The Search for Minimal Search: A Graph-Theoretic Approach
This paper examines Minimal Search, an operation that is at the core of current Minimalist inquiry. We argue that, given Minimalist assumptions about structure building consisting of unordered set-formation, there are serious difficulties in defining Minimal Search as a search algorithm. Furthermore...
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| Format: | Article |
| Language: | English |
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PsychOpen GOLD/ Leibniz Institute for Psychology
2023-03-01
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| Series: | Biolinguistics |
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| Online Access: | https://doi.org/10.5964/bioling.9793 |
| _version_ | 1797338169709953024 |
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| author | Diego Gabriel Krivochen |
| author_facet | Diego Gabriel Krivochen |
| author_sort | Diego Gabriel Krivochen |
| collection | DOAJ |
| description | This paper examines Minimal Search, an operation that is at the core of current Minimalist inquiry. We argue that, given Minimalist assumptions about structure building consisting of unordered set-formation, there are serious difficulties in defining Minimal Search as a search algorithm. Furthermore, some problematic configurations for Minimal Search (namely, {XP, YP} and {X, Y}) are argued to be an artefact of these set-theoretic commitments. However, if unordered sets are given up as the format of structural descriptions in favour of directed graphs such that Merge(X, Y) creates an arc from X to Y, Minimal Search can be straightforwardly characterised as a sequential deterministic search algorithm: the total order required to define MS as a sequential search algorithm is provided by structure building. |
| first_indexed | 2024-03-08T09:27:08Z |
| format | Article |
| id | doaj.art-995842e3bcef4e99ad48cc9fc10cbf5d |
| institution | Directory Open Access Journal |
| issn | 1450-3417 |
| language | English |
| last_indexed | 2024-03-08T09:27:08Z |
| publishDate | 2023-03-01 |
| publisher | PsychOpen GOLD/ Leibniz Institute for Psychology |
| record_format | Article |
| series | Biolinguistics |
| spelling | doaj.art-995842e3bcef4e99ad48cc9fc10cbf5d2024-01-31T08:19:46ZengPsychOpen GOLD/ Leibniz Institute for PsychologyBiolinguistics1450-34172023-03-011710.5964/bioling.9793bioling.9793The Search for Minimal Search: A Graph-Theoretic ApproachDiego Gabriel Krivochen0https://orcid.org/0000-0001-6145-1057Faculty of Linguistics, Philology and Phonetics, University of Oxford, Oxford, United KingdomThis paper examines Minimal Search, an operation that is at the core of current Minimalist inquiry. We argue that, given Minimalist assumptions about structure building consisting of unordered set-formation, there are serious difficulties in defining Minimal Search as a search algorithm. Furthermore, some problematic configurations for Minimal Search (namely, {XP, YP} and {X, Y}) are argued to be an artefact of these set-theoretic commitments. However, if unordered sets are given up as the format of structural descriptions in favour of directed graphs such that Merge(X, Y) creates an arc from X to Y, Minimal Search can be straightforwardly characterised as a sequential deterministic search algorithm: the total order required to define MS as a sequential search algorithm is provided by structure building.https://doi.org/10.5964/bioling.9793set theorygraph theoryminimal searchphrase structure |
| spellingShingle | Diego Gabriel Krivochen The Search for Minimal Search: A Graph-Theoretic Approach Biolinguistics set theory graph theory minimal search phrase structure |
| title | The Search for Minimal Search: A Graph-Theoretic Approach |
| title_full | The Search for Minimal Search: A Graph-Theoretic Approach |
| title_fullStr | The Search for Minimal Search: A Graph-Theoretic Approach |
| title_full_unstemmed | The Search for Minimal Search: A Graph-Theoretic Approach |
| title_short | The Search for Minimal Search: A Graph-Theoretic Approach |
| title_sort | search for minimal search a graph theoretic approach |
| topic | set theory graph theory minimal search phrase structure |
| url | https://doi.org/10.5964/bioling.9793 |
| work_keys_str_mv | AT diegogabrielkrivochen thesearchforminimalsearchagraphtheoreticapproach AT diegogabrielkrivochen searchforminimalsearchagraphtheoreticapproach |