Linguists rarely employed formal semantics until richard montague showed how english or any natural language could be treated like a formal language. Although its basic orientation is linguistic, the book should also be of interest to logicians and computer scientists seeking connections between logical systems and natural language. Semantics, also called semiotics, semology, or semasiology, the philosophical and scientific study of meaning in natural and artificial languages. The term is one of a group of english words formed from the various derivatives of the greek verb semaino to mean or to signify.
Logical semantics article about logical semantics by the. The strength of type logical semantics lies with the latter, but type logical theories can be combined with many competing hypotheses. Anaphora and type logical grammar gerhard jager springer. This semantics for feature structures extends the ideas of pereira and shieber 11, by providing an interpretation for values which are specified by disjunctions and path values embedded within disjunctions. This book, type logical semantics by carpenter, explores this particular approach. Such a grammar is necessarily surface oriented and. Essentially, it relies on techniques from type theory. Reinhard muskens 2011 routledge encyclopedia of philosophy online. Formal semantics tries to describe the meaning of language using the descriptive apparatus of formal logic. Formal syntax and formal semantics so far we have kept syntax and semantics rather informal but, in metalogic we want to prove things about logic this requires us to get really precise about syntax and semantics we are going to give syntax and semantics of propositional logic a mathematical treatment. This paper aims to give an introduction to type logical grammar. Typelogical semantics studies linguistic meaning with the help of the theory of types. A piece of language conveys its dictionary meaning, connotations beyond the dictionary meaning, information about the social context of language use, speakers feelings and attitudes rubbing off of one meaning on the another meaning of the same word when it has two meanings and meaning because of habit occurrence.
A gentle introduction to type logical gram semantics archive. In particular, by embedding ontological types in our predi. The first and foremost task of logical semantics is to define precisely the. Type logical grammar is a framework that emerged from the synthesis of two traditions. Riccardo pucella stephen chong department of computer science cornell university january 30, 2001 introduction one of the many roles of linguistics is to address the semantics of natural languages, that is, the meaning of sentences.
Categorical semantics for logicenriched type theories robin adams royal holloway, university of london types 2011, 8 september 2011 robin adams rhul categorical semantics for ltts types 2011 1 21. This assumption can make it awkward, or even impossible, to. The book, which stepwise develops successively more powerful logical and grammatical systems, covers an unusually broad range of material. Pucella and chong, dept of cs, cornell univ introduction one of the many roles of linguistics is to address the semantics of natural languages, that is, the meaning of sentences in natural languages. Simply typed lambdacalculus higherorder logic applicative categorial grammar the lambek calculus coordination and unbounded dependencies quantifiers and scope plurals pronouns and dependency modal logic intentionality tense and aspect. For any process p, we assume defined as usual the set fnp of free names of p. The first five chapters develop the theoretical background in some detail.
Bob carpenter typelogical semantics semantics truth scribd. As in the case forchapter 2, the concepts and methods introduced are illustrated throughout with reference to the most familiar logical system, classical propositional logic. Prooftheoretic semantics for a natural language fragment. In categorial grammar, expressions are classified by structured types. The logical expressions are called predicates, or assertions. Recent developments in the semantics of natural language seem to lead to a genuine. Type logical semantics grammatical structure and its.
The textbook is available at the word 469 milton street. Categorical semantics for logicenriched type theories. In other words, kb j g if there is no interpretation in which kb is true and g is false. Semantics definition of semantics by the free dictionary. Topics covered include higherorder logic, applicative categorial grammar, the lambek.
Column definition specification of the create table statement. Grammatical composition is conceived as resource conscious logical deduction. Contributions to functional syntax, semantics, and language comprehension. We have described a logical form language that includes terms, predicates, propositions, logical operators, quantifiers including special nl quantifiers such as the, and shown how this language can be used to represent ambiguous sentences. In application to the meaning of logical symbols, his approach could be called, in contemporary terminology, a version of prooftheoretic semantics or logical inferentialism. Antonelli 2000, for example, advocated such a singledomain free logic, which he called protosemantics, but more recently 2007, p. Related though not identical denominations for this type of semantics are truthconditional semantics, modeltheoretic semantics, logical semantics, etc. The mit press is selling the hardbound edition at the paperbound price. The rules of categorical grammar are supposed to express the laws obeyed by the types according to the meaning of the type.
