This document discusses key concepts in sentence semantics and propositional logic. It defines sentences, utterances and propositions. A proposition is conceived as an abstract string of words that can be true or false depending on the state of affairs. The document also discusses truth conditions and how knowing the meaning of a sentence involves knowing when it is true or false. It introduces concepts of formal semantics like models and model theory. Finally, it discusses word meaning, propositions, entailment, predicate logic and propositional logic.

1. Sentence SemanticsSentence Semantics
Sentences, utterances, andSentences, utterances, and
propositionspropositions

2. ►...any stretch of talk, by one person, before...any stretch of talk, by one person, before
and after which there is silence on the partand after which there is silence on the part
of that person.of that person.
►...the use by a particular speaker, on a...the use by a particular speaker, on a
particular occasion, of a piece of language,particular occasion, of a piece of language,
such as a sequence of sentences, or asuch as a sequence of sentences, or a
single phrase, or even a single word.single phrase, or even a single word.

3. ►....is a neither a physical event nor a....is a neither a physical event nor a
physical object. It is, conceived abstractly, aphysical object. It is, conceived abstractly, a
string of words put together by thestring of words put together by the
grammatical rules of a language.grammatical rules of a language.
►.. is that part of the meaning of the utterance.. is that part of the meaning of the utterance
of a declarative sentence which describesof a declarative sentence which describes
some state of affairs.some state of affairs.

4. The notion of truthThe notion of truth
► If there is any conceivable set of circumstances in which one sentenceIf there is any conceivable set of circumstances in which one sentence
is true, while the other is false, we can be sure that they expressis true, while the other is false, we can be sure that they express
different propositions.different propositions.
► John gave Mary a book.John gave Mary a book.
► Mary was given a book by John.Mary was given a book by John.
► Isabel loves Tony.Isabel loves Tony.
► Tony loves Isabel.Tony loves Isabel.
► True propositions correspond to facts, in the ordinary sense of theTrue propositions correspond to facts, in the ordinary sense of the
word fact. False propositions do not correspond to facts.word fact. False propositions do not correspond to facts.
► One can entertain propositions in the mind regardless of whether theyOne can entertain propositions in the mind regardless of whether they
are true or false, e.g. by thinking them, or believing them. But only trueare true or false, e.g. by thinking them, or believing them. But only true
propositions can be known.propositions can be known.

5. Indicate whether each of the following sentence pairs expresses the same or differentIndicate whether each of the following sentence pairs expresses the same or different
propositions.propositions.
a Mary read the book / The book was read by Marya Mary read the book / The book was read by Mary
b Fred took back the book/ Fred took the book backb Fred took back the book/ Fred took the book back
c The cat chased the rat/ The cat was chased by thec The cat chased the rat/ The cat was chased by the
ratrat
d The chef cooked the meal/ The chef had the meald The chef cooked the meal/ The chef had the meal
cookedcooked
e Hondas are easy to fix/ It’s easy to fix Hondase Hondas are easy to fix/ It’s easy to fix Hondas

6. Decide whether each pair of sentences below has the sameDecide whether each pair of sentences below has the same
or different propositional content. If they have the sameor different propositional content. If they have the same
propositional content, identify the proposition that they bothpropositional content, identify the proposition that they both
share.share.
a Can John have some cake? John has somea Can John have some cake? John has some
cakecake
b Take out the garbage / You will take out theb Take out the garbage / You will take out the
garbagegarbage
c Can you pass the salt?/ The salt shaker isc Can you pass the salt?/ The salt shaker is
nearly emptynearly empty

7. In each of the following, indicate whether aIn each of the following, indicate whether a
proposition is asserted or not.proposition is asserted or not.
a John left yesterdaya John left yesterday
b Did John leave yesterday?b Did John leave yesterday?
c Can John leave this afternoon?c Can John leave this afternoon?
d John, get out of hered John, get out of here
e John!e John!

8. ►Explain the following from the text (p.22):Explain the following from the text (p.22):
‘Normally, when a speaker utters a simple‘Normally, when a speaker utters a simple
declarative sentence, he commits himself todeclarative sentence, he commits himself to
the truth of the corresponding proposition:the truth of the corresponding proposition:
i.e. he asserts the proposition. By uttering ai.e. he asserts the proposition. By uttering a
simple interrogative or imperative, a speakersimple interrogative or imperative, a speaker
can mention a particular proposition, withoutcan mention a particular proposition, without
asserting its truth.’asserting its truth.’

