Lecture7 semanticsSENTENCE MEANING AND PROPOSITIONAL CONTENT

SENTENCE MEANING AND PROPOSITIONAL CONTENT CHAPTER OUTLINE 1.1 Proposition 1.2 Propositional content 1.3 Notational representation of propositions 1.4 Truth functionality 1.5 Sentence types and their meaning The truth value of a proposition should be distinguished from the truth conditions of a sentence e.g. Mary married a rich man. Truth value of a proposition: The proposition can be either true or false (hence a twovalued proposition). Truth conditions of the sentence: Mary must be a woman. Mary is of a marriageable age.

CHAPTER 7 SENTENCE MEANING AND

PROPOSITIONAL CONTENT

1.1 Proposition (Revisited)

• A Proposition is defined as the invariant meaning expressed by a sentence, devoid of

any modality.

e.g She is probably right.

• Proposition: She is right

• Modality: varying from probable to impossible

• In semantics, the letters ‘p, q, r’ are often used as symbols of propositions.

• Propositions involve in the meanings of not only declarative, but also interrogative and

imperative sentences.

e.g Is she right? (You) be careful

Truth-value vs Truth-conditions

• The truth value of a proposition should be distinguished from the truth conditions of a sentence

e.g Mary married a rich man.

• Truth value of a proposition: The proposition can be either true or false (hence a two-valued proposition).

Propositional content

• A proposition usually consists of (a) something which is named or talked about known as

ARGUMENT (tham tố/tham thể) or entity, and (b) an assertion or predication made about the arguments expressed by the PREDICATE (vị từ).

e.g The man bit the dog.

The dog bit the man.

• Predicate: BITE

• Two arguments: MAN & DOG

• The meaning of a sentence consists of the predicate, argument(s), and the role of each

• Not all entities are arguments

e.g It rained heavily.

• The arguments may fall into two sub-groups: participant and non-participant.

• Participants are those necessitated by the predication, and answer the question: Who

does what to whom?

• Non-participants are optional and answer the questions: why, when, where, how?

e.g The woman hit the man (with a ruler)

• There are three arguments: the woman, the man, ruler

• In standard grammatical treatment, participant arguments surface as subject, direct or

indirect object whereas non-participant arguments occur as adverbials.

Predicator - Predicate

• A PREDICATE is any word, or sequence of words, which, in a given single sense, can

function as the predicator of a sentence.

e.g hungry, in, asleep, hit, show, bottle: are predicates

and, or, but, not: are not predicates

• Predicate (vị từ / vị thể) and predicator (vị tố) are terms of quite different sorts The term

‘predicate’ identifies elements in the language system, independently of particular example sentences.

• The term ‘predicator’ identifies the semantic role played by a particular word (or groups

of words) in a particular sentence.

Degrees of predicates

• The combination of predicate and arguments can be defined in terms of degree The

DEGREE of a predicate is a number indicating the number of arguments it is normally understood to have in a simple sentence.

• A predicate of degree one (often called a one-place predicate) is used with one argument.

e.g asleep, beautiful

• A prediate of degree two (often called a two-place predicate) is used with two arguments.

e.g kill, see

• A predicate of degree three (often called a three-place predicate) is used with three

arguments.

e.g give, make

Arguments vs predicates

• Arguments refer to entities while predicates deal with events, properties,

attributes and states.

• Those individuals that are independent and can stand alone are arguments.

• Things like qualities, relations, actions and processes that are dependent and

cannot stand alone are termed predicates.

e.g my computer

break down, fast, new

• The relationship between entities as arguments and events, qualities, states as predicates is

predication.

• Frawley (1992) defines predication as the way that individuals instantiate – embody, carry

out, take on or are linked to – properties, actions, events, attributes or states.

e.g My wife is writing a report.

• The event is “writing” because “writing” must be done by someone, an entity, and of

something, another entity.

• Each of the entities “my wife”, and “a report” is the argument of the predicate because they

instantiate the “writing”

• However, not all events are predicates (true of intensive verbs like be)

• In English, not only verbs, but also nouns, adjectives and propositions can function as

predicates.

