We introduce a weighted extension of the recently proposed notion of order-preserving hyperedge-replacement grammars and prove that the weight of a graph according to such a weighted graph grammar ...
我们引入了最近提出的保序超边缘替换语法概念的加权扩展，并证明了基于这种加权图语法的图的权值。
{"title":"Parsing Weighted Order-Preserving Hyperedge Replacement Grammars","authors":"Henrik Björklund, F. Drewes, Petter Ericson","doi":"10.18653/v1/W19-5701","DOIUrl":"https://doi.org/10.18653/v1/W19-5701","url":null,"abstract":"We introduce a weighted extension of the recently proposed notion of order-preserving hyperedge-replacement grammars and prove that the weight of a graph according to such a weighted graph grammar ...","PeriodicalId":298538,"journal":{"name":"Proceedings of the 16th Meeting on the Mathematics of Language","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124464349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We derive abstract characterizations of the Strictly Piecewise Local (SPL) and Piecewise Locally Testable (PLT) stringsets. These generalize both the Strictly Local/Locally Testable stringsets (SL and LT) and Strictly Piecewise/Piecewise Testable stringsets (SP and PT) in that SPL constraints can be stated in terms of both adjacency and precedence. We do this in a fully abstract setting which applies to any class of purely relational models that label the points in their domain with some finite labeling alphabet. This includes, for example, labeled trees and graphs. The actual structure of the class of intended models only shows up in interpreting the abstract characterizations of the definable sets in terms of the structure of the models themselves.
{"title":"Some classes of sets of structures definable without quantifiers","authors":"J. Rogers, D. Lambert","doi":"10.18653/v1/W19-5706","DOIUrl":"https://doi.org/10.18653/v1/W19-5706","url":null,"abstract":"We derive abstract characterizations of the Strictly Piecewise Local (SPL) and Piecewise Locally Testable (PLT) stringsets. These generalize both the Strictly Local/Locally Testable stringsets (SL and LT) and Strictly Piecewise/Piecewise Testable stringsets (SP and PT) in that SPL constraints can be stated in terms of both adjacency and precedence. We do this in a fully abstract setting which applies to any class of purely relational models that label the points in their domain with some finite labeling alphabet. This includes, for example, labeled trees and graphs. The actual structure of the class of intended models only shows up in interpreting the abstract characterizations of the definable sets in terms of the structure of the models themselves.","PeriodicalId":298538,"journal":{"name":"Proceedings of the 16th Meeting on the Mathematics of Language","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115851858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Various aspects of syntax have recently been characterized in subregular terms. However, these characterizations operate over very different representations, including string encodings of c-command relations as well as tiers projected from derivation trees. We present a way to unify these approaches via sensing tree automata over Minimalist grammar dependency trees. Sensing tree automata are deterministic top-down tree automata that may inspect the labels of all daughter nodes before assigning them specific states. It is already known that these automata cannot correctly enforce all movement dependencies in Minimalist grammars, but we show that this result no longer holds if one takes into account several well-established empirical restrictions on movement. Sensing tree automata thus furnish a strong yet uniform upper bound on the complexity of syntactic dependencies.
{"title":"Sensing Tree Automata as a Model of Syntactic Dependencies","authors":"T. Graf, Aniello De Santo","doi":"10.18653/v1/W19-5702","DOIUrl":"https://doi.org/10.18653/v1/W19-5702","url":null,"abstract":"Various aspects of syntax have recently been characterized in subregular terms. However, these characterizations operate over very different representations, including string encodings of c-command relations as well as tiers projected from derivation trees. We present a way to unify these approaches via sensing tree automata over Minimalist grammar dependency trees. Sensing tree automata are deterministic top-down tree automata that may inspect the labels of all daughter nodes before assigning them specific states. It is already known that these automata cannot correctly enforce all movement dependencies in Minimalist grammars, but we show that this result no longer holds if one takes into account several well-established empirical restrictions on movement. Sensing tree automata thus furnish a strong yet uniform upper bound on the complexity of syntactic dependencies.","PeriodicalId":298538,"journal":{"name":"Proceedings of the 16th Meeting on the Mathematics of Language","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128345437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper proves that for every class C of stochastic languages defined with the coemission product of finitely many probabilistic, deterministic finite-state acceptors (PDFA) and for every data sequence D of finitely many strings drawn i.i.d. from some stochastic language, the Maximum Likelihood Estimate of D with respect to C can be found efficiently by locally optimizing the parameter values. We show that a consequence of the co-emission product is that each PDFA behaves like an independent factor in a joint distribution. Thus, the likelihood function decomposes in a natural way. We also show that the negative log likelihood function is convex. These results are motivated by the study of Strictly k-Piecewise (SPk) Stochastic Languages, which form a class of stochastic languages which is both linguistically motivated and naturally understood in terms of the coemission product of certain PDFAs.
