| { | |
| "paper_id": "W18-0316", | |
| "header": { | |
| "generated_with": "S2ORC 1.0.0", | |
| "date_generated": "2023-01-19T05:22:01.515206Z" | |
| }, | |
| "title": "Towards a Formal Description of NPI Licensing Patterns *", | |
| "authors": [ | |
| { | |
| "first": "Mai", | |
| "middle": [ | |
| "Ha" | |
| ], | |
| "last": "Vu", | |
| "suffix": "", | |
| "affiliation": { | |
| "laboratory": "", | |
| "institution": "University of Delaware", | |
| "location": {} | |
| }, | |
| "email": "[email protected]" | |
| } | |
| ], | |
| "year": "", | |
| "venue": null, | |
| "identifiers": {}, | |
| "abstract": "This paper is a formal study of a simplified version of Negative Polarity Item (NPI) licensing requirements in two languages, English and Hungarian. In the framework of Model-Theoretic Syntax, using logical formalisms defined over tree-languages, I show that neither pattern can be described with Tierbased Strictly Local (TSL) constraints only, and suggest that they need a more complex logical formula. In particular, Hungarian patterns can be described using a combination of Tier-based Strictly 2-Local constraints over dominance relations and Locally 1-Testable constraints over the left-of relations between nodes. For English, there are no sufficient local constraints, either with or without tiers. As part of the analysis, I give a definition of a generalized tree-language that uses Tier-based 2-Local constraints over dominance relations, while it remains underspecified for left-of relations.", | |
| "pdf_parse": { | |
| "paper_id": "W18-0316", | |
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| "abstract": [ | |
| { | |
| "text": "This paper is a formal study of a simplified version of Negative Polarity Item (NPI) licensing requirements in two languages, English and Hungarian. In the framework of Model-Theoretic Syntax, using logical formalisms defined over tree-languages, I show that neither pattern can be described with Tierbased Strictly Local (TSL) constraints only, and suggest that they need a more complex logical formula. In particular, Hungarian patterns can be described using a combination of Tier-based Strictly 2-Local constraints over dominance relations and Locally 1-Testable constraints over the left-of relations between nodes. For English, there are no sufficient local constraints, either with or without tiers. As part of the analysis, I give a definition of a generalized tree-language that uses Tier-based 2-Local constraints over dominance relations, while it remains underspecified for left-of relations.", | |
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| "section": "Abstract", | |
| "sec_num": null | |
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| "text": "Model-theoretic syntax is a way to study linguistic structures formally by describing them in terms of logical constraints, rather than in terms of sequences of derivational steps. While its roots can be traced back to early studies in generative grammar, it gained prominence with James Rogers' 1998 work, A Descriptive Approach to Language-Theoretic Complexity (Pullum, 2007) . Rogers' (1998) results showed that a significant portion of Government and Binding Theory can be described with a version of Monadic Second-order (MSO) constraints over phrase-structure trees. Incidentally, structures that can be described with MSO logic are members of the regular class of languages in terms of complexity (Rogers and Pullum, 2011) .", | |
| "cite_spans": [ | |
| { | |
| "start": 288, | |
| "end": 300, | |
| "text": "Rogers' 1998", | |
| "ref_id": null | |
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| { | |
| "start": 363, | |
| "end": 377, | |
| "text": "(Pullum, 2007)", | |
| "ref_id": "BIBREF16" | |
| }, | |
| { | |
| "start": 380, | |
| "end": 394, | |
| "text": "Rogers' (1998)", | |
| "ref_id": null | |
| }, | |
| { | |
| "start": 704, | |
| "end": 729, | |
| "text": "(Rogers and Pullum, 2011)", | |
| "ref_id": "BIBREF17" | |
| } | |
| ], | |
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| "eq_spans": [], | |
| "section": "Introduction", | |
| "sec_num": "1" | |
| }, | |
| { | |
| "text": "It is known, however, that many regular languages are not plausible patterns in human natural language (Heinz and Idsardi, 2013) . As an example, the evena language, which is defined as a set of strings that can only contain an even number of as, is widely considered implausible. As a result, recent work has focused on identifying subregular regions relevant to natural language. While progress has been made on phonotactic patterns (Heinz, 2009; Heinz, 2010; Jardine, 2016) and phonological transformations (Chandlee, 2014) , less has been said in this regard about syntactic patterns.", | |
| "cite_spans": [ | |
| { | |
| "start": 103, | |
| "end": 128, | |
| "text": "(Heinz and Idsardi, 2013)", | |
| "ref_id": "BIBREF8" | |
| }, | |
| { | |
| "start": 435, | |
| "end": 448, | |
| "text": "(Heinz, 2009;", | |
| "ref_id": "BIBREF10" | |
| }, | |
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| "start": 449, | |
| "end": 461, | |
| "text": "Heinz, 2010;", | |
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| }, | |
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| "start": 462, | |
| "end": 476, | |
| "text": "Jardine, 2016)", | |
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| "text": "(Chandlee, 2014)", | |
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| "section": "Introduction", | |
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| "text": "Relevant work on syntax in this vein has been done by Thomas Graf, who has argued that most linguistic patterns, including syntactic and morphological ones, fit in the Tier-based Strictly Local (TSL) class (Graf and Heinz, 2015; Graf, 2017) . While the TSL class was originally used to describe stringsets (Heinz et al., 2011) , we use the class in a more abstract way, and apply it to tree-sets in the current paper.", | |