10. The word meaningThe word meaning
► There can be no simple answer to the question of
what the meaning of a sentence is. The word
meaning has many different senses. This is why in
linguistics we tend to be very explicit about the
kinds of meanings we are studying. Here are two
examples:
► (1) What is the meaning of a natural language
expression?
a. that to which it refers
b. that which the speaker intends to communicate
with it

11. ► The first answer to the question, (1-a), is what is normally associated
with the study of natural language semantics. Central to semantics is
the relationship between a sentence and the world.
► So, the meaning of John is the individual we refer to by the word
‘John’ and the meaning of John hates Bill is what needs to be the case
in order for this sentence to be true.
► One could see the answer in (1-b) as typical to pragmatic inquiry.
Beyond mere reference, pragmatic meanings are about the use of a
sentence in a particular context. For instance, consider the following
context. Someone has just asked Will John invite Bill to the party? If in
this context, I answer John hates Bill, it is likely that I intend this
sentence to be understood as a negative answer to the question
whether John will invite Bill to the party.

12. Truth conditionsTruth conditions
► Apart from the referential nature of meaning, one crucial
assumption in formal semantics concerns what it means to
know the (semantic) meaning of a sentence. Consider, (2).
(2) Rick has a 50 cent coin in his wallet.
► To know (semantically) what (2) means is to be able to
distinguish a situation in which (2) is true, from one in
which (2) is false. You clearly know how you would go
about this: all you need to do is look in my wallet and sift
through the coins on the lookout for a 50c coin.
Consequently, you know what (2) means, even though you
don’t know whether or not it is true.
► To know the meaning of S is to know when S is true; that
is, to know the conditions that make
it true: its truth-conditions.

13. ► Crucially, (2) tells us something very specific about the world we live in,
namely that if you were to look in my wallet you would find a 50c coin.
This information is very specific in the sense that it leaves a lot of other
stuff open: whether there is more than one coin in my wallet; whether
there are any other coins in my wallet; what my wallet looks like; etc. In
other words, there exists an infinity of situations that make (2) true, but
all these situations have one thing in common. This one thing is what
the meaning of (2) corresponds to.
► If you haven’t looked in my wallet yet, and I assert (2) and you believe
me, then you will have gained information. Before accepting (2), you
did not know whether the world you lived in was one in which I have a
50c coin in my wallet. Afterwards, you did know (or at least believed
so). This is what meanings in the relevant sense do: they convey
information about the world.

14. ►Formal or truth-conditional semantics is
sometimes called model-theoretic
semantics. The idea is that a sentence is
true or false only with respect to a particular
way things are, a particular model of what is
reality. In some state of affairs, the sentence
is true, and in some others it will be false.

15. Sentence semanticsSentence semantics
►PropositionsPropositions
►EntailmentEntailment
►Predicate LogicPredicate Logic

16. Word meaningWord meaning
►Function words (and, however)Function words (and, however)
►Cross linguistic problems where sameCross linguistic problems where same
concepts may include different level ofconcepts may include different level of
transparencytransparency
►Metaphors (time is money) the wordsMetaphors (time is money) the words
involved do not reflect overall meaninginvolved do not reflect overall meaning
►Idioms (it is raining cats and dogs)Idioms (it is raining cats and dogs)

17. PropositionsPropositions
►John is killing Mary.John is killing Mary.
►Mary is being killed by John.Mary is being killed by John.
►John is doing smth to Mary.John is doing smth to Mary.

