Copredication in homotopy type theory

This paper applies homotopy type theory to formal semantics of natural languages and proposes a new model for the linguistic phenomenon of copredication. Copredication refers to sentences where two predicates which assume different requirements for their arguments are asserted for one single entity, e.g., "the lunch was delicious but took forever". This paper is particularly concerned with copredication sentences with quantification, i.e., cases where the two predicates impose distinct criteria of quantification and individuation, e.g., "Fred picked up and mastered three books." In our solution developed in homotopy type theory and using the rule of existential closure following Heim analysis of indefinites, common nouns are modeled as identifications of their aspects using HoTT identity types, e.g., the common noun book is modeled as identifications of its physical and informational aspects. The previous treatments of copredication in systems of semantics which are based on simple type theory and dependent type theories make the correct predictions but at the expense of ad hoc extensions (e.g., partial functions, dot types and coercive subtyping). The model proposed here, also predicts the correct results but using a conceptually simpler foundation and no ad hoc extensions

Restrictions on copredication: a situation theoretic approach

This paper proposes a situation-theoretic account of polysemy: polysemous nouns denote situations that witness (i.e. contain) multiple entities of different types. For instance, lunch denotes situations that contain an eating event and some food where these stand in a patient relation. A puzzle regarding more than two ways polysemous nouns such as statement is the restrictions on copredication they exhibit, namely, where multiple, potentially incompatible predicates are applied based on a single antecedent, but not all combinations of readings are possible. Such restrictions fall naturally out of the situation-theoretic account of polysemy

Plurals: individuals and sets in a richly typed semantics

We developed a type-theoretical framework for natural lan- guage semantics that, in addition to the usual Montagovian treatment of compositional semantics, includes a treatment of some phenomena of lex- ical semantic: coercions, meaning, transfers, (in)felicitous co-predication. In this setting we see how the various readings of plurals (collective, dis- tributive, coverings,...) can be modelled

Linguistic Representation and Processing of Copredication

This thesis addresses the lexical and psycholinguistic properties of copredication. In particular, it explores its acceptability, frequency, crosslinguistic and electrophysiological features. It proposes a general parsing bias to account for novel acceptability data, through which Complex-Simple predicate orderings are degraded across distinct nominal types relative to the reverse order. This bias, Incremental Semantic Complexity, states that the parser seeks to process linguistic representations in incremental stages of semantic complexity. English and Italian acceptability data are presented which demonstrate that predicate order preferences are based not on sense dominance but rather sense complexity. Initial evidence is presented indicating that pragmatic factors centred on coherence relations can impact copredication acceptability when such copredications host complex (but not simple) predicates. The real-time processing and electrophysiological properties of copredication are also presented, which serve to replicate and ground the acceptability dynamics presented in the thesis

Semantic Types, Lexical Sorts and Classifiers

We propose a cognitively and linguistically motivated set of sorts for lexical semantics in a compositional setting: the classifiers in languages that do have such pronouns. These sorts are needed to include lexical considerations in a semantical analyser such as Boxer or Grail. Indeed, all proposed lexical extensions of usual Montague semantics to model restriction of selection, felicitous and infelicitous copredication require a rich and refined type system whose base types are the lexical sorts, the basis of the many-sorted logic in which semantical representations of sentences are stated. However, none of those approaches define precisely the actual base types or sorts to be used in the lexicon. In this article, we shall discuss some of the options commonly adopted by researchers in formal lexical semantics, and defend the view that classifiers in the languages which have such pronouns are an appealing solution, both linguistically and cognitively motivated