| "cite_spans": [ | |
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| "end": 228, | |
| "text": "(Graf and Heinz, 2015;", | |
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| "text": "Graf, 2017)", | |
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| "text": "(Heinz et al., 2011)", | |
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| "text": "Because trees are two-dimensional structures with two types of ordering relations in them (Rogers, 2003) , the type of ordering relation over which a certain class of language applies has to be specified. The TSL tree-language as described by Graf and Heinz (2015) has TSL constraints over both the dominance and left-of ordering relations. This paper provides a more generalized definition of Tier-based Strictly 2-Local tree-grammars: tree-grammars where the constraints are Tier-based Strictly 2-Local over dominance (TSL 2 ), but can be of different complexity over left-of relations.", | |
| "cite_spans": [ | |
| { | |
| "start": 90, | |
| "end": 104, | |
| "text": "(Rogers, 2003)", | |
| "ref_id": "BIBREF19" | |
| }, | |
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| "start": 243, | |
| "end": 264, | |
| "text": "Graf and Heinz (2015)", | |
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| "text": "We then demonstrate that a particular type of pattern where the existence of one item in the structure requires the existence of another one, formalized as a \u2192 b, cannot be described with TSL constraints in the sense of Graf and Heinz (2015) . NPIs fall into this category of patterns, as an NPI cannot occur without a licensor.", | |
| "cite_spans": [ | |
| { | |
| "start": 220, | |
| "end": 241, | |
| "text": "Graf and Heinz (2015)", | |
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| "section": "Introduction", | |
| "sec_num": "1" | |
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| "text": "The scope of this paper is restricted to describing well-formed surface structures, without any assumption of underlying features or syntactic movement. We are thus agnostic about any in-depth theory of NPI-licensing, and are not addressing specific proposals suggesting movement or agreement (cf. Giannakidou and Zeijlstra (2016)); neither do we look at proposed Logical Forms of these sentences, which might differ from the observed surface word orders.", | |
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| "section": "Introduction", | |
| "sec_num": "1" | |
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| "text": "Lastly, the choice of syntactic data structure needs a few words. Two common data structures used to describe syntactic structures are phrase-structure trees and derivation trees. For a detailed discussion of the two, the reader is referred to Stabler (1997) . We choose to use phrase-structure trees as the data structure for the sentences discussed in this paper, instead of derivation trees. Graf (2013) gives an in-depth analysis of the nature of syntactic constraints, both over phrase-structure trees and derivation trees. He shows that representational constraints (i.e. those over phrase-structure trees), are subsumed by translocal constraints (i.e. those over derivation trees). We thus believe that modeling NPI-licensing with constraints over phrase-structure trees will not take away from the overall generalizability of our results regarding the complexity of necessary constraints in natural language syntax.", | |
| "cite_spans": [ | |
| { | |
| "start": 244, | |
| "end": 258, | |
| "text": "Stabler (1997)", | |
| "ref_id": "BIBREF20" | |
| }, | |
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| "start": 395, | |
| "end": 406, | |
| "text": "Graf (2013)", | |
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| "section": "Introduction", | |
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| "text": "The paper is organized as follows. Section 2 states the definitions of key concepts needed to understand the discussion in the rest of the paper. Section 3 introduces the syntactic data in question: NPIlicensing in English and Hungarian. Section 4 shows that these patterns need TLT and First-Order Logic to be described. Section 5 concludes.", | |
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| "section": "Introduction", | |
| "sec_num": "1" | |
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| { | |
| "text": "These definitions of Strictly Local (SL) and Locally Testable (LT) stringsets are largely based on Heinz et al. (2011) , Rogers and Pullum (2011) , and Rogers et al. (2013) . We assume familiarity with monadic second-order (MSO) logic (Enderton, 2001 ). First, k-factors over strings are defined below. Let \u03a3 be the alphabet, and \u03a3 * be all strings of finite length over \u03a3. Then string u is a factor of string w iff (\u2203x, y \u2208 \u03a3 * ) such that w = xuy. If |u| = k, then u is a k-factor of w. The function F k maps a string to a set of k-factors within it:", | |
| "cite_spans": [ | |
| { | |
| "start": 99, | |
| "end": 118, | |
| "text": "Heinz et al. (2011)", | |
| "ref_id": "BIBREF9" | |
| }, | |
| { | |
| "start": 121, | |
| "end": 145, | |
| "text": "Rogers and Pullum (2011)", | |
| "ref_id": "BIBREF17" | |
| }, | |
| { | |
| "start": 152, | |
| "end": 172, | |
| "text": "Rogers et al. (2013)", | |
| "ref_id": "BIBREF18" | |
| }, | |
| { | |
| "start": 235, | |
| "end": 250, | |
| "text": "(Enderton, 2001", | |
| "ref_id": "BIBREF2" | |
| } | |
| ], | |
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| "eq_spans": [], | |
| "section": "Strictly Local and Locally Testable Stringsets", | |
