1 What semantic rules look like General conventions All our rules - - PDF document

1

Feb-4-09 Human Communication 1

Semantic rules: First steps

Human Communication 1 Lecture 10

Feb-4-09 Human Communication 2

Contents

Our aim today is to sketch a simple system for constructing a compositional semantics for a small part of English.

• We will provide a set of semantic rules, just as we did for

the arithmetic grammar which will process syntactic trees to produce a representation of the literal meaning of English sentences.

• What is important here is that you understand in general

how the system works, and how it makes predictions about the meaning of sentences.

• In answering exam questions, etc, you will be provided with

sets of rules. So, you will not have to reproduce all the details.

• There is lots of back-up material available in the course

notes and in exercises and tutorials.

Feb-4-09 Human Communication 3

But why?

The function of the grammar is: – To allow you to see the nuts and bolts of a current theory – To make predictions about the relationship between form and meaning (sometimes incorrect ones) – And gain an insight into the scientific study of language. The model will:

• be deficient in many respects, but
• will help to bring into focus questions about the nature of

meaning and language more generally. Its failings will be as interesting as its good points. Such models form the basis of technology which has a major impact on our day-to-day lives including communication between humans, and between humans and computers. Important to understand what such models can and cannot do.

Feb-4-09 Human Communication 4

Reminder of DRSs (a)

We will think of the translation of Pip barked as the following DRS: (Recall that we are only going to deal with past tenses) Why does the symbol x occur twice?

• To indicate that the individual called “Pip” and the individual

doing the barking are the same. A DRS can be true or false with respect to a model, a collection of facts about individuals. We can examine possible models to see whether or not we think we have captured the literal meaning. Pip(x) bark(x) x

Feb-4-09 Human Communication 5

The parts of a DRS

Remember the names for the parts of the DRS: The part above the line represents the individuals that a sentence (or sequence of sentences) talks about, or REFERS to. The part below the line expresses the conditions that hold of the referents. Later in the course, we will use a slightly different format for DRSs. “conditions” “discourse referents”

Feb-4-09 Human Communication 6

What we want to achieve

We want to come up with a set of rules which will successively replace parts of the tree shown below, to come up with the box shown below. S NP VP PN V0 Pip barked

The correspondence between some parts is relatively

• bvious.

e.g. Pip corresponds to “Pip”, likewise barked and “bark”. The main trick will involve arranging the referents correctly. Pip(x) bark(x) x

2

Feb-4-09 Human Communication 7

What semantic rules look like

All our rules will be of the form: If you are looking at a tree of a particular kind, you can erase part of the tree, and add conditions or referents to the DRS.

• Our first step is to draw a box around our

syntactic tree.

• A tree inside a box represents “work to be done”

to achieve a translation. The box provides a context within which to do the translation. The goal in producing a DRS is to remove all of such a tree, typically in a series of steps.

Feb-4-09 Human Communication 8

General conventions

• The tree on the LHS shows what to remove.
• Any tree on the RHS shows what replaces it.
• The lower part of the RHS contains any conditions to be

introduced.

• A discourse referent at the top of the RHS means that a

new discourse referent has to be introduced.

• You have a collection of referents to draw from at will.

Unless otherwise stated, choose a new one.

• An equation between two referents can be eliminated by

replacing one referent by the other throughout. becomes Left hand side Right hand side

Feb-4-09 Human Communication 9

An example rule: intransitive verbs

Pick any referent, call it z Then:

• Substitute that referent for the tree below, and including,

VP and

• Add “verb( z )” to the DRS’s conditions, where “verb” is

the translation of verb. becomes

VP V0 verb verb(z) z

Feb-4-09 Human Communication 10

Example: a dog barked (tree)

S NP VP Det N V0 A dog barked

Feb-4-09 Human Communication 11

Surround this with empty DRS

S NP VP Det N V0 A dog barked

Feb-4-09 Human Communication 12

Finding matching rules

We have one of the rules we need already:

• Intransitive verbs (above)

We need one for NPs which begin with a or an: Note that previous rule instructs us to add a discourse referent to the top part of our DRS. NP Det N a(n) noun noun (x) x x becomes

3

Feb-4-09 Human Communication 13

The rule for intransitive verbs

Applying the rule for intransitive verbs gives: assuming barked translates to “bark”.

bark (y) S NP y Det N a dog

Feb-4-09 Human Communication 14

The rule for a

We can apply the rule for a to give: assuming dog translates to “dog”.

bark (y) dog (x) S x y x

Feb-4-09 Human Communication 15

Example: a dog barked, concluded

The rule for sentences goes like this:

S x z substitute all occurrences

• f z in the DRS conditions

with x becomes

Feb-4-09 Human Communication 16

Applying this rule for sentences to:

yields: bark(y) dog(x) S x y x bark(x) dog(x) x This will be true in any model containing these two conditions holding of a single individual, e.g. dog(p) bark(p) p

Feb-4-09 Human Communication 17

Summary

Today we have seen:

• Examples of semantic rules
• How to apply semantic rules to compute DRSs
• Our first example

Notice the overall similarities with the semantic rules for arithmetic, and also three differences. In the case of English, there are

– Larger units (i.e. translation operates over several subtrees at once) – Referents (expressions in arithmetic do not refer as they do in natural language) – Interpretation refers to a more complex domain (representations of the meanings of sentences, rather than to just numbers)

Next time: More semantic rules

Feb-4-09 Human Communication 18

Exercises

1. In how many different orders may we apply the rules for the above example? Does it make any difference which

• ne we choose?

2. Provide a complete set of rules which will allow you to analyse: (a) Pip miaowed Make certain to specify everything you need to add. What do you not need to change? 3. Provide a model for the above sentence