Gr7.ppt
- 1. 1 Group 7 Sentence meaning and propositional content • What is a proposition • Proposition content • Notational representation of propositions • Truth functionality • Sentence types and their meaning
- 2. 2 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: probable - 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
- 3. 3 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. • Truth conditions of the sentence: Mary must be a woman Mary is of a marriageable age
- 4. 4 Propositional content 1. Propositional content 2. Semantic roles 3. Predicates & Arguments
- 5. 5 Propositional content • A proposition usually consists of (a) something which is named or talked about known as ARGUMENT or entity, and (b) an assertion or predication made about the arguments expressed by the PREDICATE. 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 argument. When we specify all these elements, we are talking about the propositional content of the sentence.
- 6. 6 Arguments • 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 treatement, participant arguments surface as subject, direct or indirect object whereas non-participant arguments occur as adverbials
- 7. 7 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 and predicator are terms of quite different sorts. The term ‘predicate’ identifies elements in the language system, independently of particular example sentences. • The term ‘predicator’ indentifies the semantic role played by a particular word (or groups of words) in a particular sentence. • A simple sentence has one predicator, although it may well contain more than one instance of a prediate.
- 8. 8 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
- 9. 9 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
- 10. 10 Predication • 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 arguments of the predicate because they instantiate the “writing” • However, not all events are predicates. • In English, not only verbs, but also nouns, adjectives and propositions can function as predicates
- 11. 11 Semantic roles 1. Definition 2. Levels of generality 3. Types of semantic roles
- 12. 12 Definition • 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
- 13. 13 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…)
- 14. 14 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
- 15. 15 SVO Examples Roles surfacing as S Roles surfacing as O The wind opened the door Instrument Patient The girl opened the door Agent Patient Bob received a mail Recipient Theme She robbed me of my love Agent Source
- 16. 16 Notational representation of propositions 1. Arguments: single lower-case letters Predicate: capital letters • Tom loves Mary tLOVEm
- 17. 17 Notational representation of simple propositions 2. Argument: bracketed full words Predicate: capital letters • Joe was in Hanoi (Joe) IN (Hanoi)
- 18. 18 Notes 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. • She is a bartender.
- 19. 19 Notes 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. • Whoever did it must be brought to course.
- 20. 20 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.
- 21. 21 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 She told us what to do f. The beginning, continuing, or termination of an event e.g. I started to smoke We will continue to have perfect leaders.
- 22. 22 • 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.
- 23. 23 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 Putting the two together we have: sSAYx x = sWAITm
- 24. 24 Truth Functionality • Definition • Terminologies • Five operations
- 25. 25 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 If he passes his driving test, I am a Dutchman.
- 26. 26 Definition • 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
- 27. 27 Compositional variables f(p,q) She dances and he sings. p q
- 28. 28 Logical variables Negation ~ Conjunction & Disjunction V Implication Equivalence
- 29. 29 Conjunction • The English words and and or correspond roughly to logical connectives. Connectives 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 wellformed formula. • E.g. The three simple formulae: jGREETm (John greeted Mary), jHUGm (John hug Marry) and jKISSm (John kissed Mary) can be joined together to form: (jGREETm) & (jHUGm) & (jKISSm)
- 30. 30 Conjunction • Truth table for & p q p & q T T T T F F F T F F F F She left and I stayed
- 31. 31 Conjunction • 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 Terry resigned is both true, then Henry died and Terry resigned is true • In a situation where Henry died is true, but Terry resigned is false, then Henry died and Terry resigned is false • Where Henry died is false, but Terry resigned is true, then Henry died and Terry resigned is also false. • Where Henry died and Terry resigned are both false, then Henry died and Terry resigned is also false
- 32. 32 Disjunction • 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 cDUTCHMAN Charlie is a Dutchman 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
- 33. 33 Disjunction p Q p V q T T T T F T F T T F F F You can get there (either) by train or by bus. • Truth table for V-inclusive
- 34. 34 Disjunction p q p V q T T F T F T F T T F F F Either you are her mother or that lady is • Truth table for V-exclusive
- 35. 35 Disjunction • 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 Terry resigned is both true, then (Either) Henry died or Terry resigned is true • Where Henry died is true, but Terry resigned is false, then (Either) Henry died or Terry resigned is true • Where Henry died is false, but Terry resigned is true, then (Either) Henry died or Terry resigned is also true. • Where Henry died and Terry resigned are both false, then (Either) Henry died or Terry resigned is also false
- 36. 36 Implication • 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
- 37. 37 Material Implication • Truth table p q p q T T T T F F F T T F F T If Mary invited John, he will go.
- 38. 38 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.
- 39. 39 • 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.
- 40. 40 Equivalence • Truth table for ≡ p q p ≡ q T T T T F F F T F F F T If the horse is a mammal, the shark is a fish. The conjunction of two implications
- 41. 41 Equivalence • 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)
- 42. 42 Negation • 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 Clare is not married to Bill = ~cMARRYb
- 43. 43 Negation • Truth table for ~ P ~ P T F F T I love you.
- 44. 44 Exercise Find out the truth-value of the following composite propositions in the following cases (a, b, c, d) 1. I passed the driving test and got the license a week later. (a). It was true that I passed the driving test, but I received the license four weeks later. (b). It was true that I passed my driving test, and I got the license a week later. (c). It was true that I did not pass my driving test, but it was true that I got the license a week later. (d). Neither of the situations was true.
- 45. 45 Exercise 2. If you marry her, I will kill my self (a). If it is true: ”you marry her”, and it is also true: “I will kill myself”. (b). If it is true: ”you marry her”, but it is not true: “I will kill myself”. (c). If it is not true: ”you marry her”, but it is true: “I will kill myself”. (d). Neither is true.