| "sec_num": "2.1" | |
| }, | |
| { | |
| "text": "F k (w) = {u|u is a k-factor of w} A Strictly k-Local (SL k )", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Strictly Local and Locally Testable Stringsets", | |
| "sec_num": "2.1" | |
| }, | |
| { | |
| "text": "grammar for a string language is understood as a list of possible k-factors in the language, or equivalently, a list of banned kfactors.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Strictly Local and Locally Testable Stringsets", | |
| "sec_num": "2.1" | |
| }, | |
| { | |
| "text": "G, a Strictly k-Local description over some alphabet \u03a3, is a set of k-factors of \u03a3 \u222a { , }, where and mark the beginning and ending of a string, respectively.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Definition 1 (Strictly Local Stringsets)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "G \u2286 F k ( \u2022 \u03a3 * \u2022 )", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Definition 1 (Strictly Local Stringsets)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "A string w satisfies G, iff the set of k-factors of the augmented string \u2022 w \u2022 is a subset of G:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Definition 1 (Strictly Local Stringsets)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "w |= G \u21d4 F k ( \u2022 w \u2022 ) \u2286 G", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Definition 1 (Strictly Local Stringsets)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The stringset licensed by a description G is the set of words that satisfy it.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Definition 1 (Strictly Local Stringsets)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "L(G) def = {w|w |= G} A set of strings is Strictly k-Local (SL k ) iff it is L(G) for some strictly k-local definition of G. It is Strictly Local iff it is SL k for some k.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Definition 1 (Strictly Local Stringsets)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Next, the definition of local k-expressions is given below.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Definition 1 (Strictly Local Stringsets)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The language of k-expressions is the smallest set including the following forms, with the intended semantics indicated.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Definition 2 (Local k-expressions)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "\u2022 Atomic formulae: f \u2208 F k (\u03a3 * ) is a kexpression.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Definition 2 (Local k-expressions)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "\u2022 Conjunction: If \u03d5 1 and \u03d5 2 are k-expressions, then (\u03d5 1 \u2227 \u03d5 2 ) is a k-expression.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Definition 2 (Local k-expressions)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "\u2022 Negation: If \u03d5 1 is a k-expression, then (\u00ac\u03d5 1 ) is a k-expression.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Definition 2 (Local k-expressions)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "If w is a string and \u03d5 a k-expression, then", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Definition 2 (Local k-expressions)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "w |= \u03d5 def \u21d4 \uf8f1 \uf8f4 \uf8f2 \uf8f4 \uf8f3 \u03d5 = f \u2208 F k (\u03a3 * ) and f \u2208 F k (w) \u03d5 = (\u03d5 1 \u2227 \u03d5 2 )", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Definition 2 (Local k-expressions)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "and w |= \u03d5 1 and w |= \u03d5 2 \u03d5 = (\u00ac\u03d5 1 ) and w \u03d5 1 Now we can define Locally Testable Stringsets with the help of k-expressions.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Definition 2 (Local k-expressions)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "A stringset L over \u03a3 is k-Locally Testable (LT k ) iff there is some local k-expression \u03d5 over \u03a3 (for some k) such that L is the set of all strings that satisfy \u03d5.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Definition 3 (Locally Testable Stringsets)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "L = L(\u03d5) def = {w \u2208 \u03a3 * |w |= \u03d5} A stringset is LT iff it is LT k for some k.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Definition 3 (Locally Testable Stringsets)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Notice that implicational statements can be derived from k-expressions, because a \u2192 b is equivalent to \u00ac(a \u2227 \u00acb).", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Definition 3 (Locally Testable Stringsets)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Our understanding of trees is based on the idea of multi-dimensional trees, as discussed in Rogers (2003) . For the purposes of this paper, we exclusively work with 2-dimensional trees, and thus restrict our formal descriptions to them.", | |
| "cite_spans": [ | |
| { | |
| "start": 92, | |
| "end": 105, | |
| "text": "Rogers (2003)", | |
| "ref_id": "BIBREF19" | |
| } | |
