Related papers: Indexed Languages and Unification Grammars
We identify a subclass of the regular commutative languages that is closed under the iterated shuffle, or shuffle closure. In particular, it is regularity-preserving on this subclass. This subclass contains the commutative group languages…
We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined…
The world's 7,000+ languages vary widely in the availability of resources for NLP, motivating efforts to systematically categorize them by their degree of resourcefulness (Joshi et al., 2020). A similar disparity exists among programming…
Zero-resource word segmentation and clustering systems aim to tokenise speech into word-like units without access to text labels. Despite progress, the induced lexicons are still far from perfect. In an idealised setting with gold word…
Unsupervised parsing, also known as grammar induction, aims to infer syntactic structure from raw text. Recently, binary representation has exhibited remarkable information-preserving capabilities at both lexicon and syntax levels. In this…
Language is contextual and sheaf theory provides a high level mathematical framework to model contextuality. We show how sheaf theory can model the contextual nature of natural language and how gluing can be used to provide a global…
The dot-depth hierarchy is a classification of star-free languages. It is related to the quantifier alternation hierarchy of first-order logic over finite words. We consider fragments of languages with dot-depth 1/2 and dot-depth 1 obtained…
The \emph{index set} of a computable structure $\mathcal{A}$ is the set of indices for computable copies of $\mathcal{A}$. We determine the complexity of the index sets of various mathematically interesting structures, including arbitrary…
Language understanding is a key scientific issue in the fields of cognitive and computer science. However, the two disciplines differ substantially in the specific research questions. Cognitive science focuses on analyzing the specific…
In the article the fact is verified that the list of words selected by formal statistical methods (frequency and functional genre unrestrictedness) is not a conglomerate of non-related words. It creates a system of interrelated items and it…
Lexicon-Grammar tables are a very rich syntactic lexicon for the French language. This linguistic database is nevertheless not directly suitable for use by computer programs, as it is incomplete and lacks consistency. Tables are defined on…
Finite chase, or alternatively chase termination, is an important condition to ensure the decidability of existential rule languages. In the past few years, a number of rule languages with finite chase have been studied. In this work, we…
The idea of Universal Grammar (UG) as the hypothetical linguistic structure shared by all human languages harkens back at least to the 13th century. The best known modern elaborations of the idea are due to Chomsky. Following a devastating…
Scheduling languages express to a compiler a sequence of optimizations to apply. Compilers that support a scheduling language interface allow exploration of compiler optimizations, i.e., exploratory compilers. While scheduling languages…
Clans are combinatorial objects indexing the orbits of $GL(\mathbb{C}^p) \times GL(\mathbb{C}^q)$ on the variety of flags in $\mathbb{C}^{p+q}$. This geometry leads to a partial order on the set of clans analogous to weak Bruhat order on…
While context-free grammars are characterized by a simple proof-theoretic grammatical formalism namely categorial grammar and its logic the Lambek calculus, no such characterizations were known for tree-adjoining grammars, and even for any…
Dictionaries are inherently circular in nature. A given word is linked to a set of alternative words (the definition) which in turn point to further descendants. Iterating through definitions in this way, one typically finds that…
Controlled natural languages (CNL) with a direct mapping to formal logic have been proposed to improve the usability of knowledge representation systems, query interfaces, and formal specifications. Predictive editors are a popular approach…
Understanding the representations of different languages in multilingual language models is essential for comprehending their cross-lingual properties, predicting their performance on downstream tasks, and identifying any biases across…
This paper introduces an objective metric for evaluating a parsing scheme. It is based on Shannon's original work with letter sequences, which can be extended to part-of-speech tag sequences. It is shown that this regular language is an…