Logic Natural Language

Thus, the logic and semantics of sentences of natural language cannot be captured by the calculus. One distorts the semantics and logic of natural language when one studies them by means of the calculus. By contrast, the calculus, ...

Frege's invention of the predicate calculus has been the most influential event in the history of modern logic. The calculus’ place in logic is so central that many philosophers think, in fact, of it when they think of logic. This book challenges the position in contemporary logic and philosophy of language of the predicate calculus claiming that it is based on mistaken assumptions. Ben-Yami shows that the predicate calculus is different from natural language in its fundamental semantic characteristics, primarily in its treatment of reference and quantification, and that as a result the calculus is inadequate for the analysis of the semantics and logic of natural language. Ben-Yami develops both an alternative analysis of the semantics of natural language and an alternative deductive system comparable in its deductive power to first order predicate calculus but more adequate than it for the representation of the logic of natural language. Ben-Yami's book is a revolutionary challenge to classical first order predicate calculus, casting doubt on many of the central claims of modern logic.

Eliminating The Universe Logical Properties Of Natural Language

“Computational complexity of polyadic lifts of generalized quantifiers in natural language.” In: Linguistics and Philosophy 33, pp. 215–250. Tarski, Alfred (1931). “The concept of truth in formalized languages.” In: Logic, Semantics and ...

This book synthesizes the author's work (1980s-2015) on the logical expressive power of natural language. It extends the tools and concepts of model theory as used in (higher order) predicate logic to the study of natural language semantics. It focuses on boolean structure, generalized quantification (separated from variable binding), covering some cases of anaphora. Different categories — predicates, adjective, quantifiers — are modeled by non-isomorphic boolean lattices.Of empirical linguistic interest is the expressibility of many natural classes of quantifiers defined in terms of their logical (automorphism invariant) properties. Some of these correlate with classes used syntactically in generative grammar. In other cases we find general (possibly universal) constraints on possible quantifier denotations in natural language.Also of novel logical interest are entailment paradigms that depend on relations between pairs or triples of generalized quantifier denoting expressions, ones that are in some cases inherently vague. In addition we note novel binary quantifiers that lie beyond the 'Frege boundary' in that they are provably not identical to any iterated application of unary quantifiers.Of philosophical interest is the existence of models which make the same sentences true as standard models but which lack a universe and hence, seemingly, a notion of 'reference'. Moreover, these models generalize to ones in which we can represent (some) intensional expressions without the use of novel ontological objects, such as 'possible worlds' or 'propositions'.

Deductive Logic in Natural Language

others , that discuss possible worlds , a metaphysical notion related to our possible situations and preferred by some as a conceptual basis for logic . Ludlow , Peter , Readings in the Philosophy of Language ( Cambridge , Mass .

This text offers an innovative approach to the teaching of logic, which is rigorous but entirely non-symbolic. By introducing students to deductive inferences in natural language, the book breaks new ground pedagogically. Cannon focuses on such topics as using a tableaux technique to assess inconsistency; using generative grammar; employing logical analyses of sentences; and dealing with quantifier expressions and syllogisms. An appendix covers truth-functional logic.

Logic Natural Language

The main purpose of this volume is to demonstrate several significant distinctions between the predicate calculus and natural language, distinctions that make the former inadequate for the study of the semantics and logic of the latter.

The main purpose of this volume is to demonstrate several significant distinctions between the predicate calculus and natural language, distinctions that make the former inadequate for the study of the semantics and logic of the latter.

Logical Aspects of Quantification in Natural Language

paper , appearing under the title of English as a Formal Language . ... expressed in so many words since Frege's invention of his logical notation in Begriffsschrift ( 1879 ) , according to which linguistic form in natural language is ...

Elucidates the relation between quantifiers in formal logic and quantifiers in natural language. Demystifies the theoretical apparatus of contemporary logic as it provides theoretical explanations concerning quantification in natural language, and idiomatic quantifiers in ordinary English in particular.

Prolog and Natural Language Analysis

On the utilitarianside, we shall introducethe logic-programminglanguage Prolog, whose backbone is the definite-clause formalism, as a tool for implementing the basic components of natural-language-processingsystems.

Natural Language Processing with Python

In the remainder of this chapter, we will represent the meaning of natural language expressions by translating them into first-order logic. Not all of natural language se- mantics can be expressed in first-order logic.