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| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "The basic intuition is as follows. Strings are onedimensional trees, whose nodes are related to each other via one-dimensional successor relations. To add a second dimension, we first build a local tree (a tree of at most one depth) by connecting a single point a to each node in a one-dimensional tree S through second-dimensional successor relations ( Figure 1a ). The adjoined point is called the root in this case, and the nodes in S are the yield. A composite tree, where trees have depths greater than one, can be built by identifying the root of one local tree with some point in the yield of another (Figure 1b ). In the trees in Figure 1 , the solid lines represent the one-dimensional successor relations, and the dashed lines represent the second-dimensional successor relations. We give our formal definition for twodimensional trees within the model-theoretic framework. Model theory provides a way to describe a particular object using mathematical logic. A model requires a signature and a set of logical statements. Along with the usual logical connectives, x \u2248 y denotes that x and y are equivalent.", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 354, | |
| "end": 363, | |
| "text": "Figure 1a", | |
| "ref_id": null | |
| }, | |
| { | |
| "start": 608, | |
| "end": 618, | |
| "text": "(Figure 1b", | |
| "ref_id": null | |
| }, | |
| { | |
| "start": 638, | |
| "end": 646, | |
| "text": "Figure 1", | |
| "ref_id": null | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "The signature of the two-dimensional tree-model for linguistic trees is shown in Figure 2 . Let \u03a3 = \u03a3 Cat \u222a \u03a3 Lex be the alphabet, where \u03a3 Cat is the set of syntactic categories, and \u03a3 Lex is the set of lexical items. We write \u03c3", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 81, | |
| "end": 89, | |
| "text": "Figure 2", | |
| "ref_id": null | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "(x) if node x is labeled with \u03c3, for all \u03c3 \u2208 \u03a3. D, \u227a, , L \u03c3 \u03c3\u2208\u03a3 , where", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "\u2022 D is the finite domain", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "\u2022 \u227a is a binary ordering relation immediate leftof", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "\u2022 is a binary ordering relation immediate dominance", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "\u2022 L \u03c3 is a set of unary relations for labeling elements in D with \u03c3 for all \u03c3 \u2208 \u03a3 Figure 2 : Model for two-dimensional trees Following Rogers (2003) , * is defined as the reflexive transitive closure, and + as the transitive closure of . This is explicitly monadic secondorder definable through Branch: a set of nodes that are upwards closed with regard to, and linearlyordered by the immediate dominance relation, . The depth of any tree then can be understood as the length of the longest Branch in the tree.", | |
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| "start": 82, | |
| "end": 90, | |
| "text": "Figure 2", | |
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| } | |
| ], | |
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| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "(", | |
| "cite_spans": [], | |
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| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "1) Branch(X) \u2261 (\u2200x, y)[(X(x) \u2227 y x) \u2192 X(y)] \u2227 (\u2200x, y, z)[(X(x) \u2227 X(y) \u2227 X(z) \u2227 x y \u2227 x z) \u2192 y \u2248 z] (2) x * y \u2261 (\u2200X)[(Branch(X) \u2227 X(y)) \u2192 X(x)] (3) x + y \u2261 x * y \u2227 x \u2248 y", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "The predicates \u227a * and \u227a + are definable in a similar fashion.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "(4) String(X) \u2261 (\u2200x, y)[(X(x) \u2227 y \u227a x) \u2192 X(y)] \u2227 (\u2200x, y, z)[(X(x) \u2227 X(y) \u2227 X(z) \u2227 x \u227a y \u2227 x \u227a z) \u2192 y \u2248 z] (5) x \u227a * y \u2261 (\u2200X)[(String(X) \u2227 X(y)) \u2192 X(x)] (6) x \u227a + y \u2261 x \u227a * y \u2227 x \u2248 y", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "Based on \u227a * , we also can also define the inherited left-of relation, < * . If z is left-of w in a tree, then all nodes that are reflexively dominated by z are inherited left-of all nodes that are reflexively dominated by w.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "(7) x < * y \u2261 (\u2203z, w)[z * x \u2227 w * y \u2227 z \u227a * w]", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "The following tree-axioms restrict all possible structures to the desired two-dimensional treestructures described previously (and illustrated in Figure 1 ): (8) There is a root that dominates all nodes:", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 146, | |
| "end": 154, | |
| "text": "Figure 1", | |
| "ref_id": null | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "(\u2203x)(\u2200y)[x * y \u2227 \u00ac\u2203z(z x)] (9) At most one parent/direct precedent per node:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "EQUATION", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [ | |
| { | |
| "start": 0, | |
| "end": 8, | |
| "text": "EQUATION", | |
| "ref_id": "EQREF", | |
| "raw_str": "(\u2200x, y, z)[[(x \u227a z \u2227 y \u227a z) \u2228 (x z \u2227 y z)] \u2192 x \u2248 y] (10) Irreflexivity of \u227a and : (\u2200x, y)[(x \u227a y \u2228 x y) \u2192 x \u2248 y]", | |
| "eq_num": "(" | |
| } | |
| ], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "11) Two nodes cannot be both in * and \u227a * relations:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "(\u2200x, y)[(x * y \u2228 y * x) \u2194 \u00ac(x \u227a * y \u2228 y \u227a * x)]", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "We add two final assumptions that are specific to linguistic trees. Each node can only have one label, and a node can only have a label l \u2208 \u03a3 Lex iff that node is a leaf (i.e. it does not dominate any other node).", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "(12) (\u2200x)[(\u03b1(x) \u2227 \u03b2(x)) \u2192 \u03b1 \u2248 \u03b2] (13) (\u2200x)[\u00ac\u2203y(x y) \u2194 \u03b1(x) \u2227 \u03b1 \u2208 \u03a3 Lex ]", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "As an example, see tree T1 in Figure 3b , a modeltheoretic representation of Figure 3a . For this nonlinguistic tree, \u03a3 = {a, b, c}, with no distinction between \u03a3 Cat and \u03a3 Lex . The solid lines represent the first-dimensional successor relations \u227a, and the dashed lines represent the second-dimensional successor relations . Then TI can be described with the following list of statements:", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 30, | |