18. Propositional logicPropositional logic
The sky is blue.The sky is blue.
pp
The sky is blue and it is raining.The sky is blue and it is raining.
p qp q
The sky is blue, it is raining and it is cold.The sky is blue, it is raining and it is cold.
p q rp q r

19. Propositional LogicPropositional Logic
The sky is blue.The sky is blue.
p T Fp T F
p= T p=T/F p= Fp= T p=T/F p= F

20. ConnectivesConnectives
NameName SymbolsSymbols NL EquivalentNL Equivalent
ConjunctionConjunction &, ∧ &, ∧ andand
DisjunctionDisjunction ∨ ∨ ,, oror
ImplicationImplication → → , ⊃ , ⊃ If...thenIf...then
NegationNegation ¬ , ~¬ , ~ notnot
EquivalenceEquivalence ↔↔ , ≡, ≡ IffIff
If and only ifIf and only if

21. ConjunctionConjunction
► The bank was robbed and the police are on theThe bank was robbed and the police are on the
way.way.
pp qq p & qp & q
TT TT TT
FF TT FF
TT FF FF
FF FF FF

22. EntailmentEntailment
►⇒⇒
►p ⇒ q, iff p=T & q=Tp ⇒ q, iff p=T & q=T
John regrets studying maths.John regrets studying maths.
p= John regrets studying maths.p= John regrets studying maths.
q= John studies maths.q= John studies maths.
p ⇒ qp ⇒ q

23. Brutus killed Caesar.Brutus killed Caesar.
► p= Brutus killed Caesar.p= Brutus killed Caesar.
► q= Caesar died.q= Caesar died.
► p ⇒ qp ⇒ q

24. ► One of the prime sources of data for the study of
semantics are entailments. You can use (intuitions
about) entailments to establish whether two
(declarative) sentences are semantically
independent, semantically related or semantically
identical.
► Entailment —Sentence S entails sentence S’ if
and only if whenever S is true, S’ is true too
► In (7), you find an example of an entailment,
indicated with).
(7) a. John owns a blue sweater.
b. John owns a sweater.

25. (7) a. John owns a blue sweater.(7) a. John owns a blue sweater.
b. John owns a sweater.b. John owns a sweater.
► Given the notion of entailment, there are three kinds of meaning
relations that may exist between two sentences.
► (9) either S ⇒⇒ S’ or S’ ⇒⇒ S truth-conditionally related
► neither S⇒⇒ S’ nor S’ ⇒⇒ S truth-conditionally unrelated
► both S ⇒⇒ S’ and S’ ⇒⇒ S truth-conditionally equivalent
► The sentences in (7) are truth-conditionally related. That is, John owns
a blue sweater entails John owns a sweater, but not vice versa.
Consequently, we cannot find a situation in which the former is true,
but the latter false, while we can find a situation in which it is true that
John owns a sweater, but false that he owns a blue one. (Just take a
situation in which John’s sweater is red.)
► Two truth-conditionally equivalent sentences, i.e. two sentences that
entail one-another, have exactly the same semantic meaning. This
means that there are no situations in which their truth value differs:
when one of the two sentences is true, then both of them are true;
when one of the two sentences is false, then both of them are false.

26. ► For instance, (10-a) both entails and is entailed by (10-b).
This suggests that the dative alternation in English has no
semantic import.
► (10) a. John gave Mary an apple.
► b. John gave an apple to Mary.
► In summary, the relation between entailments and truth-
conditions is a tight one. Above we said that S entail S’ if
whenever S is true, S’ is true too. An alternative way of
saying the same thing is to make use of the notion of
possible world:
► Entailment — Sentence S entails sentence S’ if and only
if S’ is true in all possible worlds in which S is true

27. We can depict truth-conditions by sketching the worlds in which
sentences are true by means of Venn
diagrams.
S
S’
S entails S’
S
S’
S and S’ are contradictory

28. No entailment relation
S
S’
Equivalence

29. Entailment TestsEntailment Tests
Step 1: Assumption of any qStep 1: Assumption of any q
Step 2: Make q negativeStep 2: Make q negative
Step 3: p & ¬ qStep 3: p & ¬ q
Evaluation: if p & ¬ q ~ nonsense: p ⇒ qEvaluation: if p & ¬ q ~ nonsense: p ⇒ q
Brutus killed Caesar.Brutus killed Caesar.
p = Brutus killed Caesar.p = Brutus killed Caesar.
q= Caesar died.q= Caesar died.
¬ q = Caesar did not die.¬ q = Caesar did not die.
p & ¬ q Brutus killed Caesar and Caesar did not die.p & ¬ q Brutus killed Caesar and Caesar did not die.