This book offers a highly accessible introduction to natural language processing, the field that supports a variety of language technologies, from predictive text and email filtering to automatic summarization and translation. With it, you'll learn how to write Python programs that work with large collections of unstructured text. You'll access richly annotated datasets using a comprehensive range of linguistic data structures, and you'll understand the main algorithms for analyzing the content and structure of written communication. Packed with examples and exercises, Natural Language Processing with Python will help you: Extract information from unstructured text, either to guess the topic or identify "named entities" Analyze linguistic structure in text, including parsing and semantic analysis Access popular linguistic databases, including WordNet and treebanks Integrate techniques drawn from fields as diverse as linguistics and artificial intelligence This book will help you gain practical skills in natural language processing using the Python programming language and the Natural Language Toolkit (NLTK) open source library. If you're interested in developing web applications, analyzing multilingual news sources, or documenting endangered languages -- or if you're simply curious to have a programmer's perspective on how human language works -- you'll find Natural Language Processing with Python both fascinating and immensely useful.

Studies in Functional Logical Semiotics of Natural Language

... Elements of Symbolic Logic, § 48. * Cf. Aristotle, Categories, footnote 16 above. * Cf. Frege, “Úber Sinn und Bedeutung”, footnote 6 above. circumstances. He adds that we must demand that in a PROPER NAMES IN NATURAL LANGUAGE 107.

Model Generation for Natural Language Interpretation and Analysis

(Moneypenny, Tomorrow never dies) The primary hypothesis of computational logic-based semantics is that logic can be used to capture the meaning of natural language. A logic consist of a formal language, i.e., a syntax, and a semantics ...

Mathematical theorem proving has undergone an impressive development during the last two decades, resulting in a variety of powerful systems for applications in mathematical deduction and knowledge processing. Natural language processing has become a topic of outstanding relevance in information technology, mainly due to the explosive growth of the Web, where by far the largest part of information is encoded in natural language documents. This monograph focuses on the development of inference tools tailored to applications in natural language processing by demonstrating how the model generation paradigm can be used as a framework for the support of specific tasks in natural language interpretation and natural language based inference in a natural way. The book appears at a pivotal moment, when much attention is being paid to the task of adding a semantic layer to the Web, and representation and processing of natural language based semantic information pops up as a primary requirement for further technological progress.

Language Form and Logic

1 Introduction When we use the expression ' Natural Logic ' , we intend a conception of logic wherein logic ( or at least some part of it ) and logical relations are expressed in terms of natural language forms or structures .

This book takes an idea first explored by medieval logicians 800 years ago and revisits it armed with the tools of contemporary linguistics, logic, and computer science. The idea - the Holy Grail of the medieval logicians - was the thought that all of logic could be reduced to two very simple rules that are sensitive to logical polarity (for example, the presence and absence of negations). Ludlow and Živanović pursue this idea and show how it has profound consequences for our understanding of the nature of human inferential capacities. They also show its consequences for some of the deepest issues in contemporary linguistics, including the nature of quantification, puzzles about discourse anaphora and pragmatics, and even insights into the source of aboutness in natural language. The key to their enterprise is a formal relation they call "p-scope" - a polarity-sensitive relation that controls the operations that can be carried out in their Dynamic Deductive System. They show that with p-scope in play, deductions can be carried out using sublogical operations like those they call COPY and PRUNE - operations that are simple syntactic operations on sentences. They prove that the resulting deductive system is complete and sound. The result is a beautiful formal tapestry in which p-scope unlocks important properties of natural language, including the property of "restrictedness," which they prove to be equivalent to the semantic notion of conservativity. More than that, they show that restrictedness is also a key to understanding quantification and discourse anaphora, and many other linguistic phenomena.

Formal Semantics and Pragmatics for Natural Languages

NEGATIVE COREFERENCE: GENERALIZING QUANTIFICATION FOR NATURAL LANG UAGE I shall argue here that standard logic is not sufficiently rich to represent the means natural languages use to restrict the coreference of noun phrases.

The essays in this collection are the outgrowth of a workshop, held in June 1976, on formal approaches to the semantics and pragmatics of natural languages. They document in an astoundingly uniform way the develop ments in the formal analysis of natural languages since the late sixties. The avowed aim of the' workshop was in fact to assess the progress made in the application of formal methods to semantics, to confront different approaches to essentially the same problems on the one hand, and, on the other, to show the way in relating semantic and pragmatic explanations of linguistic phenomena. Several of these papers can in fact be regarded as attempts to close the 'semiotic circle' by bringing together the syntactic, semantic and pragmatic properties of certain constructions in an explanatory framework thereby making it more than obvious that these three components of an integrated linguistic theory cannot be as neatly separated as one would have liked to believe. In other words, not only can we not elaborate a syntactic description of (a fragment of) a language and then proceed to the semantics (as Montague pointed out already forcefully in 1968), we cannot hope to achieve an adequate integrated syntax and semantics without paying heed to the pragmatic aspects of the constructions involved. The behavior of polarity items, 'quantifiers' like any, conditionals or even logical particles like and and or in non-indicative sentences is clear-cut evidence for the need to let each component of the grammar inform the other.