| "end": 39, | |
| "text": "Figure 3b", | |
| "ref_id": null | |
| }, | |
| { | |
| "start": 77, | |
| "end": 86, | |
| "text": "Figure 3a", | |
| "ref_id": null | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "(14) Labeling statement:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "a(0) \u2227 b(1) \u2227 a(2) \u2227 a(3) \u2227 c(4) \u2227 b(5) \u2227 c(6) \u2227 c(7) \u2227 a(8) \u2227 b(9) (15) Statement about \u227a: 1 \u227a 2 \u2227 3 \u227a 4 \u2227 5 \u227a 6 \u2227 8 \u227a 9 (16) Statement about : 0 1 \u2227 0 2 \u2227 1 3 \u2227 1 4 \u2227 2 5 \u2227 2 6 \u2227 3 7 \u2227 4 8 \u2227 4 9", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "Next, we generalize k-factors to two-dimensional trees. For strings, k-factors are substrings of k length. For trees, this will mean subtrees with depth of k-1 (since the depth of the root node is 0, but one node is an 1-factor of a tree).", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "(17) Subtree(X) \u2261 (\u2203x)(\u2200y)[(X(x) \u2227 x * y) \u2192 X(y)]", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "A 2-factor can be easily defined by changing the * relation to in the definition of subtrees. While this is not a generalized definition of k-factors in trees, it will be sufficient for the purposes of this paper.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "(18) 2-Factor(X) \u2261 (\u2203x)(\u2200y)[(X(x) \u2227 x y) \u2192 X(y)]", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "For example, the 2-factors of T1 is the set of trees in Figure 4 . In our linguistic examples, the labels will be syntactic categories (e.g. CP, NP, C', N', etc.) and language-specific lexical items. For the purposes of NPI-licensing, a specific set of lexical items are of interest only: NPIs and negation for both English and Hungarian, and CPs for Hungarian. Below we simply define the lexical items for NPIs and negation, in English and Hungarian.", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 56, | |
| "end": 64, | |
| "text": "Figure 4", | |
| "ref_id": null | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "(19) NPI eng (x) \u2261 anybody(x) \u2228 anything(x) \u2228 anywhere(x) (20) neg eng (x) \u2261 not(x) \u2228 no(x) \u2228 nobody(x) \u2228 nothing(x) \u2228 nowhere(x) (21) NPI hun (x) \u2261 senki(x) \u2228 semmi(x) \u2228 sehol(x) (22) neg hun (x) \u2261 nem(x)", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "2.3 Tier-based tree-languages Heinz et al. (2011) defined Tier-based Strictly Local (TSL) languages for strings. We use their definition of tiers complete with the one found in Graf and Heinz (2015) to discuss the projection of tier-trees. A tier is denoted as T \u2286 \u03a3, and there is an erasing function that erases all elements in the string that are not labeled on the tier (Heinz et al., 2011) .", | |
| "cite_spans": [ | |
| { | |
| "start": 30, | |
| "end": 49, | |
| "text": "Heinz et al. (2011)", | |
| "ref_id": "BIBREF9" | |
| }, | |
| { | |
| "start": 177, | |
| "end": 198, | |
| "text": "Graf and Heinz (2015)", | |
| "ref_id": "BIBREF5" | |
| }, | |
| { | |
| "start": 373, | |
| "end": 393, | |
| "text": "(Heinz et al., 2011)", | |
| "ref_id": "BIBREF9" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "Generalizing to our two-dimensional tree-model, a tree-tier is projected by taking only the nodes that are labeled with elements of T , while keeping all inherited left-of relations (< * ) and dominance relations ( * ) between these nodes.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "For example, let T = {a, b}. Applying the erasing function to T1 (3) then yields a tier-tree (5). We say that T1 projects a tier-tree. Figure 5 : Tier-tree, T ={a,b} TSL string languages were characterized by a finite list of banned k-factors over the string-tier. The equivalent is not possible for tree-languages, because in tier-trees, there is no bound on the number of daughters for a given node.", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 135, | |
| "end": 143, | |
| "text": "Figure 5", | |
| "ref_id": null | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "To see why, take a tree T2 such that the starting node labeled S mothers a node labeled b, and each node b mothers a node a and b (6a). In linguistic terms, node a's never dominate each other, neither are they ever sisters; the higher ones c-command the lower ones. Now suppose that the tier we want to project is T ={S,a}. We then get a tree where S directly dominates an unbounded number of a nodes, where that number is equivalent to the depth of the original tree. We thus cannot list a finite-list of banned (or permitted) k-factors over a tree-tier without knowing a bound on the depth of the tree first. Instead, we give a general description of tree languages that are Tier-based Strictly 2-Local over the dominance relation (T SL 2 ). Recall that in the framework laid out in Rogers (2003) , twodimensional trees consist of strings (i.e. onedimensional trees) that are dominated by a single node. We use this insight to define our tier-based grammar. Informally, the grammar contains a tier as described above, and string-based grammars that apply over sisters dominated by the same node. There are potentially as many string-based grammars as nodes labeled with a syntactic category on the tier. Formally, each grammar contains a quadruple as in Figure 7 . G = T, T Cat , H, \u03b3 , where:", | |
