammar with an ellipsis-based analysis of the same phenomena in the recent HPSG literature. We provide a set of empirical evidence, consisting of cases in which non-canonical coordinations interact with scopal operators of various sorts, which systematically falsifies the predictions of the latter, ‘linearization-based’ ellipsis approach to coordination. We propose an alternative analysis in a variant of categorial grammar called Hybrid Type-Logical Categorial Grammar. The proposed framework builds on both the Lambek-inspired variants of categorial grammar and a more recent line of work modelling word order via a lambda calculus for the prosodic component. The flexible syntax–semantics interface of this framework straightforwardly captures the interactions between non-canonical coordinations and scopal expressions, demonstrating the broader empirical payoff of the direct constituent coordination analysis of non-canonical coordinations pioneered by Steedman (Language 61(3):523–568, 1985; Linguist Philos 13(2):207–263, 1990) and Dowty (Categorial grammars and natural language structures, 1988) hitherto not explicitly recognized in the literature.


Coordination Nonconstituent coordination Scope Categorial grammar Hybrid Type-Logical Categorial Grammar 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abbott, B. (1976). Right node raising as a test for constituenthood. Linguistic Inquiry, 7, 639–642.Google Scholar
  2. Abeillé, A., Bîlbîie, G., & Mouret, F. (2014). A Romance perspective on Gapping constructions. In H. Boas & F. G. García (Eds.), Romance in Construction Grammar (pp. 227–265). Amsterdam: John Benjamins.Google Scholar
  3. Ades, A. F., & Steedman, M. J. (1982). On the order of words. Linguistics and Philosophy, 4(4), 517–558.Google Scholar
  4. Ajdukiewicz, K. (1935). Die syntaktische Konnexität. In S. McCall (Ed.), Polish Logic 1920–1939 (pp. 207–231).Oxford: OUP (Translated from Studia Philosophica, 1, 1–27.)Google Scholar
  5. Baldridge, J. (2002). Lexically specified derivational control in combinatory categorial grammar. Ph.D. Thesis, University of Edinburgh.Google Scholar
  6. Bar-Hillel, Y. (1953). A quasi-arithmetic notation for syntactic descriptions. Language, 29, 47–58.Google Scholar
  7. Barker, C. (2007). Parasitic scope. Linguistics and Philosophy, 30, 407–444.Google Scholar
  8. Barker, C., & Shan, C. (2015). Continuations and natural language. Oxford: OUP.Google Scholar
  9. Beavers, J., & Sag, I. A. (2004). Coordinate ellipsis and apparent non-constituent coordination. In S. Müller (Ed.), The Proceedings of the 11th International Conference on Head-driven phrase Structure Grammar (pp. 48–69). Stanford: CSLI.Google Scholar
  10. Bekki, D. (2006). Heikooteki-kaishaku-niokeru yoosokan-junjo-to bunmyaku-izon-sei (The order of elements and context dependence in the ‘respective’ interpretation). In Nihon Gengo-Gakkai Dai 132-kai Taikai Yokooshuu (Proceedings from the 132nd Meeting of the Linguistic Society of Japan) (pp. 47–52).Google Scholar
  11. Carlson, G. N. (1987). Same and different: Some consequences for syntax and semantics. Linguistics and Philosophy, 10(4), 531–565.Google Scholar
  12. Carpenter, B. (1997). Type-logical semantics. Cambridge, MA: MIT Press.Google Scholar
  13. Chaves, R. P. (2005). A linearization-based approach to gapping. In G. Jäger, P. Monachesi, G. Penn, & S. Wintner (Eds.), FG-MOL 2005: The 10th Conference on formal Grammar and the 9th Meeting on Mathematics of Language (pp. 207–220). Edinburgh: University of edinburgh.Google Scholar
  14. Chaves, R. P. (2007). Coordinate structures—constraint-based syntax-semantics processing. Ph.D. Thesis, University of Lisbon.Google Scholar
  15. Chaves, R. P. (2008). Linearization-based word-part ellipsis. Linguistics and Philosophy, 31(3), 261–307.Google Scholar
  16. Chaves, R. P. (2012). Conjunction, cumulation and respectively readings. Journal of Linguistics, 48(2), 297–344.Google Scholar
  17. Cipollone, D. (2001). Morphologically complex predicates in Japanese and what they tell us about grammar architecture. In M. W. Daniels, D. Dowty, A. Feldman, & V. Metcalf (Eds.), Ohio State University working papers in linguistics (pp. 1–52). Columbus, OH: Department of Linguistics, The Ohio State University.Google Scholar
  18. Copestake, A., Flickinger, D., Pollard, C., & Sag, I. A. (2005). Minimal recursion semantics: An introduction. Research on Language and Computation, 4(3), 281–332.Google Scholar
  19. Crysmann, B. (2003). An asymmetric theory of peripheral sharing in HPSG: Conjunction reduction and coordination of unlikes. In G. Jäger, P. Monachesi, G. Penn, & S. Wintner (Eds.), Proceedings of Formal Grammar 2003 (pp. 47–62).