Polysemous nouns and copredication

190 p.La polisemia es un recurso lingüístico que utilizamos de manera habitual. De hecho, la mayor parte delas palabras que utilizamos a diario son polisémicas. Desde el punto de vista de la lingüística y lafilosofía, elucidar qué es la polisemia no es tarea fácil. Una definición bastante aceptada es que unapalabra es polisémica cuando tiene varios sentidos relacionados entre si y cuyo uso es tan habitual quese ha convencionalizado. Por ejemplo, palabras como colegio, zorro o ángel tienen más de unsignificado: la palabra colegio puede referir tanto a un edificio en la oración el colegio se incendió comoa un grupo de personas, por ejemplo en el colegio mañana celebra el fin de curso. La palabra zorropuede utilizarse para referir a un animal o a una persona muy inteligente y la palabra ángel puedeutilizarse para hablar de un ser místico o para hablar de una muy buena persona.Desde el punto de vista académico, la polisemia genera varios problemas que aún no tienen unarespuesta bien consolidada. Entre estos se encuentra el fenómeno de la copredicación. La copredicaciónocurre cuando dos sentidos de un sustantivo polisémico son utilizados en una misma oración y hay unpredicado que refiere para cada uno de esos sentidos. Por ejemplo, en el caso de la palabra escuela,tenemos los sentidos: escuela como institución y escuela como edificio. Ambos son utilizados en laoración: la escuela celebraba el día del euskera cuando prendió fuego. Uno de los objetivosprimordiales de la tesis es estudiar la copredicación. Este fenómeno ha sido utilizado como test paradeterminar cuando una palabra es polisémica y cuando no. Incluso, se ha utilizado para distinguir entrepolisemia y homonomia. Sin embargo, no todas las palabras poliseémicas copredican.En esta tesis se defiende que la diferencia entre polisemia y homonimia no puede determinarse dentro deunos límites estrcitos. Ambos fenóemnos forman parte de un espectro en el que las palabras quecopredican están en un extremo y la homonimia en el otro.La tesis se divide en tres partes. La Parte I está dedicada a estudiar la polisemia, en concreto las teoríasde la representación de los sentidos de los nombres polisémicos. En la Parte II se estudia lacopredicación. Se intenta responder a tres preguntas: (i) ¿por qué unas palabras polisémicas copredican yotras no?; (ii) ¿cómo se interpretan las oraciones copredicativas?; (iii) ¿cuál es la denotación de losnombres copredicativos? Para ello, se analizan las aportaciones que la Teoría de los Paquetes deActivación puede hacer a las teorías de la semántica rica en loss debate en torno a estas preguntas. Porúltimo, la Parte III de la tesis resume las conclusiones generales que se extraen de la tesis, así como lascontribuciones y límites de las propuesta

The Montagovian Generative Lexicon ΛT yn: a Type Theoretical Framework for Natural Language Semantics

International audienceWe present a framework, named the Montagovian generative lexicon, for computing the semantics of natural language sentences, expressed in many-sorted higher order logic. Word meaning is described by several lambda terms of second order lambda calculus (Girard’s system F): the principal lambda term encodes the argument structure, while the other lambda terms implement meaning transfers. The base types include a type for propositions and many types for sorts of a many-sorted logic for expressing restriction of selection. This framework is able to integrate a proper treatment of lexical phenomena into a Montagovian compositional semantics, like the (im)possible arguments of a predicate, and the adaptation of a word meaning to some contexts. Among these adaptations of a word meaning to contexts, ontological inclusions are handled by coercive subtyping, an extension of system F introduced in the present paper. The benefits of this framework for lexical semantics and pragmatics are illustrated on meaning transfers and coercions, on possible and impossible copredication over different senses, on deverbal ambiguities, and on “fictive motion”. Next we show that the compositional treatment of determiners, quantifiers, plurals, and other semantic phenomena is richer in our framework. We then conclude with the linguistic, logical and computational perspectives opened by the Montagovian generative lexicon

