CHAPTER 14 The Representation of Sentence Meaning

CHAPTER 14 The Representation of Sentence Meaning

Speech and Language Processing ed3 读书笔记

The meaning of linguistic expressions can be captured in formal structures called meaning representations. Correspondingly, the frameworks that specify the syntax and semantics of these representations are called meaning representation languages.

The process of creating and assigning representations to linguistic inputs is called semantic analysis, and the entire enterprise of designing meaning representations and associated semantic analyzers is referred to as computational semantics.

14.1 Computational Desiderata for Representations

14.1.1 Verifiability

The notion of verifiability describes a system’s ability to compare the state of affairs described by a representation to the state of affairs in some world as modeled in a knowledge base.

14.1.2 Unambiguous Representations

ambiguity vs vagueness

ambiguity: has different meanings

vagueness: to some extent has the meaning of

14.1.3 Canonical Form

14.1.4 Inference and Variables

14.1.5 Expressiveness

14.2 Model-Theoretic Semantics

A model is a formal construct that stands for the particular state of affairs in the world. Expressions in a meaning representation language can be mapped in a systematic way to the elements of the model. If the model accurately captures the facts we’re interested in concerning some state of affairs, then a consistent mapping between the meaning
representation and the model provides the bridge between the meaning representation and world being considered.

First, some terminology. The vocabulary of a meaning representation consists of two parts: the non-logical vocabulary and the logical vocabulary. The non-logical vocabulary consists of the open-ended set of names for the objects, properties, and relations that make up the world we’re trying to represent. These appear in various schemes as predicates, nodes, labels on links, or labels in slots in frames, The logical vocabulary consists of the closed set of symbols, operators, quantifiers, links, etc., that provide the formal means for composing expressions in a given meaning representation language.

We’ll start by requiring that each element of the non-logical vocabulary have a denotation in the model. By denotation, we simply mean that every element of the non-logical vocabulary corresponds to a fixed, well-defined part of the model. Let’s start with objects, the most basic notion in most representational schemes. The domain of a model is simply the set of objects that are part of the application, or state of affairs, being represented. Each distinct concept, category, or individual in an application denotes a unique element in the domain. A domain is therefore formally a set.

• Objects denote elements of the domain
• Properties denote sets of elements of the domain
• Relations denote sets of tuples of elements of the domain

A function that maps from the non-logical vocabulary of our meaning representation to the proper denotations in the model is called an interpretation.

One possible state of affairs using this scheme is given in Fig. 14.2.

truth-conditional semantics for conjunction operator

14.3 First-Order Logic

14.3.1 Basic Elements of First-Order Logic

Figure 14.3, which provides a complete context-free grammar for the particular syntax of FOL that we will use, is our roadmap for this section.

14.3.2 Variables and Quantifiers

14.3.3 Lambda Notation

The lambda notation extends the syntax of FOL to include expressions of the following form:
$$\lambda x.P(x)$$
The usefulness of these $\lambda$-expressions is based on the ability to apply them to logical terms to yield new FOL expressions where the formal parameter variables are bound to the specified terms. This process is known as $\lambda$-reduction and consists of a simple textual replacement of the $\lambda$ variables with the specified FOL terms, accompanied by the subsequent removal of the $\lambda$. The following expressions illustrate the application of a $\lambda$-expression to the constant $A$, followed by the result of performing a $\lambda$-reduction on this expression:
$$\begin{gathered} \lambda x.P(x)(A) \\ P(A) \end{gathered}$$
An important and useful variation of this technique is the use of one $\lambda$-expression as the body of another as in the following expression:
$$\lambda x.\lambda y.Near(x,y)$$

$$\begin{gathered} \lambda x.\lambda y.Near(x,y)(Bacaro) \\ \lambda y.Near(Bacaro,y) \end{gathered}$$

$$\begin{gathered} \lambda y.Near(Bacaro,y)(Centro) \\ Near(Bacaro,Centro) \end{gathered}$$

14.3.4 The Semantics of First-Order Logic

14.3.5 Inference

Modus ponens

Forward chaining, backward chaining, resolution

plausible reasoning (abduction)

14.4 Event and State Representations

In the neo-Davidsonian approach to event representations:

• Events are captured with predicates that take a single event variable as an argument.
• There is no need to specify a fixed number of arguments for a given FOL predicate; rather, as many roles and fillers can be glued on as are provided in the input.
• No more roles are postulated than are mentioned in the input.
• The logical connections among closely related inputs that share the same predicate are satisfied without the need for additional inference.

14.4.1 Representing Time

temporal logic

tense logic

(14.48) I arrived in New York.
(14.49) I am arriving in New York.
(14.50) I will arrive in New York.
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14.4.2 Aspect

Stative: I know my departure gate.
Activity: John is flying.
Accomplishment: Sally booked her flight.
Achievement: She found her gate.

14.5 Description Logics

14.6 Summary

This chapter has introduced the representational approach to meaning. The following are some of the highlights of this chapter:

• A major approach to meaning in computational linguistics involves the creation of formal meaning representations that capture the meaning-related content of linguistic inputs. These representations are intended to bridge the gap from language to common-sense knowledge of the world.
• The frameworks that specify the syntax and semantics of these representations are called meaning representation languages. A wide variety of such languages are used in natural language processing and artificial intelligence.
• Such representations need to be able to support the practical computational requirements of semantic processing. Among these are the need to determine the truth of propositions, to support unambiguous representations, to represent variables, to support inference, and to be sufficiently expressive.
• Human languages have a wide variety of features that are used to convey meaning. Among the most important of these is the ability to convey a predicate-argument structure.
• First-Order Logic is a well-understood, computationally tractable meaning representation language that offers much of what is needed in a meaning representation language.
• Important elements of semantic representation including states and events can be captured in FOL.
• Semantic networks and frames can be captured within the FOL framework.
• Modern Description Logics consist of useful and computationally tractable subsets of full First-Order Logic. The most prominent use of a description logic is the Web Ontology Language (OWL), used in the specification of the Semantic Web.