| "cite_spans": [ | |
| { | |
| "start": 785, | |
| "end": 798, | |
| "text": "Rogers (2003)", | |
| "ref_id": "BIBREF19" | |
| } | |
| ], | |
| "ref_spans": [ | |
| { | |
| "start": 1256, | |
| "end": 1264, | |
| "text": "Figure 7", | |
| "ref_id": null | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "\u2022 T \u2282 \u03a3 is the finite set of tier-nodes", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "\u2022 T Cat = (T \u2229 \u03a3 Cat )", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "\u2022 H is a set of string-based grammars", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "\u2022 \u03b3 : T Cat \u00d7H is a bijection that maps every node labeled \u03ba \u2208 T Cat to a string-based grammar h \u2208 H Figure 7 : Grammar of tier-trees", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 101, | |
| "end": 109, | |
| "text": "Figure 7", | |
| "ref_id": null | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "The grammar defined here is thus T SL 2 , but there can still be different types of grammar over the left-of relations. Following Graf and Heinz (2015) then, a TSL grammar for trees is a specific instance of the grammar defined here: in this case, H must be a set of TSL string-languages.", | |
| "cite_spans": [ | |
| { | |
| "start": 130, | |
| "end": 151, | |
| "text": "Graf and Heinz (2015)", | |
| "ref_id": "BIBREF5" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Tree languages", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "We understand Negative Polarity Items (NPIs) as expressions that are ungrammatical in positive declarative clauses, but they are grammatical in their negative counterpart. This understanding of NPIs echoes the one for negative dependencies in Giannakidou and Zeijlstra (2016) . For example, English anything is an NPI according this definition, because it shows the following contrast:", | |
| "cite_spans": [ | |
| { | |
| "start": 243, | |
| "end": 275, | |
| "text": "Giannakidou and Zeijlstra (2016)", | |
| "ref_id": "BIBREF4" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "NPI patterns", | |
| "sec_num": "3" | |
| }, | |
| { | |
| "text": "(23) a. *John has read anything. b. John hasn't read anything.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "NPI patterns", | |
| "sec_num": "3" | |
| }, | |
| { | |
| "text": "English-type NPIs are typical in English, Chinese (Lin, 1998) , and Vietnamese (Tran and Bruening, 2013) , among others. They are weak NPI-languages, which means that their NPIs are licensed not only by negation, but also in questions, protasis of conditionals, and in general, downward entailment contexts (Ladusaw, 1983) . For the sake of simplicity, I will focus only on the cases where English NPIs are licensed by sentential negation.", | |
| "cite_spans": [ | |
| { | |
| "start": 50, | |
| "end": 61, | |
| "text": "(Lin, 1998)", | |
| "ref_id": "BIBREF14" | |
| }, | |
| { | |
| "start": 79, | |
| "end": 104, | |
| "text": "(Tran and Bruening, 2013)", | |
| "ref_id": "BIBREF21" | |
| }, | |
| { | |
| "start": 307, | |
| "end": 322, | |
| "text": "(Ladusaw, 1983)", | |
| "ref_id": "BIBREF13" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "English-type", | |
| "sec_num": "3.1" | |
| }, | |
| { | |
| "text": "The general observation is that English NPIs must be c-commanded by negation (24-26), over an arbitrary number of clause boundaries (27). 1 The NPI item anybody is not c-commanded by negation (not, nobody) in (25) and 26 A straightforward way then to formalize the English-NPI licensing requirement is to state it in first-order logic with the help of defining ccommand relations.", | |
| "cite_spans": [ | |
| { | |
| "start": 138, | |
| "end": 139, | |
| "text": "1", | |
| "ref_id": null | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "English-type", | |
| "sec_num": "3.1" | |
| }, | |
| { | |
| "text": "(28) c-com(x, y) \u2261 \u00ac(x + y) \u2227 x \u2248 y \u2227 \u2200z[z + x \u2192 z + y] (29) English NPI-licensing constraint: \u2200y[NPI eng (y) \u2192 \u2203x[c-com(x, y) \u2227 neg eng (x)]]", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "English-type", | |
| "sec_num": "3.1" | |
| }, | |
| { | |
| "text": "Here we cite our own data collected from Hungarian, but we suspect that a similar distribution is found in Slavic languages (Progovac, 1994) . Hungarian NPIs show the same contrast that is found in English: Their similarity to English NPIs stops here. Hungarian NPIs must be licensed locally by clausemate negation (32), but there is no c-command requirement for the relation between licensor and licensee (33). We assume that the domain of licensing is restricted to CP boundaries, as NPIs are licensed in sentences with negated raising predicates (34), but not in ones with negated control predicates (35 The constraint can be formalized with First-order logic with the help of defining closest-CP(x, y), which says that x is labeled CP, and it is the closest node labeled such to y.", | |
| "cite_spans": [ | |
| { | |
| "start": 124, | |
| "end": 140, | |
| "text": "(Progovac, 1994)", | |
| "ref_id": "BIBREF15" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Hungarian-type", | |
| "sec_num": "3.2" | |
| }, | |
| { | |
| "text": "(30) *Jancsi", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Hungarian-type", | |
| "sec_num": "3.2" | |
| }, | |
| { | |
| "text": "(36) closest-CP(x, y) \u2261 CP(x) \u2227 x * y \u2227 \u00ac\u2203z[CP(z) \u2227 x * + z \u2227 z * y]", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Hungarian-type", | |
| "sec_num": "3.2" | |
| }, | |
| { | |
