Type-logical semantics

2018 ◽  
Author(s):  
Reinhard Muskens
Keyword(s):  
Type Theory ◽  
Predicate Logic ◽  
Logical Form ◽  
Ordinary Language ◽  
Linguistic Meaning ◽  
Lexical Meaning ◽  
Logical Language ◽  
Competing Hypotheses ◽  
Richard Montague ◽  
Logical Semantics

Type-logical semantics studies linguistic meaning with the help of the theory of types. The latter originated with Russell as an answer to the paradoxes, but has the additional virtue that it is very close to ordinary language. In fact, type theory is so much more similar to language than predicate logic is, that adopting it as a vehicle of representation can overcome the mismatches between grammatical form and predicate logical form that were observed by Frege and Russell. The grammatical forms of ordinary language sentences consequently may be taken to be much less misleading than logicians in the first half of the twentieth century often thought them to be. This was realized by Richard Montague, who used the theory of types to translate fragments of ordinary language into a logical language. Semantics is commonly divided into lexical semantics, which studies the meaning of words, and compositional semantics, which studies the way in which complex phrases obtain a meaning from their constituents. The strength of type-logical semantics lies with the latter, but type-logical theories can be combined with many competing hypotheses about lexical meaning, provided these hypotheses are expressed using the language of type theory.

Pohľad Na Pomenovanie Cez Prizmu Teoretických Rámcov A Slovníkového Hesla

2018 ◽  
Vol 69 (3) ◽  
pp. 277-301
Author(s):  
Alexandra Jarošová
Keyword(s):  
Corpus Linguistics ◽  
Cognitive Linguistics ◽  
Linguistic Meaning ◽  
Extended Model ◽  
Theoretical Frameworks ◽  
Departure Point ◽  
Lexical Meaning ◽  
Linguistic Pragmatics ◽  
Situational Contexts ◽  
Methodological Procedures

Abstract The first part of this paper outlines the relevant aspects of functional structuralism serving lexicographers as a departure point for building a model of lexical meaning useable in the Dictionary of Contemporary Slovak Language. This section also points to some aspects of Klára Buzássyová’s research on lexis and word­formation that have enriched the functional­structuralist paradigm. The second section shows other theoretical and methodological frameworks, such as linguistic pragmatics, cognitive linguistics and corpus linguistics (all of them departing in some respect from the structuralism and, in other aspects, being complementary with it) that can enhance the structuralist basis of the model. The third section outlines an extended model of lexical meaning that represents a synthesis of all those theoretical frameworks and, at the same time, represents a reflection of three language constituents: 1. The social constituent is present in consideration of communicative functions of utterances, naming functions of lexical units, functional styles and registers, language norms, and situational contexts; 2. The psychological component takes the form of consideration of the prototype effect, the abolition of boundaries between linguistic meaning and other parts of cognition; 3. Thanks to the structural/systematic component, a description of paradigmatic and syntagmatic behaviour of words can be performed, and an inventory of formal­content units and categories (lexemes, lexies, word­forming and grammatical structures) can be provided. In our dictionary practice, the above­mentioned model is reflected in the methodological procedures as follows: 1. Systemization of repetitive (regular, standardized) phenomena; 2. Prototypicalization of meaning description; 3. Contextualization/encyclopedization of meaning description; 4. Pragmatization of meaning description; 5. Continualized presentation of language phenomena, i.e., introduction of numerous phenomena of transient and indeterminate nature and indicating the existence of a semantic­pragmatic and lexical­grammatical continuum; 6. “Discretization” of combinatorial continuum, i.e., identification and description of entrenched word combinations with naming functions.

