Sorcha Gilroy, Adam Lopez, S. Maneth, Pijus Simonaitis
{"title":"(Re)introducing Regular Graph Languages","authors":"Sorcha Gilroy, Adam Lopez, S. Maneth, Pijus Simonaitis","doi":"10.18653/v1/W17-3410","DOIUrl":"https://doi.org/10.18653/v1/W17-3410","url":null,"abstract":"Distributions over strings and trees can be represented by probabilistic regular languages, which characterise many models in natural language processing. Recently, several datasets have become avail-able which represent natural language phe-nomena as graphs, so it is natural to ask whether there is an equivalent of probabilistic regular languages for graphs. This paper presents regular graph languages , a formalism due to Courcelle (1991) that has not previously been studied in natural language processing. RGL is cru-cially a subfamily of both Hyperedge Replacement Languages (HRL), which can be made probabilistic; and Monadic Second Order Languages (MSOL), which are closed under intersection. We give an accessible introduction to Courcelle’s proof that RGLs are in MSOL, providing clues about how RGL may relate to other recently introduced graph grammar formalisms.","PeriodicalId":133680,"journal":{"name":"Mathematics of Language","volume":"357 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115861029","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}
{"title":"How Many Stemmata with Root Degree k?","authors":"Armin Hoenen, Steffen Eger, Ralf Gehrke","doi":"10.18653/v1/W17-3402","DOIUrl":"https://doi.org/10.18653/v1/W17-3402","url":null,"abstract":"We are investigating parts of the mathematical foundations of stemmatology, the science reconstructing the copying history of manuscripts. After Joseph Bédier in 1928 got suspicious about large amounts of root bifurcations he found in reconstructed stemmata, Paul Maas replied in 1937 using a mathematical argument that the proportion of root bifurcating stemmata among all possible stemmata is so large that one should not become suspicious to find them abundant. While Maas’ argument was based on one example with a tradition of three surviving manuscripts, we show in this paper that for the whole class of trees corresponding to Maasian reconstructed stemmata and likewise for the class of trees corresponding to complete historical manuscript genealogies, root bifurcations are apriori the most expectable root degree type. We do this by providing a combinatorial formula for the numbers of possible so-called Greg trees according to their root degree (Flight, 1990). Additionally, for complete historical manuscript trees (regardless of loss), which coincide mathematically with rooted labeled trees, we provide formulas for root degrees and derive the asymptotic degree distribution. We find that root bifurcations are extremely numerous in both kinds of trees. Therefore, while previously other studies have shown that root bifurcations are expectable for true stemmata, we enhance this finding to all three philologically relevant types of trees discussed in breadth until today.","PeriodicalId":133680,"journal":{"name":"Mathematics of Language","volume":"444 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116752636","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}
{"title":"Extracting Forbidden Factors from Regular Stringsets","authors":"J. Rogers, D. Lambert","doi":"10.18653/v1/W17-3404","DOIUrl":"https://doi.org/10.18653/v1/W17-3404","url":null,"abstract":"The work presented here continues a program of completely characterizing the constraints on the distribution of stress in human languages that are documented in the StressTyp2 database with respect to the Local and Piecewise sub-regular hierarchies. We introduce algorithms that, given a Finite-State Automaton, compute a set of forbidden words, units, initial factors, free factors and final factors that define a Strictly Local (SL) approximation of the stringset recognized by the FSA, along with a minimal DFA that recognizes the residue set: the set of strings in the approximation that are not in the stringset recognized by the FSA. If the FSA recognizes an SL stringset, then the approximation is exact (otherwise it overgenerates). We have applied these tools to the 106 lects that have associated DFAs in the StressTyp2 database, a wide-coverage corpus of stress patterns that are attested in human languages. The results include a large number of strictly local constraints that have not been included in prior work categorizing these patterns with respect to the Local and Piecewise Sub-Regular hierarchies of Rogers et al. (2012), although, of course, they do not contradict the central result of that work, which establishes an upper bound on their complexity that includes strictly local constraints.","PeriodicalId":133680,"journal":{"name":"Mathematics of Language","volume":"139 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114455685","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}
{"title":"On the Logical Complexity of Autosegmental Representations","authors":"Adam Jardine","doi":"10.18653/v1/W17-3403","DOIUrl":"https://doi.org/10.18653/v1/W17-3403","url":null,"abstract":"Autosegmental mapping from disjoint strings of tones and tone-bearing units, a commonly used mechanism in phonological analyses of tone patterns, is shown to not be definable in monadic second-order logic. This is abnormally complex in comparison to other phonological mappings, which have been shown to be monadic second-order definable. In contrast, generation of autosegmental structures from strings is demonstrated to be first-order definable.","PeriodicalId":133680,"journal":{"name":"Mathematics of Language","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117076514","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}
