Montague Grammar

Partee, Barbara H.

doi:10.1016/b978-0-08-097086-8.53022-0

Cited by 4 publications

(3 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For automated commonsense reasoning, negation in natural language has to be treated in a formal manner. Traditional approaches tackle this problem by using Montague grammars together with Kripke semantics for modal logics [23]. Here, negation is discussed in the context of performative verbs, e.g.…”

Section: Commonsense Reasoning and Negationmentioning

confidence: 99%

Negation in Cognitive Reasoning

Schon,

Siebert,

Stolzenburg

2020

Preprint

View full text Add to dashboard Cite

Negation is both an operation in formal logic and in natural language by which a proposition is replaced by one stating the opposite, as by the addition of "not" or another negation cue. Treating negation in an adequate way is required for cognitive reasoning, which comprises commonsense reasoning and text comprehension. One task of cognitive reasoning is answering questions given by sentences in natural language. There are tools based on discourse representation theory to convert sentences automatically into a formal logical representation. However, since the knowledge in logical databases in practice always is incomplete, forward reasoning of automated reasoning systems alone does not suffice to derive answers to questions because, instead of complete proofs, often only partial positive knowledge can be derived. In consequence, negative information from negated expressions does not help in this context, because only negative knowledge can be derived from this. Therefore, we aim at reducing syntactic negation, strictly speaking, the negated event or property, to its inverse. This lays the basis of cognitive reasoning employing both logic and machine learning for general question answering. In this paper, we describe an effective procedure to determine the negated event or property in order to replace it with it inverse and our overall system for cognitive reasoning. We demonstrate the procedure with examples and evaluate it with several benchmarks.

show abstract

Section: Commonsense Reasoning and Negationmentioning

confidence: 99%

Negation in Cognitive Reasoning

Schon,

Siebert,

Stolzenburg

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…It is not only grammatical structure that imposes consecutive restrictions on sample-space of words as the sentence progresses, the need for intelligibility has the same effect. Without (at least partial) hierarchical structures in the formation of sentences, their interpretation would become very hard [46]. However, nested structures in sentences will generally not be strictly realised.…”

Section: Fig 1: Rank Ordered Distribution Of Word Frequencies Formentioning

confidence: 99%

Understanding Zipf's law of word frequencies through sample-space collapse in sentence formation

Thurner

Hanel

Liu

et al. 2015

J. R. Soc. Interface.

View full text Add to dashboard Cite

The formation of sentences is a highly structured and history-dependent process. The probability of using a specific word in a sentence strongly depends on the 'history' of word usage earlier in that sentence. We study a simple history-dependent model of text generation assuming that the sample-space of word usage reduces along sentence formation, on average. We first show that the model explains the approximate Zipf law found in word frequencies as a direct consequence of sample-space reduction. We then empirically quantify the amount of sample-space reduction in the sentences of 10 famous English books, by analysis of corresponding word-transition tables that capture which words can follow any given word in a text. We find a highly nested structure in these transition tables and show that this 'nestedness' is tightly related to the power law exponents of the observed word frequency distributions. With the proposed model, it is possible to understand that the nestedness of a text can be the origin of the actual scaling exponent and that deviations from the exact Zipf law can be understood by variations of the degree of nestedness on a book-by-book basis. On a theoretical level, we are able to show that in the case of weak nesting, Zipf's law breaks down in a fast transition. Unlike previous attempts to understand Zipf's law in language the sample-space reducing model is not based on assumptions of multiplicative, preferential or self-organized critical mechanisms behind language formation, but simply uses the empirically quantifiable parameter 'nestedness' to understand the statistics of word frequencies.

show abstract

“…The existence of grammatical and contextual constraints allow us-at the receiving part of a communication-to complete sentences in advance, and to anticipate words that will appear later. This (at least partially) ordered hierarchical structure guides sentence formation and allows a receiver to robustly decode messages [20].…”

Section: Introductionmentioning

confidence: 99%

The role of grammar in transition-probabilities of subsequent words in English text

Hanel¹,

Thurner²

2018

Preprint

View full text Add to dashboard Cite

Sentence formation is a highly structured, history-dependent, and sample-space reducing (SSR) process. While the first word in a sentence can be chosen from the entire vocabulary, typically, the freedom of choosing subsequent words gets more and more constrained by grammar and context, as the sentence progresses. This sample-space reducing property offers a natural explanation of Zipf's law in word frequencies, however, it fails to capture the structure of the word-to-word transition probability matrices of English text. Here we adopt the view that grammatical constraints (such as subject-predicate-object) locally re-order the word order in sentences that are sampled with a SSR word generation process. We demonstrate that superimposing grammatical structure-as a local word re-ordering (permutation) process-on a sample-space reducing process is sufficient to explain both, word frequencies and word-to-word transition probabilities. We compare the quality of the grammatically ordered SSR model in reproducing several test statistics of real texts with other text generation models, such as the Bernoulli model, the Simon model, and the Monkey typewriting model.

show abstract

Montague Grammar

Cited by 4 publications

References 36 publications

Negation in Cognitive Reasoning

Negation in Cognitive Reasoning

Understanding Zipf's law of word frequencies through sample-space collapse in sentence formation

The role of grammar in transition-probabilities of subsequent words in English text

Contact Info

Product

Resources

About