  20. Culicover, P. W., & Jackendoff, R. (2005). Simpler syntax. Oxford: OUP.Google Scholar
  21. Curry, H. B. (1961). Some logical aspects of grammatical structure. In R. Jakobson (Ed.), Structure of language and its mathematical aspects (Vol. 12, pp. 56–68)., Symposia on applied mathematics Providence: American Mathematical Society.Google Scholar
  22. Dalrymple, M., Kanazawa, M., Kim, Y., Mchombo, S., & Peters, Stanley. (1998). Reciprocal expressions and the concept of reciprocity. Linguistics and Philosophy, 21(2), 159–210.Google Scholar
  23. de Groote, P. (2001). Towards abstract categorial grammars. In Association for Computational Linguistics, 39th Annual Meeting and 10th onference of the European Chapter (pp. 148–155).Google Scholar
  24. Deane, P. (1991). Limits to attention: A cognitive theory of island phenomena. Cognitive Linguistics, 2(1), 1–63.Google Scholar
  25. Dowty, D. (1988). Type raising, functional composition, and non-constituent conjunction. In R. T. Oehrle, E. Bach, & D. Wheeler (Eds.), Categorial grammars and natural language structures, 153–197. Dordrecht: D. Reidel Publishing Company.Google Scholar
  26. Dowty, D. (1996a). Non-constituent coordination, wrapping, and multimodal categorial grammars. In M. L. D. Chiara, K. Doets, D. Mundici, & J. van Benthem (Eds.), Structures and norms in science: Tenth international congress of logic, methodology and philosophy of science, Florence, August 1995 (pp. 347–368). Dordrecht: Kluwer.Google Scholar
  27. Dowty, D. R. (1996b). Toward a minimalist theory of syntactic structure. In H. Bunt & A. van Horck (Eds.), Discontinuous constituency, Vol. 6 of Natural Language Processing (pp. 11–62). Berlin: Mouton de Gruyter.Google Scholar
  28. Dowty, D. (2007). Compositionality as an empirical problem. In C. Barker & P. Jacobson (Eds.), Direct compositionality (pp. 23–101). Oxford: OUP.Google Scholar
  29. Fodor, J. D. (1978). Parsing strategies and constraints on transformations. Linguistic Inquiry, 9(3), 427–473.Google Scholar
  30. Fodor, J. D. (1983). Phrase structure parsing and the island constraints. Linguistics and Philosophy, 6, 163–223.Google Scholar
  31. Gawron, J. M., & Kehler, A. (2004). The semantics of respective readings, conjunction, and filler-gap dependencies. Linguistics and Philosophy, 27(2), 169–207.Google Scholar
  32. Gleitman, L. (1965). Coordination conjunctions in English. Language, 41, 260–293.Google Scholar
  33. Goldberg, A. E. (1995). Constructions: A construction grammar approach to argument structure. Chicago: University of Chicago Press.Google Scholar
  34. Hendriks, H. (1993). Studied flexibility. Ph.D. Thesis, University of Amsterdam.Google Scholar
  35. Hendriks, P. (1995). Ellipsis and multimodal categorial type logic. In G. V. Morrill & R. T. Oehrle (Eds.), Formal Grammar: Proceedings of the Conference of the European Summer School in Logic, Language and Information (pp. 107–122). Barcelona.Google Scholar
  36. Hepple, M. (1997). Maximal incrementality in linear categorial deduction. In 35th Annual Meeting of the Association for Computational Linguistics (ACL) (pp. 344–351).Google Scholar
  37. Hofmeister, P. (2010). A linearization account of either..r constructions. Natural Language and Linguistic Theory, 28, 275–314.Google Scholar
  38. Hofmeister, P., Casasanto, L. S., & Sag, I. (2012a). How do individual cognitive differences relate to acceptability judgments?: A reply to Sprouse, Wagers, & Phillips. Language, 88, 390–400.Google Scholar
  39. Hofmeister, P., Casasanto, L. S., & Sag, I. (2012b). Misapplying working memory tests: A reductio ad absurdum. Language, 88, 408–409.Google Scholar