Natural Language and Speech

In D. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, vol. II, pages 497–604, Reidel, ... Hintikka, J.: Logic, Language Games and Information. ... Sanchez Valencia, V.: Studies on Natural Logic and Categorial Grammar.

This volume in the Basic Research Series consists of the proceedings of the Symposium on Natural Language and Speech held during the ESPRIT Conference of November 1991 - a conference that serves to open up ESPRIT results not only to the ESPRIT community but also to the entire European IT industry and its users. The symposium is organised by the newly launched Network of Excellence on Language and Speech (3701) which brings together the foremost European experts and institutions in these two domains. By bringing together these two communities, which have so far been working in relative isolation from each other, the network aims to augment the focusing of research onto the long-term goal of the "construction of an integrated model of the cognitive chain linking speech to reasoning via natural language". To advance towards this industrially significant goal, the network operates at different levels - a strategy for research, a coordination for the training of needed researchers and a coordination of the use of its resource and communication infrastructure for the most efficient interworking of the members of the community who are spread all over Europe. This symposium is a small but significant building block for the achievement of the goals of the network.

Natural Language Processing and Computational Linguistics 2

In short, propositional logic is a declarative system that makes it possible to express partial knowledge, disjunctions, negatives, etc. However, contrary to natural languages, in propositional logic, meaning is independent of the ...

Natural Language Processing (NLP) is a scientific discipline which is found at the intersection of fields such as Artificial Intelligence, Linguistics, and Cognitive Psychology. This book presents in four chapters the state of the art and fundamental concepts of key NLP areas. Are presented in the first chapter the fundamental concepts in lexical semantics, lexical databases, knowledge representation paradigms, and ontologies. The second chapter is about combinatorial and formal semantics. Discourse and text representation as well as automatic discourse segmentation and interpretation, and anaphora resolution are the subject of the third chapter. Finally, in the fourth chapter, I will cover some aspects of large scale applications of NLP such as software architecture and their relations to cognitive models of NLP as well as the evaluation paradigms of NLP software. Furthermore, I will present in this chapter the main NLP applications such as Machine Translation (MT), Information Retrieval (IR), as well as Big Data and Information Extraction such as event extraction, sentiment analysis and opinion mining.

Reflective Equilibrium and the Principles of Logical Analysis

The key root of modern modal logic was C. I. Lewis's effort to offer a (“strict”) implication that would more faithfully capture the behaviour of common natural language conditionals (see Lewis, 1917). Relevant logic (Anderson and ...

This book offers a comprehensive account of logic that addresses fundamental issues concerning the nature and foundations of the discipline. The authors claim that these foundations can not only be established without the need for strong metaphysical assumptions, but also without hypostasizing logical forms as specific entities. They present a systematic argument that the primary subject matter of logic is our linguistic interaction rather than our private reasoning and it is thus misleading to see logic as revealing "the laws of thought". In this sense, fundamental logical laws are implicit to our "language games" and are thus more similar to social norms than to the laws of nature. Peregrin and Svoboda also show that logical theories, despite the fact that they rely on rules implicit to our actual linguistic practice, firm up these rules and make them explicit. By carefully scrutinizing the project of logical analysis, the authors demonstrate that logical rules can be best seen as products of the so called reflective equilibrium. They suggest that we can profit from viewing languages as "inferential landscapes" and logicians as "geographers" who map them and try to pave safe routes through them. This book is an essential resource for scholars and researchers engaged with the foundations of logical theories and the philosophy of language.

Controlled Natural Language

Workshop on Controlled Natural Language, CNL 2009, Marettimo Island, Italy, June 8-10, 2009, Revised Papers Norbert E ... Kamp, H., Reyle, U.: From Discourse to Logic; An Introduction to Modeltheoretic Semantics of Natural Language, ...