4 Type Theory and Ordinary Language

1979 ◽  
pp. 127-152
Author(s):  
Terence Parsons
Keyword(s):  
Type Theory ◽  
Ordinary Language

scholarly journals Integrating Type Theory and Distributional Semantics: A Case Study on Adjective–Noun Compositions

2016 ◽  
Vol 42 (4) ◽  
pp. 703-725 ◽  
Author(s):  
Nicholas Asher ◽  
Tim Van de Cruys ◽  
Antoine Bride ◽  
Márta Abrusán
Keyword(s):  
Type Theory ◽  
Semantic Information ◽  
Semantic Theory ◽  
Formal Semantic ◽  
Distributional Semantics ◽  
Semantic Approach ◽  
Lexical Meaning ◽  
Semantic Framework ◽  
Algebraic Interpretation

In this article, we explore an integration of a formal semantic approach to lexical meaning and an approach based on distributional methods. First, we outline a formal semantic theory that aims to combine the virtues of both formal and distributional frameworks. We then proceed to develop an algebraic interpretation of that formal semantic theory and show how at least two kinds of distributional models make this interpretation concrete. Focusing on the case of adjective–noun composition, we compare several distributional models with respect to the semantic information that a formal semantic theory would need, and we show how to integrate the information provided by distributional models back into the formal semantic framework.

scholarly journals The Speech Acts in Nali and Salim’s Two Poems

2021 ◽  
Vol 8 (2) ◽  
pp. 56-80
Author(s):  
Hersh Chato Hussein
Keyword(s):  
Speech Acts ◽  
Scientific Research ◽  
Ordinary Language ◽  
Point Of View ◽  
Linguistic Meaning ◽  
Research Institutions ◽  
Classical Poetry

This study is under the title of “The Speech Acts in Nali and Salim’s Two Poems”. It is an attempt to analyze these two poems in a pragmatic point of view, particularly in terms of speech acts. The significance of speech acts is not to recognize linguistic meaning of words in sentences and utterances, but it is according to the sender’s purpose in the context that they occur. Thus, the language of poetry as a way of using language, especially classical poetry, is not an ordinary language. Consequently, the paper hypothesizes that the speech acts have to be embodied in the poems accurately because there is supposed to be a hidden and invisible meaning in every verse behind its expression and form. The scope of the study is to examine the two poems, and it is benefited from their investigation that has been done in their anthology. In addition, whenever needed, the speech acts are identified in short because much has been mentioned about them in the scientific research institutions.

Martin-Löf ’s type theory

2001 ◽  
Author(s):  
B. Nördstrom ◽  
K. Petersson
Keyword(s):  
Computer Program ◽  
Programming Language ◽  
Type Theory ◽  
Predicate Logic ◽  
Propositional Calculus ◽  
Constructive Proof ◽  
Intuitionistic Propositional Calculus ◽  
Problem Description ◽  
Program Construction ◽  
Correct Program

The type theory described in this chapter has been developed by Martin-Löf with the original aim of being a clarification of constructive mathematics. Unlike most other formalizations of mathematics, type theory is not based on predicate logic. Instead, the logical constants are interpreted within type theory through the Curry-Howard correspondence between propositions and sets [Curry and Feys, 1958; Howard, 1980]: a proposition is interpreted as a set whose elements represent the proofs of the proposition. It is also possible to view a set as a problem description in a way similar to Kolmogorov’s explanation of the intuitionistic propositional calculus [Kolmogorov, 1932]. In particular, a set can be seen as a specification of a programming problem; the elements of the set are then the programs that satisfy the specification. An advantage of using type theory for program construction is that it is possible to express both specifications and programs within the same formalism. Furthermore, the proof rules can be used to derive a correct program from a specification as well as to verify that a given program has a certain property. As a programming language, type theory is similar to typed functional languages such as ML [Gordon et al., 1979; Milner et al., 1990] and Haskell [Hudak et al, 1992], but a major difference is that the evaluation of a well-typed program always terminates. The notion of constructive proof is closely related to the notion of computer program. To prove a proposition ("x Î A)($yÎB)P(x,y) constructively means to give a function f which when applied to an element a in A gives an element b in B such that P(a, b) holds. So if the proposition ("xÎ A)($yÎB)P(x,y) expresses a specification, then the function f obtained from the proof is a program satisfying the specification. A constructive proof could therefore itself be seen as a computer program and the process of computing the value of a program corresponds to the process of normalizing a proof. It is by this computational content of a constructive proof that type theory can be used as a programming language; and since the program is obtained from a proof of its specification, type theory can be used as a programming logic.