Polysemous nouns and copredication

190 p.La polisemia es un recurso lingüístico que utilizamos de manera habitual. De hecho, la mayor parte delas palabras que utilizamos a diario son polisémicas. Desde el punto de vista de la lingüística y lafilosofía, elucidar qué es la polisemia no es tarea fácil. Una definición bastante aceptada es que unapalabra es polisémica cuando tiene varios sentidos relacionados entre si y cuyo uso es tan habitual quese ha convencionalizado. Por ejemplo, palabras como colegio, zorro o ángel tienen más de unsignificado: la palabra colegio puede referir tanto a un edificio en la oración el colegio se incendió comoa un grupo de personas, por ejemplo en el colegio mañana celebra el fin de curso. La palabra zorropuede utilizarse para referir a un animal o a una persona muy inteligente y la palabra ángel puedeutilizarse para hablar de un ser místico o para hablar de una muy buena persona.Desde el punto de vista académico, la polisemia genera varios problemas que aún no tienen unarespuesta bien consolidada. Entre estos se encuentra el fenómeno de la copredicación. La copredicaciónocurre cuando dos sentidos de un sustantivo polisémico son utilizados en una misma oración y hay unpredicado que refiere para cada uno de esos sentidos. Por ejemplo, en el caso de la palabra escuela,tenemos los sentidos: escuela como institución y escuela como edificio. Ambos son utilizados en laoración: la escuela celebraba el día del euskera cuando prendió fuego. Uno de los objetivosprimordiales de la tesis es estudiar la copredicación. Este fenómeno ha sido utilizado como test paradeterminar cuando una palabra es polisémica y cuando no. Incluso, se ha utilizado para distinguir entrepolisemia y homonomia. Sin embargo, no todas las palabras poliseémicas copredican.En esta tesis se defiende que la diferencia entre polisemia y homonimia no puede determinarse dentro deunos límites estrcitos. Ambos fenóemnos forman parte de un espectro en el que las palabras quecopredican están en un extremo y la homonimia en el otro.La tesis se divide en tres partes. La Parte I está dedicada a estudiar la polisemia, en concreto las teoríasde la representación de los sentidos de los nombres polisémicos. En la Parte II se estudia lacopredicación. Se intenta responder a tres preguntas: (i) ¿por qué unas palabras polisémicas copredican yotras no?; (ii) ¿cómo se interpretan las oraciones copredicativas?; (iii) ¿cuál es la denotación de losnombres copredicativos? Para ello, se analizan las aportaciones que la Teoría de los Paquetes deActivación puede hacer a las teorías de la semántica rica en loss debate en torno a estas preguntas. Porúltimo, la Parte III de la tesis resume las conclusiones generales que se extraen de la tesis, así como lascontribuciones y límites de las propuesta

Copredication, quantification and individuation

This thesis addresses the various problems of copredication: the phenomenon whereby two predicates are applied to a single argument, but they appear to require that their argument denote different things. For instance, in the sentence ‘The lunch was delicious but went on for hours’, the predicate ‘delicious’ appears to require that ‘the lunch’ denote food, while ‘went on’ appears to require that it denote an event. Copredication raises philosophical issues regarding the place of a reference relation in semantic theory. It also raises issues concerning the ascription of sortal requirements to predicates in framing a theory of semantic anomaly. Finally, many quantified copredication sentences have truth conditions that cannot be accounted for given standard assumptions, because the predicates used impose distinct criteria of individuation on the objects to which they apply. For instance, the sentence ‘Three books are heavy and informative’ cannot be true in a situation involving only a trilogy (informationally three books, but physically only one), nor in a situation involving only three copies of the same book (physically three books, but informationally only one): the three books involved must be both physically and informationally distinct. The central claims of this thesis are that nouns supporting copredication denote sets of complex objects, and that lexical entries incorporate information about their criteria of individuation, defined in terms of equivalence relations on subsets of the domain of discourse. Criteria of individuation are combined during semantic composition, then accessed and exploited by quantifiers in order to specify that the objects quantified over are distinct in defined ways. This novel approach is presented formally in Chapters 2 and 3, then compared with others in the literature in Chapter 4. In Chapter 5, the discussion is extended to the question of the implications of this approach for the form that a semantic theory should take

Formal semantics in modern type theories with coercive subtyping

Abstract. In the formal semantics based on modern type theories, common nouns are interpreted as types, rather than as predicates of entities as in Montague's semantics. This brings about important advantages in linguistic interpretations but also leads to a limitation of expressive power because there are fewer operations on types as compared with those on predicates. The theory of coercive subtyping adequately extends the modern type theories and, as shown in this paper, plays a very useful role in making type theories more expressive for formal semantics. It not only gives a satisfactory solution to the basic problem of 'multiple categorisation' caused by interpreting common nouns as types, but provides a powerful formal framework to model interesting linguistic phenomena such as copredication, whose formal treatment has been found difficult in a Montagovian setting. In particular, we show how to formally introduce dot-types in a type theory with coercive subtyping and study some type-theoretic constructs that provide useful representational tools for reference transfers and multiple word meanings in formal lexical semantics