  40. Hofmeister, P., & Sag, I. A. (2010). Cognitive constraints and island effects. Language, 86(2), 366–415.Google Scholar
  41. Jackendoff, R. (1977). X-bar syntax: A study of phrase structure. Cambridge, MA: MIT Press.Google Scholar
  42. Jackendoff, R. S. (1971). Gapping and related rules. Linguistic Inquiry, 2(1), 21–35.Google Scholar
  43. Jäger, G. (2005). Anaphora and Type-Logical Grammar. Berlin: Springer.Google Scholar
  44. Jayaseelan, K. A. (1990). Incomplete VP deletion and Gapping. Linguistic Analysis, 20(1–2), 64–81.Google Scholar
  45. Johnson, K. (2000). Few dogs eat Whiskers or cats Alpo. In K. Kusumoto & E. Villalta (Eds.), University of Massachusetts occasional papers (Vol. 23, pp. 47–60). Amherst, MA: GLSA Publications.Google Scholar
  46. Kathol, A. (1995). Linearization-based German syntax. Ph.D. Thesis, Ohio State University.Google Scholar
  47. Keenan, E. L. (1992). Beyond the Frege boundary. Linguistics and Philosophy, 15(2), 199–221.Google Scholar
  48. Kehler, A. (2002). Coherence, reference and the theory of grammar. Stanford, CA: CSLI Publications.Google Scholar
  49. Kluender, R. (1992). Deriving island constraints from principles of predication. In H. Goodluck & M. Rochemont (Eds.), Island constraints: Theory, acquisition, and processing (pp. 223–258). Dordrecht: Kluwer.Google Scholar
  50. Kluender, R. (1998). On the distinction between strong and weak islands: A processing perspective. In P. Culicover & L. McNally (Eds.), The limits of syntax Vol. 29 of Syntax and semantics. San Diego: Academic Press.Google Scholar
  51. Kubota, Y. (2007). The scope interpretation of complex predicates in Japanese: A unified lexicalist analysis. Journal of Linguistics, 43(3), 489–530.Google Scholar
  52. Kubota, Y. (2008). Solving the morpho-syntactic puzzle of the Japanese -te form complex predicate: A multi-modal combinatory categorial grammar analysis. In O. Bonami & P. C. Hofherr (Eds.), Empirical issues in syntax and semantics (Vol. 7, pp. 283–306). Paris: Presses de l’Université Paris.Google Scholar
  53. Kubota, Y. (2010). (In)flexibility of constituency in Japanese in Multi-modal Categorial Grammar with Structured Phonology. Ph.D. Thesis, Ohio State University.Google Scholar
  54. Kubota, Y. (2014). The logic of complex predicates: A deductive synthesis of ‘argument sharing’ and ‘verb raising’. Natural Language and Linguistic Theory, 32(4), 1145–1204.Google Scholar
  55. Kubota, Y. (2015). Nonconstituent coordination in Japanese as constituent coordination: An analysis in Hybrid Type-Logical Categorial Grammar. Linguistic Inquiry, 46(1), 1–42.Google Scholar
  56. Kubota, Y., & Levine, R. (2012). Gapping as like-category coordination. In D. Béchet & A. Dikovsky (Eds.), Logical aspects of computational linguistics 2012 (pp. 135–150). Heidelberg: Springer.Google Scholar
  57. Kubota, Y., & Levine, R. (2013a). Coordination in Hybrid Type-Logical Categorial Grammar. In OSU working papers in linguistics (Vol. 60, pp. 21–50). Columbus, OH: Department of Linguistics, Ohio State University.Google Scholar
  58. Kubota, Y., & Levine, R. (2013b). Determiner gapping as higher-order discontinuous constituency. In G. Morrill & M.-J. Nederhof (Eds.), Proceedings of Formal Grammar 2012 and 2013 (pp. 225–241). Heidelberg: Springer.Google Scholar
  59. Kubota, Y., & Levine, R. (2014a). Scope anomaly of Gapping. In Proceedings of NELS 44 (pp. 247–260). Amherst: GLSA.Google Scholar
  60. Kubota, Y., & Levine, R. (2014b). Gapping as hypothetical reasoning. Natural Language and Linguistic Theory. (in press).
