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

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 Semantic rules: First steps 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. Human Communication 1 • In answering exam questions, etc, you will be provided with Lecture 10 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 1 Feb-4-09 Human Communication 2 But why? Reminder of DRSs (a) The function of the grammar is: We will think of the translation of Pip barked as the following – T o allow you to see the nuts and bolts of a current theory DRS: x – T o make predictions about the relationship between form and meaning (sometimes incorrect ones) Pip( x ) – A nd gain an insight into the scientific study of language. bark( x ) The model will: (Recall that we are only going to deal with past tenses) • be deficient in many respects, but Why does the symbol x occur twice? • will help to bring into focus questions about the nature of • To indicate that the individual called “Pip” and the individual meaning and language more generally. doing the barking are the same. Its failings will be as interesting as its good points. A DRS can be true or false with respect to a model, a Such models form the basis of technology which has a major collection of facts about individuals. impact on our day-to-day lives including communication We can examine possible models to see whether or not we between humans, and between humans and computers. think we have captured the literal meaning. Important to understand what such models can and cannot do. Feb-4-09 Human Communication 3 Feb-4-09 Human Communication 4 The parts of a DRS What we want to achieve Remember the names for the parts of the DRS: 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. “discourse referents” S “conditions” NP VP x Pip( x ) The part above the line represents the individuals that a PN V0 bark( x ) sentence (or sequence of sentences) talks about, or REFERS to. Pip barked The part below the line expresses the conditions that hold of the referents. The correspondence between some parts is relatively Later in the course, we will use a slightly different format for obvious. DRSs. e.g. Pip corresponds to “Pip”, likewise barked and “bark”. The main trick will involve arranging the referents correctly. Feb-4-09 Human Communication 5 Feb-4-09 Human Communication 6 1

What semantic rules look like General conventions All our rules will be of the form: Right Left hand becomes If you are looking at a tree of a particular kind, hand side side you can erase part of the tree, and add conditions or referents to the DRS. • The tree on the LHS shows what to remove. • Any tree on the RHS shows what replaces it. • Our first step is to draw a box around our • The lower part of the RHS contains any conditions to be syntactic tree. introduced. • A tree inside a box represents “work to be done” • A discourse referent at the top of the RHS means that a to achieve a translation. The box provides a new discourse referent has to be introduced. context within which to do the translation. • You have a collection of referents to draw from at will. The goal in producing a DRS is to remove all of such Unless otherwise stated, choose a new one. a tree, typically in a series of steps. • A n equation between two referents can be eliminated by replacing one referent by the other throughout. Feb-4-09 Human Communication 7 Feb-4-09 Human Communication 8 An example rule: intransitive verbs Example: a dog barked (tree) S becomes verb( z ) NP VP VP z V0 Det N V0 verb A dog barked Pick any referent, call it z Then: • S ubstitute that referent for the tree below, and including, VP and • A dd “verb( z )” to the DRS’s conditions, where “verb” is the translation of verb . Feb-4-09 Human Communication 9 Feb-4-09 Human Communication 10 Surround this with empty DRS Finding matching rules We have one of the rules we need already: • I ntransitive verbs (above) We need one for NPs which begin with a or an : S x NP VP noun ( x ) NP becomes Det N V0 Det N x A dog barked a(n) noun Note that previous rule instructs us to add a discourse referent to the top part of our DRS. Feb-4-09 Human Communication 11 Feb-4-09 Human Communication 12 2

The rule for intransitive verbs The rule for a Applying the rule for intransitive verbs gives: We can apply the rule for a to give: x S S NP y x y Det N bark ( y ) a dog dog ( x ) bark (y) assuming barked translates to “ bark” . assuming dog translates to “dog”. Feb-4-09 Human Communication 13 Feb-4-09 Human Communication 14 Example: a dog barked , concluded Applying this rule for sentences to: x The rule for sentences goes like this: S x yields: x y bark( x ) bark( y ) dog( x ) S substitute all occurrences dog( x ) becomes of z in the DRS conditions with x x z This will be true in any model p containing these two conditions dog(p) holding of a single individual, e.g. bark(p) Feb-4-09 Human Communication 15 Feb-4-09 Human Communication 16 Summary Exercises Today we have seen: 1. In how many different orders may we apply the rules for • E xamples of semantic rules the above example? Does it make any difference which one we choose? • H ow to apply semantic rules to compute DRSs 2. Provide a complete set of rules which will allow you to • O ur first example analyse: Notice the overall similarities with the semantic rules for arithmetic, and also three differences. (a) Pip miaowed In the case of English, there are Make certain to specify everything you need to add. – L arger units (i.e. translation operates over several subtrees at once) What do you not need to change? – R eferents (expressions in arithmetic do not refer as they do in 3. Provide a model for the above sentence natural language) – I nterpretation refers to a more complex domain (representations of the meanings of sentences, rather than to just numbers) Next time: M ore semantic rules Feb-4-09 Human Communication 17 Feb-4-09 Human Communication 18 3