Related papers: Priority Union and Generalization in Discourse Gra…
This paper studies combinatorial properties of the 'complex of planar injective words', a chain complex of modules over the Temperley-Lieb algebra that arose in our work on homological stability. Despite being a linear rather than a…
We address the problem of structural disambiguation in syntactic parsing. In psycholinguistics, a number of principles of disambiguation have been proposed, notably the Lexical Preference Rule (LPR), the Right Association Principle (RAP),…
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…
This paper provides a general framework to explore the possibility of agenda manipulation-proof and proper consensus-based preference aggregation rules, so powerfully called in doubt by a disputable if widely shared understanding of Arrow's…
In this paper we provide for parsing with respect to grammars expressed in a general TFS-based formalism, a restriction of ALE. Our motivation being the design of an abstract (WAM-like) machine for the formalism, we consider parsing as a…
Anaphora resolution is one of the most active research areas in natural language processing. This study examines focusing as a tool for the resolution of pronouns which are a kind of anaphora. Focusing is a discourse phenomenon like…
Although unification can be used to implement a weak form of $\beta$-reduction, several linguistic phenomena are better handled by using some form of $\lambda$-calculus. In this paper we present a higher order feature description calculus…
Most current models of word representations(e.g.,GloVe) have successfully captured fine-grained semantics. However, semantic similarity exhibited in these word embeddings is not suitable for resolving bridging anaphora, which requires the…
Different constructions in the recursion theory use the so-called priority arguments. A general scheme was suggested by A.~Lachlan. Based on his work, we define the notion of a priority-closed class of requirements. Then, for a specific…
Given an order of the underlying alphabet we can lift it to the states of a finite deterministic automaton: to compare states we use the order of the strings reaching them. When the order on strings is the co-lexicographic one \emph{and}…
The Abella interactive theorem prover has proven to be an effective vehicle for reasoning about relational specifications. However, the system has a limitation that arises from the fact that it is based on a simply typed logic:…
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…
The aim of this paper is to summarize some recently obtained relations between the Ablowitz-Ladik hierarchy (ALH) and other integrable equations. It has been shown that solutions of finite subsystems of the ALH can be used to derive a wide…
Aligning language models to human expectations, e.g., being helpful and harmless, has become a pressing challenge for large language models. A typical alignment procedure consists of supervised fine-tuning and preference learning. Most…
This paper focuses on two disparate aspects of German syntax from the perspective of parallel grammar development. As part of a cooperative project, we present an innovative approach to auxiliaries and multiple genitive NPs in German. The…
The theory of finite automata concerns itself with words in a free monoid together with concatenation and without further structure. There are, however, important applications which use alphabets which are structured in some sense. We…
The expression problem describes a fundamental tradeoff between two types of extensibility: extending a type with new operations, such as by pattern matching on an algebraic data type in functional programming, and extending a type with new…
We provide a unified account of sentence-level and text-level anaphora within the framework of a dependency-based grammar model. Criteria for anaphora resolution within sentence boundaries rephrase major concepts from GB's binding theory,…
We extend Agler's notion of a function algebra defined in terms of test functions to include products, in analogy with the practice in real algebraic geometry, and hence the term preordering in the title. This is done over abstract sets and…
For the word $\omega = \underbrace{11\ldots 1}_{x_1}\underbrace{22\ldots2}_{x_2}\ldots\underbrace{nn\ldots n}_{x_n},$ denote by $\mathsf{A}(x_1, x_2, \ldots, x_n)$ the number of its anagrams without fixed letters. While the function…