  61. Kubota, Y., & Levine, R. (2014c). Pseudogapping as pseudo-VP ellipsis. In N. Asher & S. Soloviev (Eds.), Logical aspects of computational linguistics 2014 (pp. 122–137). Heidelberg: Springer.Google Scholar
  62. Kubota, Y., & Levine, R. (2014d). The syntax–semantics interface of ‘respective’ predication: A unified analysis in Hybrid Type-Logical Categorial Grammar. Natural Language and Linguistic Theory, ms., University of Tsukuba and Ohio State University. (Accepted).
  63. Kubota, Y., & Levine, R. (2014e). Unifying local and nonlocal modelling of respective and symmetrical predicates. In G. Morrill, R. Muskens, R. Osswald, & F. Richter (Eds.), Proceedings of Formal Grammar 2014 (pp. 104–120). Heidelberg: Springer.Google Scholar
  64. Kubota, Y., & Smith, E. A. (2006). Syntax and semantics of Japanese nonconstituent clefting in Combinatory Categorial Grammar. In C. Davis, A. R. Deal, & Y. Zabbal (Eds.), Proceedings of the Thirty-Sixth Annual Meeting of the North East Linguistic Society (pp. 413–426). Amherst, MA: GLSA Publications.Google Scholar
  65. Lambek, J. (1958). The mathematics of sentence structure. American Mathematical Monthly, 65, 154– 170.Google Scholar
  66. Lasnik, H. (1999). Pseudogapping puzzles. In S. Lappin & E. Benmamoun (Eds.), Fragments: Studies in ellipsis and Gapping (pp. 141–174). Oxford: OUP.Google Scholar
  67. Levine, R. (2011). Linerarization and its discontents. In S. Müller (Ed.), The proceedings of the 18th International Conference on Head-driven Phrase Structure Grammar (pp. 126–146). Stanford: CSLI Publications.Google Scholar
  68. Maxwell, J. T., & Manning, C. D. (1996). A theory of non-constituent coordination based on finite-state rules. In M. Butt & T. H. King (Eds.), Proceedings of the LFG ’96 Conference. Stanford: CSLI.