• Semantic roles are a means to represent sentence meaning in logical terms

They are usually assigned to nouns and noun phrases according to the relation they hold with the predicate.

e.g John is writing a letter.

Mary kicked the dog.

My mother bought me a car.

Levels of Generality

• Semantic roles can exist at three levels of generality:

1 “Verb-specific” roles

Runner, killer, hater, smeller, receiver, located, sent to…

2 Relation or thematic roles: are generalizations across the verb-specific roles like:

Agent (giver, speaker, dancer, runner), instrument, experiencer (liker, thinker, feeler, presumer, lover), patient…

3 Generalized or macro-roles: are generalizations across thematic relations.

Actor (agent, instrument, recipient…), Undergoer (experiencer, patient, stimulus…)

Levels of Generality

• Van Valin, Jr (1999) claims that there are only two macro-roles: ACTOR and

UNDERGOER.

• ACTOR is generlization across agent, experiencer, instrument and other roles, which

surface as the grammatical subjects.

e.g Mary opened the door.

They liked the play very much.

The key opened this door.

• UNDERGOER is a generalization subsuming patient, theme, recipient, stimulus, and

other roles, which surface as the grammatical object.

e.g She made me a cake.

You love her because of her money.

Examples Roles surfacing as S Roles surfacing as O

1.3 Notational representation of propositions

Notational representation of simple propositions

2.

Argument: bracketed full words

Predicate: capital letters

Joe was in Hanoi  (Joe) IN (Hanoi)

1 Argument has to be a particular someone/something.

a Someone get me a drink, please

b Someone called me last night

2 Predicate can be Adj, V, Prep, N.

• She is nice.

• She smiles.

• She is in New York.

3 The less arguments, the less informative the proposition.

My mother wrote a letter.

My mother wrote me.

My mother wrote me a letter.

4 Arguments of a proposition may be expressed by another proposition.

• She said that she was well taken care of.

Embedded propositions

• The arguments of a proposition may be expressed by another proposition, not a

referring expression.

e.g I know that she is a smart person

Do you want me to go there?

I doubt if the film will start on time She did not tell me what to do

• According to Kreidler (1998), predicates that have embedded propositions as theme

arguments may include the following

a knowledge or ignorance of a possible fact.

e.g I know that she’s right

I doubt if she will come.

b an attitude or orientation towards a fact or possible fact

e.g I am happy that she was able to pass the test.

I like to become a doctor.

c causing, allowing, or preventing the occurence of a fact

e.g She stopped me from going out.

I’ll have the students rewrite their essays.

d perception of a fact

e.g I watched the boys playing football.

I heard her cry.

e saying something about a fact or possible facts

e.g She said that she had lost her belongings.

• Propositions as arguments can occupy subject or object positions, and they can surface

as nominal clauses in the following ways.

a Wh-clauses

e.g What happened last night was appalling.

I didn’t like what I saw.

b That-clauses

e.g That she cried in public was unthinkable.

She said that she would come.

c To infinitive clauses

e.g I want her to succeed.

It is rather hard to get a job these days.

d Ing-clauses

e.g I saw the teacher coming

Treating her like that is unacceptable.

Notational representation of embedded propositions

• At the first level of representation, the proposition as argument is symbolized by x.

• At the next level, this x-proposition will be presented in the usual way for a simple

proposition.

e.g She said that she would wait for me.

 At the first level we can have:

sSAYx

 At the next level down we have:

x = sWAITm

1.4 Truth Functionality

• Definition

• Terminologies

• Five operations

Simple and composite sentences

• Simple sentences : one clause

• Composite sentences : more than one clause

 Compound sentences

Either he did not pass his driving test or I am a Dutchman.

 Complex sentences

• The truth value of a composite proposition is a function (in a mathematical

sense) of the truth values of its component propositions (i.e simple propositions).

E.g., She is married and she is pregnant

Compositional variables

f(p,q)

She dances and he sings.

• The English words and and and or correspond roughly to logical connectives Connectives or

provide a way of joining simple propositions to form complex propositions A logical analysis must state exactly how joining propositions by means of a connective affects the truth of the complex propositions so formed.