Three kinds of interpretations of this system are considered. The author chose the type logical categorial grammar as his grammatical. The free variable m has been replaced by the unknown. The goal is to describe natural language in a formal, precise, unambiguous way. Semantics article about semantics by the free dictionary. The ap proach is illustrated by the development of a generic type system for. We motivate and present a logical semantic approach to types for concurrency and to the soundness of related systems. Download citation on jan 1, 2010, reinhard muskens and others published type logical semantics find, read and cite all the research you need on researchgate. Thusthereare basetypes, in particular bool, the type of truth values, nat, the type of naturalnumbersn,andint,thetypeofmathematicalintegersz.
Syntax from a signature to formulas signature usage. Define axioms or inference rules for each statement type in the language to allow transformations of expressions to other expressions. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. In 1931, carnap had rejected certain philosophical uses of meaning as metaphysical and developed a quite different formalsyntactic account of linguistic symbols.
The author chose the typelogical categorial grammar as his grammatical basis because of its broad. To understand it is raining, you have to know which conditions must obtain in the world for this sentence to be true. In truthconditional semantics, the goal is to describe the conditions that would have to be met for a sentence to be true. Typelogical semantics routledge encyclopedia of philosophy. In this paper we investigate a new type of structured classi. It also contains a great deal of original work on categorial grammar and its application to naturallanguage semantics. Review of typelogical semantics, acm sigact news 10. The empirical study of word meanings and sentence meanings in existing languages is a branch of linguistics. Hol is a typed logic whose type system resembles that of functional programminglanguages.
Simply typed lambdacalculus higherorder logic applicative categorial grammar the lambek calculus coordination and unbounded dependencies quantifiers. The semantics of logic refers to the approaches that logicians have introduced to understand and determine that part of meaning in which they are interested. Apr 01, 2000 this excellent introductory textbook on type logical semantics provides a broad overview of the field. Based on an introductory course on naturallanguage semantics, this book provides an introduction to type logical grammar and the range of linguistic phenomena that can be handled in categorial grammar.
Type choice determined by a combination of factors including coercion by demands of predicates, try simplest types first strategy, and default preferences of particular determiners. Logical semantics a branch of logic that deals with the study of the meaning and sense in russian, znachenie and smysl of concepts and propositions and of their formal analoguesthe interpretations of expressions terms and formulas of different calculi formal systems. 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. Pdf we argue that logical semantics might have faltered due to its failure in distinguishing between two fundamentally very different types of. Thusthereare basetypes, in particular bool, the type of truth values, nat, the type of. His contribution to linguistic semantics, which is now known as montague grammar, was the basis for further developments, like the categorial grammar of barhillel and colleagues, and the more recent type logical semantics or grammar. Based on an introductory course on naturallanguage semantics, this book provides an introduction to typelogical grammar and the range of linguistic phenomena that can be handled in categorial grammar. Formal and logical languages are both seen as sets of sentences of which the truth conditions have to be specified relative to a model, an abstract representation of the world.
A logical semantics for feature structures proceedings. Bob carpenter typelogical semantics free ebook download as pdf file. Oclcs webjunction has pulled together information and resources to assist library staff as they consider how to handle. This book, typelogical semantics by carpenter, explores this particular approach. His contribution to linguistic semantics, which is now known as montague grammar, was the basis for further developments, like the categorial grammar of barhillel and colleagues, and the more recent. The results are returned in a latextypeset pdf document.
Prooftheoretic semantics is an approach to logical semantics based on two ideas, of which the first is that the meaning of a logical connective can be explained by stipulating that some mode of inference, for example, a natural deduction introduction or elimination rule, is permissible. Essays in logical semantics johan van benthem springer. Logical semantics of types for concurrency di fctunl. Semantics and an example cpsc 322 logic 2, slide 6. Assertions axiomatic semantics is based on mathematical logic. Categorial grammar from formal linguistics and substructural logics from logic. An important part of the meaning of sentences can be characterized by stating the. Ruzica piskac firstorder logic syntax, semantics, resolution 25 125. Reliable information about the coronavirus covid19 is available from the world health organization current situation, international travel.
Logical semantics is the study of meaning in formal and natural languages using logic as an instrument. The set of types is the recursive closure of a set of atomic types under a number of typeconstructors, so that types are algebraic terms like arithmetic expressions or logical formulas. Chapter 3is devoted to the semantic appraisal of logical systems. The latter originated with russell as an answer to the paradoxes, but has the additional virtue that it is very close to ordinary language. The author chose the type logical categorial grammar as his grammatical basis because of its broad syntactic coverage and its strong linkage of syntax and semantics. Slides of seven types of meaning, a presentation on semantic taken from leechs book chapter 2. Linguists refer to words as a type of sign that represents a concept.
649 1114 644 362 468 784 1100 405 180 256 541 1165 534 976 579 51 793 623 1060 1187 1473 644 331 1384 717 429 143 1366 1272 754 1416 1276 110 628