  69. May, R. (1985). Logical form: Its structure and derivation. Cambridge, MA: MIT Press.Google Scholar
  70. McCawley, J. D. (1993). Gapping with shared operators. In D. A. Peterson (Ed.), Berkeley Linguistics Society (pp. 245–253). Berkeley, CA: University of California.Google Scholar
  71. Mihaliček, V. (2012). Serbo-Croatian word order: A logical approach. Ph.D. Thesis, Ohio State University.Google Scholar
  72. Mihaliček, V., & Pollard, C. (2012). Distinguishing phenogrammar from tectogrammar simplifies the analysis of interrogatives. In P. de Groote & M.-J. Nederhof (Eds.), Formal Grammar 2010(2011) (pp. 130–145). Heidelberg: Springer.Google Scholar
  73. Montague, R. (1973). The proper treatment of quantification in ordinary English. In J. Hintikka, J. M. Moravcsik, & P. Suppes (Eds.), Approaches to natural language: Proceedings of the 1970 Stanford Workshop on grammar and semantics (pp. 221–242). Dordrecht: D. Reidel.Google Scholar
  74. Moortgat, M. (1988). Categorial investigations: Logical and linguistic aspects of the Lambek Calculus. Dordrecht: Foris.Google Scholar
  75. Moortgat, M. (1997). Categorial type logics. In J. van Benthem & A. ter Meulen (Eds.), Handbook of Logic and Language (pp. 93–177). Amsterdam: Elsevier.Google Scholar
  76. Moortgat, M., & Oehrle, R. T. (1994). Adjacency, dependence, and order. In P. Dekker & M. Stokhof (Eds.), Proceedings of the Ninth Amsterdam Colloquium, 447–466 (pp. 447–466). Amsterdam: Instituut voor Taal, Logica, en Informatica, Universiteit van Amsterdam.Google Scholar
  77. Moot, R. (2014). Hybrid type-logical grammars, first-order linear logic and the descriptive inadequacy of Lambda grammars. Ms., Laboratoire Bordelais de Recherche en Informatique.Google Scholar
  78. Morrill, G. (1994). Type logical grammar: Categorial logic of signs. Dordrecht: Kluwer.Google Scholar
  79. Morrill, G., Valentín, O., & Fadda, M. (2011). The displacement calculus. Journal of Logic, Language and Information, 20, 1–48.Google Scholar
  80. Mouret, F. (2006). A phrase structure approach to argument cluster coordination. In S. Müller (Ed.), The proceedings of the 13th International Conference on Head-driven Phrase Structure Grammar (pp. 247–267). Stanford: CSLI Publications.Google Scholar
  81. Muskens, R. (2001). Categorial grammar and lexical-functional grammar. In M. Butt & T. H. King (Eds.), The proceedings of the LFG ’01 Conference. Hong Kong: University of Hong Kong.Google Scholar
  82. Muskens, R. (2003). Language, lambdas, and logic. In G.-J. Kruijff & R. Oehrle (Eds.), Resource sensitivity in binding and anaphora (pp. 23–54). Dordrecht: Kluwer.Google Scholar
  83. Muskens, R. (2007). Separating syntax and combinatorics in categorial grammar. Research on Language and Computation, 5(3), 267–285.Google Scholar
  84. Oehrle, R. T. (1971). On Gapping. ms., MIT.Google Scholar
  85. Oehrle, R. T. (1987). Boolean properties in the analysis of gapping. In G. J. Huck & A. E. Ojeda (Eds.), Syntax and semantics: Discontinuous constituency (pp. 203–220). San Diego, CA: Academic Press.Google Scholar
  86. Oehrle, R. T. (1994). Term-labeled categorial type systems. Linguistics and Philosophy, 17(6), 633–678.Google Scholar
  87. Oehrle, R. T. (2011). Multi-modal type-logical grammar. In R. D. Borsley & K. Börjars (Eds.), Non-transformational syntax (pp. 225–267). Oxford: Wiley-Blackwell.Google Scholar
  88. Partee, B., & Rooth, M. (1983). Generalized conjunction and type ambiguity. In R. Bäuerle, C. Schwarze, & A. von Stechow (Eds.), Meaning, use, and interpretation of language (pp. 361–383). Berlin: Walter de Gruyter.Google Scholar
  89. Partee, B. H. (1970). Negation, conjunction, and quantifiers: Syntax vs. semantics. Foundations of Language, 6, 153–165.Google Scholar
  90. Pogodalla, S., & Pompigne, F. (2012). Controlling extraction in Abstract Categorial Grammars. In P. de Groote & M.-J. Nederhof (Eds.), Formal Grammar 2010(2011) (pp. 162–177). Heidelberg: Springer.Google Scholar
  91. Pollard, C. (2013). Linear categorial grammar. MS., Lecture notes at ESSLLI 2013.Google Scholar