• Any number of individual well-formed formulae can be placed in a sequence with the

symbol “&” between each adjacent pair in the sequence The result is a complex formed formula.

well-• E.g The three simple formulae: jGREETm (John greeted Mary), jHUGm (John hugged

Mary) and jKISSm (John kissed Mary) can be joined together to form:

(jGREETm) & (jHUGm) & (jKISSm)

• This operation generates a composite proposition, symbolized as p & q, which is true if

and only if both p and q are true For example:

• In a situation in which Henry died and Henry died Terry resigned is both true, then Terry resigned Henry died and

Terry resigned

Terry resigned is true.

• In a situation where Henry died is true, but Henry died Terry resigned is false, then Terry resigned Henry died and

Terry resigned

Terry resigned is false.

• Where Henry died is false, but Henry died Terry resigned is true, then Terry resigned Henry died and Terry resigned Henry died and Terry resigned

is also false.

• Where Henry died and Henry died Terry resigned are both false, then Terry resigned Henry died and Terry resigned Henry died and Terry resigned

• Any number of well-formed formulae can be placed in a sequence with the symbol V

between each adjacent pair in the sequence The result is a complex well-formed formula.

• For example, from the simple propositions:

hHERE: Harry is here.

A single complex formula can be formed:

(hHERE) V (cDUTCHMAN)

• More examples:

Dorothey saw Bill or Alan.

Either John or Peter has used my computer.

• Disjunctions creates a composite proposition: p V q, which is true

a If and only if either p or q is true and

b If and only if both p and q are true

• In a situation in which Henry died and Henry died Terry resigned is both true, then Terry resigned (Either) (Either) Henry

died or Terry resigned

died or Terry resigned is true

• Where Henry died is true, but Henry died Terry resigned is false, then Terry resigned (Either) (Either) Henry died or Terry

resigned

resigned is true

• Where Henry died is false, but Henry died Terry resigned is true, then Terry resigned (Either) (Either) Henry died or Terry

resigned

resigned is also true.

• Where Henry died and Henry died Terry resigned are both false, then Terry resigned (Either) (Either) Henry died or Terry

resigned

resigned is also false

• The logical connective symbolized by → corresponds roughly to the relation between an ‘if’

clause and its sequel in English The linking of two propositions by → forms what is called

a conditional

• If Alan is here, Clive is a liar.

Material Implication

• This operation creates a composite proposition whereby p → q (p implies q) p → q is true if

and only if: (a) Both p and q are true (b) Both p and q are false (c) p is false and q is true

• It is false if p is true and q is false For example

If she has married him, they are honeymooning in HL now

• This composite proposition can be true if (1) it is true that she has married him and they are

honeymooning in HL now, or (2) it is false that she has married him and it is also false that they are honeymooning in HL now If it is true that she has married him but it is false that they are honeymooning in HL now, then the proposition is false because p does not imply q The last case is when she has not married him but they are honeymooning in HL now, which

is found by most people to be paradoxical.

• Entailment

p is true and q is necessarily true (i.e true in all possible worlds)

If dogs are mammals, they are animals

• Implicature

The truth of q can be inferred from p in certain contexts in which p is made.

If Trang’s cellphone is on, she must be writing a message or making a phone

• The logical connective symbolized by ≡ expresses the meaning ‘if and only if’ in English The linking of two propositions by ≡ produces what is called a ‘biconditional’

• E.g The meaning of “John is married to Mary if and only if Mary is married to John”

could be represented as:

(jMARRYm) ≡ (mMARRYj)

• The biconditional connective is aptly named because it is equivalent to the conjunction

of two conditionals, one ‘going in each direction’ Inother words, there is a general rule: p ≡ q is equivalent to (p → q) & (q →p)

• The connective ~ used in propositional logic is paraphrasable as English

‘not’ Strictly speaking, ~ does not CONNECT propositions, as do (&) and (V) ~ is prefixed to the formula for a single proposition, producing its negation ~ is sometimes called the ‘negation operator’, rather than ‘negation connective’.

• E.g

Alice didn’t sleep can be represented as ~ aSLEEP

THE END