30. Propositional RelationsPropositional Relations
► ParaphraseParaphrase
p: John killed Maryp: John killed Mary
q: Mary is being killed by John.q: Mary is being killed by John.
► ContradictionContradiction
p: John killed Mary.p: John killed Mary.
q1: John did not kill Mary.q1: John did not kill Mary.
q2: Mary is alive.q2: Mary is alive.
► InclusionInclusion
p: John killed Mary.p: John killed Mary.
q: John did something to Mary.q: John did something to Mary.

31. ContradictionContradiction
►The denial of something true is false, and
so, by the definition of entailment, we come
to expect that a sentence together with the
denial of one of its entailments forms a
contradiction. Contradictions cannot be
uttered felicitously.
►(8) #John owns a blue sweater, but he does
not own a sweater.

32. Identify the meaning relation for eachIdentify the meaning relation for each
of the following pairs of sentences.of the following pairs of sentences.
► a) John is single. – John is married.a) John is single. – John is married.
► ParaphraseParaphrase
► EntailmentEntailment
► contradictioncontradiction
► b)b) You should see an eye specialist. – You shouldYou should see an eye specialist. – You should
consult an oculist.consult an oculist.
► paraphraseparaphrase
► EntailmentEntailment
► contradictioncontradiction

33. ► c) The president was assassinated. - Thec) The president was assassinated. - The
president is dead.president is dead.
► ParaphraseParaphrase
► entailmententailment
► ContradictionContradiction
► d) Take the elevator to the first floor. –d) Take the elevator to the first floor. –
Take the lift to the ground floor.Take the lift to the ground floor.
► paraphraseparaphrase
► EntailmentEntailment
► contradictioncontradiction

34. ► ) Mary is younger than John. – Mary is) Mary is younger than John. – Mary is
older than John.older than John.
► ParaphraseParaphrase
► EntailmentEntailment
► contradictioncontradiction
► f) Today is Friday. – Today isn't Monday.f) Today is Friday. – Today isn't Monday.
► ParaphraseParaphrase
► entailmententailment
► contradictioncontradiction

35. Predicate LogicPredicate Logic
►p: John loves Mary.p: John loves Mary.
► Love (x,y)Love (x,y)
► x= ‘John’ y= ‘Mary’x= ‘John’ y= ‘Mary’
►Representation of internal structure of aRepresentation of internal structure of a
propositionproposition

36. ►PROPOSITIONPROPOSITION
►PREDICATIONPREDICATION
►PREDICATE (argPREDICATE (arg11,...,arg,...,argnn))

37. ►P: GB is a country.P: GB is a country.
►Country (Great Britain)Country (Great Britain)
►p: John loves Mary.p: John loves Mary.
►Love (John, Mary)Love (John, Mary)
►p: John sends Paul her love.p: John sends Paul her love.
►Send (John, Paul, love)Send (John, Paul, love)

38. List propositional coresList propositional cores
John finally bought a present for motherJohn finally bought a present for mother..

39. Answer the following:Answer the following:
► 1) State which of the following represents an utterance (U)1) State which of the following represents an utterance (U)
and which a sentence (S):and which a sentence (S):
John sang wonderfully last night S/UJohn sang wonderfully last night S/U
‘‘John sang wonderfully last night’ S/UJohn sang wonderfully last night’ S/U
2) Can a sentence be true or false? Yes/No2) Can a sentence be true or false? Yes/No
3) Is an utterance tied to a particular time and place? Yes/No3) Is an utterance tied to a particular time and place? Yes/No
4) Is a sentence tied to a particular time and place? Yes/No4) Is a sentence tied to a particular time and place? Yes/No
5) Can a proposition be said to be in any particular language?5) Can a proposition be said to be in any particular language?
Yes/NoYes/No
6) Can an utterance be true or false? Yes/No6) Can an utterance be true or false? Yes/No

40. ► https://www.youtube.com/watch?v=XLvv_5meRNMhttps://www.youtube.com/watch?v=XLvv_5meRNM
► Hurford, J. R.; Heasley, B.; Smith M. B.; (2007),Hurford, J. R.; Heasley, B.; Smith M. B.; (2007), SemanticsSemantics
A CoursebookA Coursebook – Second Edition, Cambridge University– Second Edition, Cambridge University
Press, New YorkPress, New York
► Nouwen, Rick. Foundations of Semantics I: Truth-
conditions, entailment and logic. February/March 2011,
Gent