  92. Pollard, C. (2014, March 6). What numerical determiners mean: A non-ambiguity analysis. Talk presented at the Workshop on Semantics of Cardinals, Ohio State University.Google Scholar
  93. Pollard, C., & Smith, E. A. (2012). A unified analysis of the same, phrasal comparatives and superlatives. In Proceedings of SALT 2012 (pp. 307–325).Google Scholar
  94. Pollard, C. J., & Sag, I. A. (1994). Head-driven Phrase Structure Grammar. Chicago: University of Chicago Press.Google Scholar
  95. Pullum, G., & Gazdar, G. (1982). Natural languages and context-free languages. Linguistics and Philosophy, 4(4), 471–504.Google Scholar
  96. Reape, M. (1996). Getting things in order. In H. Bunt & A. van Horck (Eds.), Discontinuous constituency, Vol. 6 of Natural language processing (p. 209). Berlin: Mouton de Gruyter.Google Scholar
  97. Rodman, R. (1976). Scope phenomena, “movement transformations”, and relative clauses. In B. Partee (Ed.), Montague grammar. New York: Academic Press.Google Scholar
  98. Ruys, E., & Winter, Y. (2010). Quantifier scope in formal linguistics. In D. Gabbay & F. Guenthner (Eds.), Handbook of philosophical logic (Vol. 16, pp. 159–225). Amsterdam: John Benjamins.Google Scholar
  99. Sag, I. A. (1997). English relative clause constructions. Journal of Linguistics, 33(2), 431–484.Google Scholar
  100. Sag, I. A. (2012). Sign-based Construction Grammar: An informal synopsis. In H. C. Boas & I. A. Sag (Eds.), Sign-based Construction Grammar (pp. 1–51). Stanford: CSLI Publications.Google Scholar
  101. Sag, I. A., Gazdar, G., Wasow, T., & Weisler, S. (1985). Coordination and how to distinguish categories. Natural Language and Linguistic Theory, 3(2), 117–171.Google Scholar
  102. Schmitt, V. (2013). More pluralities. Ph.D. Thesis, Universität Wien.Google Scholar
  103. Siegel, M. E. A. (1984). Gapping and interpretation. Linguistic Inquiry, 15(3), 523–530.Google Scholar
  104. Steedman, M. (1985). Dependency and coordination in the grammar of Dutch and English. Language, 61(3), 523–568.Google Scholar
  105. Steedman, M. (1987). Combinatory grammars and parasitic gaps. Natural Language and Linguistic Theory, 5(3), 403–439.Google Scholar
  106. Steedman, M. (1990). Gapping as constituent coordination. Linguistics and Philosophy, 13(2), 207–263.Google Scholar
  107. Steedman, M. (1996). Surface structure and interpretation. Cambridge, MA: MIT Press.Google Scholar
  108. Steedman, M. (2000). The syntactic process. Cambridge, MA: MIT Press.Google Scholar
  109. Steedman, M. (2012). Taking scope. Cambridge, MA: MIT Press.Google Scholar
  110. Szabolcsi, A. (2010). Quantification. Cambridge: CUP.Google Scholar
  111. Szabolcsi, A., & Haddican, B. (2004). Conjunction meets negation: A study in cross-linguistic variation. Journal of Semantics, 21(3), 219–249.Google Scholar
  112. Winter, Y. (1995). Syncategorematic conjunction and structured meanings. In M. Simons & T. Galloway (Eds.), Proceedings of SALT 5 (pp. 387–404). Ithaca, NY: CLC Publications.Google Scholar
  113. Winter, Y. (2001). Flexibility principles in Boolean semantics. Cambridge, MA: MIT Press.Google Scholar
  114. Worth, C. (2014). The phenogrammar of coordination. In Proceedings of the EACL 2014 workshop on type theory and natural language semantics (TTNLS) (pp. 28–36). Gothenburg: Association for Computational Linguistics.Google Scholar
  115. Yatabe, S. (2001). The syntax and semantics of left-node raising in Japanese. In D. Flickinger & A. Kathol (Eds.), Proceedings of the 7th International Conference on Head-driven Phrase Structure Grammar (pp. 325–344). Stanford: CSLI.
  116. Yatabe, S. (2012). Comparison of the ellipsis-based theory of non-constituent coordination with its alternatives. In S. Müller (Ed.), Proceedings of the 19th International Conference on Head-driven Phrase Structure Grammar (pp. 453–473).Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.University of TsukubaTsukubaJapan
  2. 2.Department of LinguisticsOhio State UniversityColumbusUSA

Personalised recommendations