Review of Type-Logical Semantics

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

Review of

Type-Logical Semantics

by B.Carpenter

Riccardo Pucella Stephen Chong

Department of Computer Science

Cornell University

January30,2001

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.An important part of the meaning of sentences can be characterized by stating the conditions that need to hold for the sentence to be true.Necessarily,this approach,called truth-conditional semantics,disre-gards some relevant aspects of meaning,but has been very useful in the analysis of natural languages.Structuralist views of language(the kind held by Saussure,for instance,and later Chomsky)have typically focused on phonology, morphology,and syntax.Little progress,however,has been shown towards the structure of meaning,or content.

A common tool for the study of content,and structure in general for that matter,has been logic.During most of the20th century,an important role of logic has been to study the structure of content of mathematical languages. Many logicians have moved on to apply the techniques developed to the analysis of natural languages—Frege,Russell, Carnap,Reichenbach,and Montague.An early introduction to such classical approaches can be found in[2].

As an illustration of the kind of problems that need to be addressed,consider the following examples.The follow-ing two sentences assert the existence of a man that both walks and talks:

Some man that walks talks

Some man that talks walks

The situations with respect to which these two sentences are true are the same,and hence a truth-conditional semantics needs to assign the same meaning to such sentences.Ambiguities arise easily in natural languages: Every man loves a woman

There are at least two distinct readings of this sentence.One says that for every man,there exists a woman that he loves,and the other says that there exists a woman that every man loves.Other problems are harder to qualify. Consider the following two sentences:

Tarzan likes Jane

Tarzan wants a girlfriend

Thefirst sentence must be false if there is no Jane.On the other hand,the second sentence can be true even if no woman exists.

Those examples are extremely simple,some might even say naive,but they exemplify the issues for which a theory of natural language semantics must account.A guiding principle,apocryphally due to Frege,in the study of semantics is the so-called Fregean principle.Essentially,it can be stated as“the meaning of a complex expression should be a function of the meaning of its parts.”Such a principle seems required to explain how natural languages can be learned. Since there is no arbitrary limit on both the length and the number of new sentences human beings can understand, some general principle such as the above must be at play.Moreover,since it would not be helpful to require an infinite

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