General synthetic domain theory – a logical approach

1999 ◽  
Vol 9 (2) ◽  
pp. 177-223 ◽  
Author(s):  
BERNHARD REUS ◽  
THOMAS STREICHER
Keyword(s):  
Type Theory ◽  
Function Spaces ◽  
Basic Type ◽  
Domain Theory ◽  
Stable Domain ◽  
Constructive Type Theory ◽  
Logical Language ◽  
Core Theory ◽  
Stable Domains ◽  
Rule Out

Synthetic domain theory (SDT) is a version of Domain Theory where ‘all functions are continuous’. Following the original suggestion of Dana Scott, several approaches to SDT have been developed that are logical or categorical, axiomatic or model-oriented in character and that are either specialised towards Scott domains or aim at providing a general theory axiomatising the structure common to the various notions of domains studied so far.In Reus and Streicher (1993), Reus (1995) and Reus (1998), we have developed a logical and axiomatic version of SDT, which is special in the sense that it captures the essence of Domain Theory à la Scott but rules out, for example, Stable Domain Theory, as it requires order on function spaces to be pointwise. In this article we will give a logical and axiomatic account of a general SDT with the aim of grasping the structure common to all notions of domains.As in loc.cit., the underlying logic is a sufficiently expressive version of constructive type theory. We start with a few basic axioms giving rise to a core theory on top of which we study various notions of predomains (such as, for example, complete and well-complete S-spaces (Longley and Simpson 1997)), define the appropriate notion of domain and verify the usual induction principles of domain theory.Although each domain carries a logically definable ‘specialization order’, we avoid order-theoretic notions as much as possible in the formulation of axioms and theorems. The reason is that the order on function spaces cannot be required to be pointwise, as this would rule out the model of stable domains à la Berry.The consequent use of logical language – understood as the internal language of some categorical model of type theory – avoids the irritating coexistence of the internal and the external view pervading purely categorical approaches. Therefore, the paper is aimed at providing an elementary introduction to synthetic domain theory, albeit requiring some knowledge of basic type theory.

An intensional type theory: motivation and cut-elimination

2001 ◽  
Vol 66 (1) ◽  
pp. 383-400 ◽  
Author(s):  
Paul C Gilmore
Keyword(s):  
Type Theory ◽  
Proof Theory ◽  
Predicate Logic ◽  
Order Term ◽  
Higher Order ◽  
Cut Elimination ◽  
Consistency Proof ◽  
Completeness Proof ◽  
Higher Order Term

AbstractBy the theory TT is meant the higher order predicate logic with the following recursively defined types:(1) 1 is the type of individuals and [] is the type of the truth values:(2) [τ1…..τn] is the type of the predicates with arguments of the types τ1…..τn.The theory ITT described in this paper is an intensional version of TT. The types of ITT are the same as the types of TT, but the membership of the type 1 of individuals in ITT is an extension of the membership in TT. The extension consists of allowing any higher order term, in which only variables of type 1 have a free occurrence, to be a term of type 1. This feature of ITT is motivated by a nominalist interpretation of higher order predication.In ITT both well-founded and non-well-founded recursive predicates can be defined as abstraction terms from which all the properties of the predicates can be derived without the use of non-logical axioms.The elementary syntax, semantics, and proof theory for ITT are defined. A semantic consistency proof for ITT is provided and the completeness proof of Takahashi and Prawitz for a version of TT without cut is adapted for ITT: a consequence is the redundancy of cut.

scholarly journals FILSAFAT ANALITIK Kritik Epistemologi Ide Analitik Logis Bertrand Russell

2016 ◽  
Vol 25 (1) ◽  
pp. 121-142
Author(s):  
Muhmidayeli Muhmidayeli
Keyword(s):  
Logical Form ◽  
The Other ◽  
Bertrand Russell ◽  
Land Area ◽  
Science Knowledge ◽  
Human Thought ◽  
Logical Language ◽  
Theology And Science ◽  
No Man's Land ◽  
The One

