One of the many roles of linguistics is to address the semantics of natural languages, that is, the meaning of sentences in natural languages. An important part of the meaning of sentences can be characterized by stating the conditions that need to hold fo

of expressions that act locally as’s but take their semantic scope over an embedding expression of cate-gory.Generalized quantifiers are given category,since they act like a noun phrase(category)in situ, but scope semantically to an embedding sentence(category).The Lambek calculus is extended with appropriate derivation rules.The issues of quantifier coordination,quantifiers within quantifiers,and the interaction with negation are discussed.Other topics related to quantifiers and determiners in general,such as definite descriptions,possessives (every kid’s toy),indefinites(some student),generics(italians),comparatives(as tall as),and expletives(it,there)are analyzed within that context.

Chapter8,Plurals,provides a type-logical account of plurality.First,the notion of group is added to the syntax and semantics.The type is considered to be a subtype of the type and thus the domain of is a subset of the domain of.A relation linking a group to the property that defines membership in the group is defined,and restrictions are imposed to ensure that every group has a unique property that defines membership of that group.With this interpretation,categories for plural noun phrases and plural nouns are studied.The notions of distributors(to view a group as a set of individuals)and collectors(to view a set of individuals as a group)are defined,to handle,for example,verbs that apply only to individuals or only to groups.The issues of coordination and negation are examined in the context of plurals.Further topics examined include plural quantificatives and,more generally,partitives(each, all,most,or numerical partitives such as three of,etc.),nonboolean coordination with and,comitative(the use of with in Tarzan climbed the tree with Cheetah),and mass terms such as snow and water.

Chapter9,Pronouns and Dependency,analyses the use of non-indexical pronouns such as him,she,itself,e-specially the dependent use of such pronouns.Dependent pronouns are characterized as having their interpretation depend on the interpretation of some other expression(the antecedent).For example,he in Jody believes he will be famous.A popular interpretation of pronouns in type-logical frameworks is as variables,although the treatment is subtle,at least for non-reflexive pronouns such as the he above.(Admittedly,this topic is an outstanding problem for type-logical grammars.)Reflexive pronouns,such as himself in Everyone likes himself,can be handled as quantifiers. Topics related to pronomial forms are examined,such as reciprocals(the each other in The three kids like each other), pied piping(the which in the table the leg of which Jody broke),ambiguous verb-phrases ellipses(Jody likes himself and Brett does too),and interrogatives.

Thefinal part,the last three chapters,extend the framework with modalities to account for intensional aspects of natural languages.

Chapter10,Modal Logic,introduces the logical tools required to deal with intensionality,tense and aspect.The key concept is that of a modal logic,where operators are used to qualify the truth of a statement.The chapter presents both a model theory(Kripke frames)and a proof theory for S5,a particular modal logic of necessity.A brief discussion of how the techniques of modal logic can be used to model indexicality precedes the presentation of a general modal model.First-order tense logics,which extendfirst order logics with modal operators about the truth of statements in the past and future,are presented in some depth,as they are able to provide a model of tenses in natural language.Time can be regarded as a collection of moments,or as a collection of possibly overlapping intervals.Higher order logic is extended to include modal operators by taking the domains of worlds and time to be basic types,on the same level as the domains of individuals and truth values,yielding a framework referred to as intensional logic.This approach avoids a number of problems associated with simply abstracting the model for higher order logic over possible worlds.

Chapter11,Intensionality,uses modal logic to extend the type-logical framework to cover intensional construc-tions.In particular,is added as a new basic type,and the assignment of types to basic categories is modified, replacing with,i.e.truth values may be different at different worlds.This change facilitates the inclusion of many constructs,such as propositional attitudes(Frank believes Brooke cheated),modal adverbs (possibly),modal auxiliaries(should,might),and so-called control verbs(persuaded,promised),although some con-structs remain problematic.The“individual concepts”approach is considered,where the type of a noun phrase is instead of,i.e.the referent of a noun phrase may differ from world to world.Other approaches to intensionality,which do not involve possible worlds,are explained briefly.Finally,the last section returns to the issue of giving a categorization of control verbs,and gives some problematic examples showing the need for more work in this area.

Chapter12,Tense and Aspect,extends the grammar and semantics with a theory of tense.It presents Reichen-bach’s approach to simple and perfect tenses,how this applies to discourse,and Vendler’s verb classes—a semantic classification of verbs that is correlated with their syntactic use.The approach Carpenter adopts for tense and aspect is based on insights derived from these works,and on further development of these works by other authors.To extend the grammar,verbs are subcategorized by classifying them based on whether they arefinite or non-finite,and whether they

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