| "text": "(37) Hungarian NPI-licensing constraint:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Hungarian-type", | |
| "sec_num": "3.2" | |
| }, | |
| { | |
| "text": "\u2200(y)[NPI hun (y) \u2192 \u2203(x, z)[closest-CP(x, y) \u2227 closest-CP(x, z) \u2227 neg hun (z)]", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Hungarian-type", | |
| "sec_num": "3.2" | |
| }, | |
| { | |
| "text": "The NPI patterns discussed above are summarized in Table 1 ", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 51, | |
| "end": 58, | |
| "text": "Table 1", | |
| "ref_id": "TABREF3" | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Interim summary", | |
| "sec_num": "3.3" | |
| }, | |
| { | |
| "text": "In what follows, we re-define the NPI-licensing constraints for Hungarian and English, in the context of the TSL 2 grammar G defined in Section 2.3. We have two results: (1) Hungarian NPI-licensing can be characterized with the tier-based grammar, but English cannot, and (2) the string-language for the Hungarian grammar is neither SL or TSL, but it is LT.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Complexity of NPI patterns", | |
| "sec_num": "4" | |
| }, | |
| { | |
| "text": "Let us define the relevant tier for Hungarian NPIlicensing as follows: T ={neg hun , NPI hun , CP}.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Hungarian", | |
| "sec_num": "4.1" | |
| }, | |
| { | |
| "text": "Then T Cat = {CP}. For examples of grammatical tier-trees, see Figure 8 . Figure 8 : Well-formed and ill-formed tier-trees for Hungarian NPI-licensing Now the question is determining the string grammar h over the nodes that CP dominates in the tier. Let us call this string-grammar h CP . We show that h CP is not SL, but it is LT. Consider the ill-formed set of trees where there is an arbitrary number of NPIs but there is no negation to license any of them (Figure 8b ). Such trees would correspond to ungrammatical sentences of the form (38). If h CP were SL, we would be able to ban a set of k-factors to successfully exclude the ill-formed trees. This is not possible for any k. For any kfactor that successfully bans a string of k-length that consists of only NPIs, there is a well-formed string of length k + 1, whose k + 1-th member is neg.", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 63, | |
| "end": 71, | |
| "text": "Figure 8", | |
| "ref_id": null | |
| }, | |
| { | |
| "start": 74, | |
| "end": 82, | |
| "text": "Figure 8", | |
| "ref_id": null | |
| }, | |
| { | |
| "start": 460, | |
| "end": 470, | |
| "text": "(Figure 8b", | |
| "ref_id": null | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Hungarian", | |
| "sec_num": "4.1" | |
| }, | |
| { | |
| "text": "To exclusively define well-formed trees, the use of LT logic is necessary (39). This formula is Locally 1-Testable.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Hungarian", | |
| "sec_num": "4.1" | |
| }, | |
| { | |
| "text": "(39) (\u2200x\u2203y)[NPI hun (x) \u2192 neg hun (y)]", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Hungarian", | |
| "sec_num": "4.1" | |
| }, | |
| { | |
| "text": "Recall that English NPI-licensing is stated as a ccommand requirement: negation must c-command the NPI. This type of constraint cannot be reduced to any type of TSL 2 grammar.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "English", | |
| "sec_num": "4.2" | |
| }, | |
| { | |
| "text": "Consider the following two sentences:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "English", | |
| "sec_num": "4.2" | |
| }, | |
| { | |
| "text": "(40) *The girl, (that X said) n that John didn't see, read anything. In 40, negation can be found buried inside a relative clause that has been constructed through an arbitrary number of recursive embedding, and thus it does not c-command the NPI anything. On the other hand, in (41), negation c-commands an NPI that is buried in the embedded clauses, and thus the NPI is licensed.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "English", | |
| "sec_num": "4.2" | |
| }, | |
| { | |
| "text": "There are no local constraints that can account for the restriction, since there is no bound on the distance between the negation and the NPI. Introducing tiers does not help either, due to the c-command requirement. There is no good way to define elements for the tier to get the relevant 2-factors within the tier-tree that would help us derive the correct constraints. In fact, there is no definable tier in order to get any relevant k-factor in the tier-tree.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "English", | |
| "sec_num": "4.2" | |
| }, | |
| { | |
| "text": "If the tier is defined to only include negation and NPI, the two obviously relevant elements for NPIlicensing in English, there is no way to tell apart tiertrees where negation c-commands the NPI compared to the ones where it does not. For example, both sentences (24) and (26) would yield the same tiertree: $ NPI neg Figure 9 : Tier-tree for (24) and (26), T ={neg, NPI} Including nodes that can immediately dominate negation (NegP and DP) would again result in tiertrees of arbitrary depth. For example, in sentences (41) and (40), one would have to list all the arbitrary number of DPs that serve as subjects for each embedded clause before getting to the NPI in the sentence. We then have the problem of not being able to determine subtrees of a bounded k-depth. Thus c-command relations cannot be defined using tiers.", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 319, | |
| "end": 327, | |
| "text": "Figure 9", | |
| "ref_id": null | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "English", | |
| "sec_num": "4.2" | |
| }, | |
| { | |