{"title":"Maximum Likelihood Estimation of Factored Regular Deterministic Stochastic Languages","authors":"Chihiro Shibata, Jeffrey Heinz","doi":"10.18653/v1/W19-5709","DOIUrl":"https://doi.org/10.18653/v1/W19-5709","url":null,"abstract":"This paper proves that for every class C of stochastic languages defined with the coemission product of finitely many probabilistic, deterministic finite-state acceptors (PDFA) and for every data sequence D of finitely many strings drawn i.i.d. from some stochastic language, the Maximum Likelihood Estimate of D with respect to C can be found efficiently by locally optimizing the parameter values. We show that a consequence of the co-emission product is that each PDFA behaves like an independent factor in a joint distribution. Thus, the likelihood function decomposes in a natural way. We also show that the negative log likelihood function is convex. These results are motivated by the study of Strictly k-Piecewise (SPk) Stochastic Languages, which form a class of stochastic languages which is both linguistically motivated and naturally understood in terms of the coemission product of certain PDFAs.","PeriodicalId":298538,"journal":{"name":"Proceedings of the 16th Meeting on the Mathematics of Language","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114162421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we define quantifier-free least fixed point functions (QFLFP) and argue that they are an appropriate and valuable approach to modeling phonological processes (construed as input-output maps). These functions, characterized in terms of first order logic interpretations over graphs, provide a close fit to the observed typology, capturing both local and long-distance phenomena, but are also restrictive in desirable ways. Namely, QFLFP logical functions approximate the computation of deterministic finite-state transducers, which have been argued to form a restrictive hypothesis for phonological processes.
{"title":"Quantifier-free least fixed point functions for phonology","authors":"Jane Chandlee, Adam Jardine","doi":"10.18653/v1/W19-5705","DOIUrl":"https://doi.org/10.18653/v1/W19-5705","url":null,"abstract":"In this paper we define quantifier-free least fixed point functions (QFLFP) and argue that they are an appropriate and valuable approach to modeling phonological processes (construed as input-output maps). These functions, characterized in terms of first order logic interpretations over graphs, provide a close fit to the observed typology, capturing both local and long-distance phenomena, but are also restrictive in desirable ways. Namely, QFLFP logical functions approximate the computation of deterministic finite-state transducers, which have been argued to form a restrictive hypothesis for phonological processes.","PeriodicalId":298538,"journal":{"name":"Proceedings of the 16th Meeting on the Mathematics of Language","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128887098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper characterizes the Output Tier-based Strictly k-Local (OTSLk) class of string-tostring functions, which are relevant for modeling long-distance phonological processes as input-output maps. After showing that any OTSLk function can be learned when k and the tier are given, we present a new algorithm that induces the tier itself when k = 2 and provably learns any total OTSL2 function in polynomial time and data—the first such learner for any class of tier-based functions.