{"title":"Conjunctive Categorial Grammars","authors":"S. Kuznetsov, A. Okhotin","doi":"10.18653/v1/W17-3414","DOIUrl":"https://doi.org/10.18653/v1/W17-3414","url":null,"abstract":"Basic categorial grammars are enriched with a conjunction operation, and it is proved that the formalism obtained in this way has the same expressive power as conjunctive grammars, that is, context-free grammars enhanced with conjunction. It is also shown that categorial grammars with conjunction can be naturally embedded into the Lambek calculus with conjunction and disjunction operations. This further implies that a certain NP-complete set can be defined in the Lambek calculus with conjunction.","PeriodicalId":133680,"journal":{"name":"Mathematics of Language","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121467889","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}
{"title":"A Monotonicity Calculus and Its Completeness","authors":"Thomas F. Icard, L. Moss, William Tune","doi":"10.18653/v1/W17-3408","DOIUrl":"https://doi.org/10.18653/v1/W17-3408","url":null,"abstract":"One of the prominent mathematical features of natural language is the prevalence of “upward” and “downward” inferences involving determiners and other functional expressions. These inferences are associated with negative and positive polarity positions in syntax, and they also feature in computer implementations of textual entailment. Formal treatments of these phenomena began in the 1980’s and have been refined and expanded in the last 10 years. This paper takes a large step in the area by extending typed lambda calculus to the ordered setting . Not only does this provide a formal tool for reasoning about upward and downward inferences in natu-ral language, it also applies to the analysis of monotonicity arguments in mathematics more generally.","PeriodicalId":133680,"journal":{"name":"Mathematics of Language","volume":"284 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122957510","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}
{"title":"Why We Speak","authors":"R. Parikh","doi":"10.18653/v1/W17-3407","DOIUrl":"https://doi.org/10.18653/v1/W17-3407","url":null,"abstract":"We explain the relevance of Nash, Hoare and others in explaining Gricean implicature and cheap talk. We also develop a general model to address cases where communication is not cooperative, i..e cases of deception as well as cases where there is common knowledge of different interests in speaker and hearer. Tow models, one qualitative and one quantitative are introduced.","PeriodicalId":133680,"journal":{"name":"Mathematics of Language","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132579257","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}
{"title":"A Proof-Theoretic Semantics for Transitive Verbs with an Implicit Object","authors":"N. Francez","doi":"10.18653/v1/W17-3406","DOIUrl":"https://doi.org/10.18653/v1/W17-3406","url":null,"abstract":"The paper presents a proof-theoretic semantics for sentences headed by transitive verbs allowing an unexpressed (implicit) object. Such sentences are shown to have the same (proof-theoretic) meaning as the same sentences with an explicit existentially quantified object something. This semantics is contrasted with a model-theoretic semantics based on truthconditions in models. The models used contain in their domain “filler” elements, that have an unclear extra-theoretic significance with an unclear ontological commitments. In contrast, the proof-theoretic meaning is appealing to formal (syntactic) resources that carry no ontological commitment. Furthermore, the sameness of meaning is based on sameness of deductive role within a meaning-conferring proofsystem, based on use.","PeriodicalId":133680,"journal":{"name":"Mathematics of Language","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117150254","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}
{"title":"Graph Transductions and Typological Gaps in Morphological Paradigms","authors":"","doi":"10.18653/v1/W17-3411","DOIUrl":"https://doi.org/10.18653/v1/W17-3411","url":null,"abstract":"Several typological gaps have attracted a lot of interest in the linguistic literature recently. These concern the Person Case Constraint and the absence of ABA patterns in adjectival gradation, pronoun suppletion, case syncretism, and singular noun allomorphy, among others. This paper is the first to provide a unified explanation of all these phenomena, and it does so via weakly non-inverting graphtransductions. A pattern P is absent from the typology whenever such transductions cannot produce the graph corresponding to P from some fixed underlying base graph. I show that weakly non-inverting graphtransductions are particularly simple from a computational perspective, and consequently all these typological gaps follow from general simplicity desiderata.","PeriodicalId":133680,"journal":{"name":"Mathematics of Language","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121670627","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}
{"title":"DAG Automata for Meaning Representation","authors":"F. Drewes","doi":"10.18653/v1/W17-3409","DOIUrl":"https://doi.org/10.18653/v1/W17-3409","url":null,"abstract":"Languages of directed acyclic graphs (DAGs) are of interest in Natural Lanuage Processing because they can be used to capture the structure of semantic graphs like those of Abstract Meaning Represe ...","PeriodicalId":133680,"journal":{"name":"Mathematics of Language","volume":"36 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132388442","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}