| "text": "This paper has offered four results. First, it provided a definition of TSL 2 languages. Second, it showed that implicational requirements, such as the surface licensing conditions of NPIs for Hungarian and English, cannot be described with TSL constraints over both dominance and precedence relations in trees.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Conclusions", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "Hungarian, which has a clausemate-requirement, can be described with a grammar that is TSL 2 with LT 1 constraints over the precedence relations. On the other hand, English NPI-licensing patterns, which have a structural c-command restriction, cannot be accommodated by TSL 2 . It is yet to be seen whether English surface NPI-licensing can be described with any logical formalism that is weaker than First-order.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Conclusions", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "These results apply to surface syntactic descriptions only. Once we consider other possible theoretical explanations for NPIs that employ either featureagreement or movement, the complexity of these syntactic constraints might be decreased. This question is to be addressed by future research.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Conclusions", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "Our class of newly defined tree-languages, TSL 2 , needs further study also. In particular, it would be interesting to see how the characterizations of subregular string languages (e.g. the Suffix Substitution Clause for SL languages, or Local Test Invariance for LT languages) hold up once the representation changes from strings to trees. It is also yet to be seen what it means for tree languages that one can mix and match different classes of languages for different ordering relations within the same treestructure. The nature of subregular tree-languages is still largely unknown.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Conclusions", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "Lastly, we might also examine different definitions of trees. For example, Frank and Vijay-Shanker (2001) proposed to define trees using ccommand as the primitive binary relation, instead of dominance. In that case, the English NPI-licensing constraint would be very easy to state by requiring that NPIs are c-commanded by a negation. We suspect that Hungarian NPI-licensing can be accounted for as well, but a careful study is needed to confirm our hypothesis.", | |
| "cite_spans": [ | |
| { | |
| "start": 75, | |
| "end": 105, | |
| "text": "Frank and Vijay-Shanker (2001)", | |
| "ref_id": null | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Conclusions", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "In conclusion, these results are only preliminary to studying the computational complexity of NPIlicensing constraints. However, they show the potential of using tools from theoretical computer science to reveal the nature of syntactic phenomena. For one, it might not be immediately obvious that on the surface level, English NPI-licensing needs more powerful tools to be described than Hungarian NPI-licensing. English is unrestricted in terms of distance between the licensor and licensee, whereas Hungarian is unrestricted in terms of structural requirements as long as the licensor and licensee are within the same clause. Formalizing these constraints using logic revealed that having an unbounded distance necessitates increased complexity compared to having no structural requirement.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Conclusions", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "Studying linguistic phenomena from a formal perspective thus can give us insight into the minimal computational requirements needed for natural language. The results in turn might bear further implications on the computational complexity needed for syntactic patterns, particularly in learning and expected cross-linguistic variation.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Conclusions", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "Proceedings of the Society for Computation in Linguistics (SCiL) 2018, pages 154-163. Salt Lake City, Utah, January 4-7, 2018", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "A reviewer suggested that a sentence such as 'Nobody's mother understood anything I said' as a counter-evidence for the general pattern. However, if mother is replaced by children, the sentence becomes much less acceptable. Our suspicion is that 'nobody's mother' has become idiomatic, meaning 'nobody'.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "In accordance withCarnie (2013), I assume that control verbs select for CPs, whereas raising verbs select for IPs.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "", | |
| "sec_num": null | |
| } | |
| ], | |
| "back_matter": [], | |
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| "text": "Figure 1: Two-dimensional trees", | |
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| "text": "Figure 3: T1", | |
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| "text": "Figure 4: 2-factors of T1", | |
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| "text": "T2 and its tier-tree", | |
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| "uris": null, | |
| "text": ", but it is c-commanded and thus licensed in (24). (24) John didn't see anybody. [John didn't think [that Charlie saw [that Mary stole anything.]]]", | |
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| "FIGREF7": { | |
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| "text": "s n anybody saw anything.'", | |
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| "text": "Summary of English and Hungarian NPI patterns.", | |
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