{"title":"Efficient learning of Output Tier-based Strictly 2-Local functions","authors":"Phillip Burness, Kevin McMullin","doi":"10.18653/v1/W19-5707","DOIUrl":"https://doi.org/10.18653/v1/W19-5707","url":null,"abstract":"This paper characterizes the Output Tier-based Strictly k-Local (OTSLk) class of string-tostring functions, which are relevant for modeling long-distance phonological processes as input-output maps. After showing that any OTSLk function can be learned when k and the tier are given, we present a new algorithm that induces the tier itself when k = 2 and provably learns any total OTSL2 function in polynomial time and data—the first such learner for any class of tier-based functions.","PeriodicalId":298538,"journal":{"name":"Proceedings of the 16th Meeting on the Mathematics of Language","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133555414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We apply the Agda-flat proof assistant (Vezzosi, 2019) to computational semantics. Computational semantics in Agda-flat is distinguished from the approach based on Coq (Chatzikyriakidis and Luo, 2014) in that it allows an implementation of the classical, intensional semantic analyses of Montague (1973). That is, it synthesizes the modern dependent type theory and Montague intensional logic traditions in the computational semantics setting. To demonstrate this, we show how to replicate Montague’s analyses in the type theory of Zwanziger (2018), which closely corresponds to the Agda-flat system. Accompanying code type-checks these analyses in Agdaflat.
{"title":"Dependently-Typed Montague Semantics in the Proof Assistant Agda-flat","authors":"C. Zwanziger","doi":"10.18653/v1/W19-5704","DOIUrl":"https://doi.org/10.18653/v1/W19-5704","url":null,"abstract":"We apply the Agda-flat proof assistant (Vezzosi, 2019) to computational semantics. Computational semantics in Agda-flat is distinguished from the approach based on Coq (Chatzikyriakidis and Luo, 2014) in that it allows an implementation of the classical, intensional semantic analyses of Montague (1973). That is, it synthesizes the modern dependent type theory and Montague intensional logic traditions in the computational semantics setting. To demonstrate this, we show how to replicate Montague’s analyses in the type theory of Zwanziger (2018), which closely corresponds to the Agda-flat system. Accompanying code type-checks these analyses in Agdaflat.","PeriodicalId":298538,"journal":{"name":"Proceedings of the 16th Meeting on the Mathematics of Language","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116932600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In binary propositional constructions S1 con S2, the Strong Kleene connectives explain filtering of S1’s and S2’s presuppositions depending on their logical relations with their non-presuppositional content. However, the presuppositions derived by the Strong Kleene connectives are weak conditional presuppositions, which raise the “proviso problem” in cases where no filtering is motivated. Weak Kleene connectives do not face this problem, but only because their presuppositions are often too strong, and hence do not account for filtering phenomena altogether. While various mechanisms have been proposed to allow filtering without the proviso problem, their relations with the standard trivalent Kleene systems have remained unclear. This paper shows that by sacrificing truth-functionality, we uncover a rich domain of possibilities in trivalent semantics in between the Weak Kleene and Strong Kleene connectives. These systems derive presupposition filtering while avoiding the proviso problem. The Kleene-style operators studied are generalized to arbitrary binary functions, which further clarifies the connection between their different “repair” strategies and presupposition projection.
{"title":"Presupposition Projection and Repair Strategies in Trivalent Semantics","authors":"Yoad Winter","doi":"10.18653/v1/W19-5703","DOIUrl":"https://doi.org/10.18653/v1/W19-5703","url":null,"abstract":"In binary propositional constructions S1 con S2, the Strong Kleene connectives explain filtering of S1’s and S2’s presuppositions depending on their logical relations with their non-presuppositional content. However, the presuppositions derived by the Strong Kleene connectives are weak conditional presuppositions, which raise the “proviso problem” in cases where no filtering is motivated. Weak Kleene connectives do not face this problem, but only because their presuppositions are often too strong, and hence do not account for filtering phenomena altogether. While various mechanisms have been proposed to allow filtering without the proviso problem, their relations with the standard trivalent Kleene systems have remained unclear. This paper shows that by sacrificing truth-functionality, we uncover a rich domain of possibilities in trivalent semantics in between the Weak Kleene and Strong Kleene connectives. These systems derive presupposition filtering while avoiding the proviso problem. The Kleene-style operators studied are generalized to arbitrary binary functions, which further clarifies the connection between their different “repair” strategies and presupposition projection.","PeriodicalId":298538,"journal":{"name":"Proceedings of the 16th Meeting on the Mathematics of Language","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124410224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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