相关论文: Information content in formal languages

The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…

Repeated idempotent elements are commonly used to characterise iterable behaviours in abstract models of computation. Therefore, given a monoid $M$, it is natural to ask how long a sequence of elements of $M$ needs to be to ensure the…

A quantitative method is suggested, where meanings of words, and grammatic rules about these, of a vocabulary are represented by real numbers. People meet randomly, and average their vocabularies if they are equal; otherwise they either…

Formal languages are sets of strings of symbols described by a set of rules specific to them. In this note, we discuss a certain class of formal languages, called regular languages, and put forward some elementary results. The properties of…

We lay the groundwork for a formal framework that studies scientific theories and can serve as a unified foundation for the different theories within physics. We define a scientific theory as a set of verifiable statements, assertions that…

Given a finite group with a generating subset there is a well-established notion of length for a group element given in terms of its minimal length expression as a product of elements from the generating set. Recently, certain quantities…

We continue our study of open and closed languages. We investigate how the properties of being open and closed are preserved under concatenation. We investigate analogues, in formal languages, of the separation axioms in topological spaces;…

Language difference is one of the factors that hinder the acquisition of second language skills. In this article, we introduce a novel solution that leverages the strength of deep neural networks to measure the semantic dissimilarity…

A filtration of a formal language L by a sequence s maps L to the set of words formed by taking the letters of words of L indexed only by s. We consider the languages resulting from filtering by all arithmetic progressions. If L is regular,…

While previous linguistic and psycholinguistic research on space has mainly analyzed spatial relations, the studies reported in this paper focus on how language distinguishes among spatial entities. Descriptive and experimental studies…

We introduce a new form of logical relation which, in the spirit of metric relations, allows us to assign each pair of programs a quantity measuring their distance, rather than a boolean value standing for their being equivalent. The…

The distance on a set is a comparative function. The smaller the distance between two elements of that set, the closer, or more similar, those elements are. Fr\'echet axiomatized the distance into what is today known as a metric. In this…

We define sequence patterns of length $n$ and level $\ell$ to be equivalence classes of sequences that have $n$ elements from the set of $\ell$ integer symbols $\{1,2,\ldots,\ell\}$ with no restriction on repetition, where the equivalence…

Measuring the distance between concepts is an important field of study of Natural Language Processing, as it can be used to improve tasks related to the interpretation of those same concepts. WordNet, which includes a wide variety of…

In this article, we present a fresh perspective on language, combining ideas from various sources, but mixed in a new synthesis. As in the minimalist program, the question is whether we can formulate an elegant formalism, a universal…

This article contains ideas and their elaboration for quantifiers, which appeared after checking in practice the experimental language of the formal knowledge representation YAFOLL [1]: - looking at for_all and exists quantifiers as…

The concepts of similarity and distance are crucial in data mining. We consider the problem of defining the distance between two data sets by comparing summary statistics computed from the data sets. The initial definition of our distance…

Languages vary widely in how meanings map to word forms. These mappings have been found to support efficient communication; however, this theory does not account for systematic relations within word forms. We examine how a restricted set of…

Accounts of semantic phenomena often involve extending types of meanings and revising composition rules at the same time. The concept of monads allows many such accounts -- for intensionality, variable binding, quantification and focus --…

Differential logical relations are a method to measure distances between higher-order programs. They differ from standard methods based on program metrics in that differences between functional programs are themselves functions, relating…