Abstract:Each logical statement reflected in the way expressed in a logical language. If a statement is expressed by a language that one would then have it wrong, therefore, necessary test of logical forms that fit with the empirical facts. In short every statement must be understood by returning to the real meaning or context. Russell offers a translation grammatically any statement that may seem misleading to the appropriate forms and logical. Bertrand Russell described his philosophy asan area of human thought that was between theology on the one hand and science on the other side. Philosophy can be said astheology, due to the nature and character of philosophy which also contains a world speculations about the definitive knowledge, but it can notbe ascertained. On the other hand, itcan be said as science, because the working procedures of philosophy that is moreleads and functioning sense like science knowledge (science). Anydogma, because it transcends knowledge certainly, including in the sphere of theology. In between there is this no man's land area that is prone to both theology and science issues. Abstrak: Setiap penyataan logis tercermin dari cara mengungkapkannya dalam bahasa logis. Jika suatu pernyataan diungkap dengan bahasa yang salah maka akan memiliki maka yang salah, oleh karena itu, diperlukan uji bentuk-bentuk logis yang cocok dengan dengan fakta empiris. Pendeknya setiap pernyataan mesti dipahami dengan mengembalikannya pada makna riil atau kontekstual. Russell menawarkan pener¬jemahan secara gramatikal setiap pernyataan yang mungkin saja tampak me¬nyesat¬¬kan ke dalam bentuk-bentuk yang tepat dan logis. Bertrand Russell menggambarkan filsafat sebagai suatu wilayah pemikiran manusia yang berada antara teologi di satu sisi dan ilmu pengetahuan di sisi lainnya. Filsafat dapat dikatakan seperti teologi, karena sifat dan watak filsafat yang juga bersikan dunia spekulasi-spekulasi tentang pengetahun yang pasti namun ia tidak dapat dipastikan. Di lain pihak, ia dapat dikatakan pula seperti ilmu pengetahuan, karena tata kerja filsafat yang memang lebih banyak mengarah dan memfungsikan akal seperti layaknya ilmu ilmu pengetahuan (sains). Segala dogma, karena ia melampaui pengetahuan pasti, termasuk dalam lingkup teologi. Di antara keduanya inilah ada daerah yang tak bertuan yang rentan terhadap kedua persoalan teologi dan sains. Keywords:filsafat analitik,analytic logic, metodologi filsafat, atomic facts, dan logical form.

scholarly journals Predicate Logic with Anaphora

1994 ◽  
Vol 4 ◽  
pp. 79 ◽  
Author(s):  
Paul Dekker
Keyword(s):  
Type Theory ◽  
Predicate Logic ◽  
Discourse Representation ◽  
Dynamic Predicate Logic ◽  
Proper Extension ◽  
Update Semantics ◽  
Anaphoric Pronouns ◽  
Separate Treatment

In this paper I make a case for a separate treatment of (singular) anaphoric pronouns within a predicate logic with anaphora (PLA). Discourse representation theoretic results (from Kamp 1981) can be formulated in a compositional way, without fid­dling with orthodox notions of scope and binding. In contrast with its predecessor dynamic predicate logic (Groenendijk and Stokhof 1991), the system of PLA is a proper extension of ordinary predicate logic and it has a genuine update semantics. Moreover, in contrast with other compositional reformulations of DRT, the seman­tics of PLA remains well within the bounds of ordinary, extensional type theory.

A Path to a New Logic

2020 ◽  
pp. 1-28
Author(s):  
David Corfield
Keyword(s):  
Natural Language ◽  
Type Theory ◽  
Philosophy Of Language ◽  
Philosophy Of Mathematics ◽  
Ordinary Language ◽  
Context Dependence ◽  
Ordinary Language Philosophy ◽  
Language Philosophy ◽  
Computer Scientists ◽  
Key Issues

This chapter explains how modal homotopy type theory combines ideas from two currents of thought: type theory and category theory. Despite what might appear to be rather different philosophical starting points, there has emerged an intrinsically structuralist language of great interest to computer scientists, mathematicians and physicists. This in itself should be enough to interest philosophers in the language, but further motivation is provided by addressing some of the kinds of objection raised to formalization in philosophy; in particular, those from ordinary language philosophy which emphasize the elasticity and context-dependence of natural language. We see that several of their concerns, such as that the definitional and descriptive uses of ‘is’ are conflated in logic, are addressed by the type theory. The prospect is then presented of an opportunity to use the new language to explore key issues in philosophy of mathematics, philosophy of language and metaphysics.

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