Related papers: Representations of Circular Words
We present a system to translate natural language sentences to formulas in a formal or a knowledge representation language. Our system uses two inverse lambda-calculus operators and using them can take as input the semantic representation…
We use evaluation representations to give a complete classification of the finite-dimensional simple modules of twisted current algebras. This generalizes and unifies recent work on multiloop algebras, current algebras, equivariant map…
Different semantic interpretation tasks such as text entailment and question answering require the classification of semantic relations between terms or entities within text. However, in most cases it is not possible to assign a direct…
Semi-direct products of finite groups have permutation representations that are constructed from the permutation representations of their constituents. One can envision these in a metaphoric sense in which a rope is made from a bundle of…
In this paper, we survey some properties, encoding, and bijections involving combinatorial maps, double occurrence words, and chord diagrams. We particularly study quasi-trees from a purely combinatorial point of view and derive a…
We consider partial words with a unique position starting a power. We show that over a $k$ letter alphabet, a partial word with a unique position starting a square can contain at most $k$ squares. This is in contrast to full words which can…
We observe that the vocabulary used to construct the "answer" to problems in computer algebra can have a dramatic effect on the computational complexity of solving that problem. We recall a formalization of this observation and explain the…
I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…
Recent work has proposed that language models perform computation by manipulating one-dimensional representations of concepts ("features") in activation space. In contrast, we explore whether some language model representations may be…
We develop a system that formally represents spatial semantics concepts within natural language descriptions of spatial arrangements. The system builds on a model of spatial semantics representation according to which words in a sentence…
We consider symbolic flows over finite alphabets and study certain kinds of repetitions in these sequences. Positive and negative results for the existence of such repetitions are given for codings of interval exchange transformations and…
The visual representation of concepts or ideas through the use of simple shapes has always been explored in the history of Humanity, and it is believed to be the origin of writing. We focus on computational generation of visual symbols to…
Word embeddings are useful for a wide variety of tasks, but they lack interpretability. By rotating word spaces, interpretable dimensions can be identified while preserving the information contained in the embeddings without any loss. In…
Techniques in which words are represented as vectors have proved useful in many applications in computational linguistics, however there is currently no general semantic formalism for representing meaning in terms of vectors. We present a…
The word inference problem is to determine languages such that the information on the number of occurrences of those subwords in the language can uniquely identify a word. A considerable amount of work has been done on this problem, but the…
Classical tensors, the familiar mathematical objects denoted by symbols such as $t_{i}$, $t^{ij}$ and $t_{k}^{ij}$, are usually interpreted either as 'coordinatizable objects' with coordinates changing in a specific way under a change of…
Binary relations are an important abstraction arising in many data representation problems. The data structures proposed so far to represent them support just a few basic operations required to fit one particular application. We identify…
This paper describes an alternative method of generating fixed points of certain substitution systems. This method centres on taking infinite words consisting of one repeated letter per word. These infinite words are then interlaced to form…
Decision trees and systems of decision rules are widely used as classifiers, as a means for knowledge representation, and as algorithms. They are among the most interpretable models for data analysis. The study of the relationships between…
Distributed representations of words learned from text have proved to be successful in various natural language processing tasks in recent times. While some methods represent words as vectors computed from text using predictive model…