This book constitutes the thoroughly refereed post-workshop proceedings of the Workshop on Controlled Natural Language, CNL 2009, held in Marettimo Island, Italy, in June 2009. The 16 revised full papers presented together with 1 invited lecture were carefully reviewed and selected during two rounds of reviewing and improvement from 31 initial submissions. The papers are roughly divided into the two groups language aspects and tools and applications. Note that some papers fall actually into both groups: using a controlled natural language in an application domain often requires domain-specific language features.

Natural Language Semantics

Context dependence, a pervasive property of natural language expressions, was surveyed in chapter 4. ... and then to assign values to their complex expressions based on values assigned to the expressions making them up—logic.

An introduction to natural language semantics that offers an overview of the empirical domain and an explanation of the mathematical concepts that underpin the discipline. This textbook offers a comprehensive introduction to the fundamentals of those approaches to natural language semantics that use the insights of logic. Many other texts on the subject focus on presenting a particular theory of natural language semantics. This text instead offers an overview of the empirical domain (drawn largely from standard descriptive grammars of English) as well as the mathematical tools that are applied to it. Readers are shown where the concepts of logic apply, where they fail to apply, and where they might apply, if suitably adjusted. The presentation of logic is completely self-contained, with concepts of logic used in the book presented in all the necessary detail. This includes propositional logic, first order predicate logic, generalized quantifier theory, and the Lambek and Lambda calculi. The chapters on logic are paired with chapters on English grammar. For example, the chapter on propositional logic is paired with a chapter on the grammar of coordination and subordination of English clauses; the chapter on predicate logic is paired with a chapter on the grammar of simple, independent English clauses; and so on. The book includes more than five hundred exercises, not only for the mathematical concepts introduced, but also for their application to the analysis of natural language. The latter exercises include some aimed at helping the reader to understand how to formulate and test hypotheses.

The Natural Language for Artificial Intelligence

It is worth noting that computation and natural language are both accompanied by logic: “From the beginning of mathematics there have been intimate connections between logic and computation. The exact nature of these connections is ...

The Natural Language for Artificial Intelligence presents the biological and logical structure typical of human language in its dynamic mediating process between reality and the human mind. The book explains linguistic functioning in the dynamic process of human cognition when forming meaning. After that, an approach to artificial intelligence (AI) is outlined, which works with a more restricted concept of natural language that leads to flaws and ambiguities. Subsequently, the characteristics of natural language and patterns of how it behaves in different branches of science are revealed to indicate ways to improve the development of AI in specific fields of science. A brief description of the universal structure of language is also presented as an algorithmic model to be followed in the development of AI. Since AI aims to imitate the process of the human mind, the book shows how the cross-fertilization between natural language and AI should be done using the logical-axiomatic structure of natural language adjusted to the logical-mathematical processes of the machine. Presents a comprehensive approach to natural language and its inherent and complex dynamics Develops language content as the next frontier, identifying the universal structure of language as a common structure that appears in both AI and cognitive computing Explains the standard structure present in cognition and AI, making them interchangeable Offers examples of the application of the universal language model in image analysis and conventional language

Natural Language Processing and Information Systems

A Natural Language Interface Supporting Complex Logic Questions for Relational Databases Ngoc Phuoc An Vo(B), Octavian Popescu, Vadim Sheinin, Elahe Khorasani, and Hangu Yeo IBM Research, Yorktown Heights, ...

This book constitutes the refereed proceedings of the 24th International Conference on Applications of Natural Language to Information Systems, NLDB 2019, held in Salford, UK, in June 2019. The 21 full papers and 16 short papers were carefully reviewed and selected from 75 submissions. The papers are organized in the following topical sections: argumentation mining and applications; deep learning, neural languages and NLP; social media and web analytics; question answering; corpus analysis; semantic web, open linked data, and ontologies; natural language in conceptual modeling; natural language and ubiquitous computing; and big data and business intelligence.

Natural Language Processing in Artificial Intelligence NLPinAI 2020

The View from Building 20: Essays in Linguistic in Honor od Sylvain Bromberger, pp. 195–227. ... In: Introduction to Model-Theoretic Semantics of Natural Language, Formal Logic and Discourse Representation Theory.

This book covers theoretical work, applications, approaches, and techniques for computational models of information and its presentation by language (artificial, human, or natural in other ways). Computational and technological developments that incorporate natural language are proliferating. Adequate coverage encounters difficult problems related to ambiguities and dependency on context and agents (humans or computational systems). The goal is to promote computational systems of intelligent natural language processing and related models of computation, language, thought, mental states, reasoning, and other cognitive processes.