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Mapa Mental por Jessica Gledhill, actualizado hace más de 1 año
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Semantics
- Kinds of
Meaning:
Lectures 1-2
- PRINCIPLE OF
COMPOSITIONALITY:
- Not all linguistic expressions
are compositional e.g. idioms
- Local and structure-dependent: determiners
and head nouns need to be able to compose
together, just like verbs and their arguments
- Based on syntax
- Meaning of linguistic expression is
determined by the meaning of its subparts,
and the rules that combine them
- Not all linguistic expressions
are compositional e.g. idioms
- DENOTATIONS
- Ostensive definition:
what it points to
- Denotations pick
out relevant sets
- Bare nouns are predicates -
they denote properties and can
occur in the copula construction
- Predicates denote sets of
individuals that have the property
ascribed
- Ostensive definition:
what it points to
- TRUTH CONDITIONS
- What the world would have to
be like in order for the
proposition to be true
- Intensions are a more
accurate
representation of word
meaning
- Presuppositions: A proposition X
presupposes Y if Y is assumed to be
true by anyone who expresses X
- What the world would have to
be like in order for the
proposition to be true
- OPPOSITES
- Extension - thing picked out in actual world
Intension - thing picked out in all possible worlds
- Literal (sentence) - derived from linguistic
expression, independent of context.
Inferred (utterance) - everything else
- Tautology - necessarily true in all worlds
Contradiction - necessarily false in all worlds
- Extension - thing picked out in actual world
Intension - thing picked out in all possible worlds
- ENTAILMENTS
- Useful to make reference to
truth relations between
statements, like the relation of
entailment
- Part of its encoded
meaning, but not encoded
directly
- Uttering a sentence
makes you committed to
the truth of the sentence
and the entailment
- A statement A entails a
statement B if wherever A is
true, B must also be true
- Upward
- Entailment towards the
superset, e.g. John likes blue
cheese entails that he likes
cheese. (towards the
GENERAL)
- Entailment towards the
superset, e.g. John likes blue
cheese entails that he likes
cheese. (towards the
GENERAL)
- Downward
- Entailment towards the subset, e.g. Every
dog barked entails that every small dog
barked. (towards the SPECIFIC)
- Entailment towards the subset, e.g. Every
dog barked entails that every small dog
barked. (towards the SPECIFIC)
- Useful to make reference to
truth relations between
statements, like the relation of
entailment
- PRINCIPLE OF
COMPOSITIONALITY:
- Logic:
Lectures 3-6
- PROPOSITIONAL
- Treats propositions as atoms and
provides a way of representing
the constructing of complex
propositions with connectives
- Conjunction ^ - typically
represented by 'and'. Order doesn't
matter, only true when T+T, all
others false
- Loss of meaning in
translation: sequential
elements, and the
distinction of 'but'
- Loss of meaning in
translation: sequential
elements, and the
distinction of 'but'
- Disjunction v - typically
represented by 'or', only
true if p is true.
- Negation ¬ -
Opposites apply
- Material implication -> - Partially
resembles 'if...then', order matters,
the antecedent 'if' must occur first.
Only false if when T+F
- Loss of meaning in translation:
logic doesn't represent the
causation implication
- Loss of meaning in translation:
logic doesn't represent the
causation implication
- Equivalence <-> -
Expressed as 'if and only
if', order is irrelevant, true
when T+T and F+F
- Equivalences in logic
are known as De
Morgan's Law
- Equivalences in logic
are known as De
Morgan's Law
- Exclusive disjunction - Often
what is expressed by 'or', but
exclusivity may be an
implicature
- Can also be derived by
adding 'but not both'
- Can also be derived by
adding 'but not both'
- The Key: Match key to
variables, propositions must
not decompose any operators
(negation), full propositions
only, order implications
correctly
- Treats propositions as atoms and
provides a way of representing
the constructing of complex
propositions with connectives
- PREDICATE
- Represents the inner
structure of propositions in
terms of arguments,
predicates and quantifiers
- Form: Melissa is tall = TALL (m)
Order of Obliqueness: Subject >
Indirect Object > Direct Object
- Prepositions left out, which
alters meaning, e.g. the
distinction between in/on
- Quantifiers
- Universal - variable bound by the universal
quantifier e.g. ∀x(ILLUMINATED(x))
- Existential - variable bound by the existential
quantifier e.g. ∃x(ILLUMINATED(x))
- Scope is read from the formula
left-to-right, and is typically
reflected by hierarchical relations
- Restricted quantification - quantificational determiner exists with a
noun that restricts it Universals require the implication symbol, and
existentials require conjunctions e.g. ∀x(BOOK(x) -> READ(s,x)) and
∃x(BOOK(x) ^ READ(s,x))
- Universal - variable bound by the universal
quantifier e.g. ∀x(ILLUMINATED(x))
- Argument positions can be occupied
by complex expressions like
embedded sentences e.g.
SAY(s(BARK(m)))
- Represents the inner
structure of propositions in
terms of arguments,
predicates and quantifiers
- GENERALIZED
QUANTIFIER THEORY
(GQT)
- Need to generalize quantifiers because a
number of quantifiers fail to translate
into the predicate logic system
- All quantifiers can be recast as
relations between sets e.g.
[Every x: CIRCLE(x)] RED(x)
- These are sensible ostensive definitions, they
point to two sets [the main predicate and the
nominal restriction], and say something
numerical about the relation between them
- Need to generalize quantifiers because a
number of quantifiers fail to translate
into the predicate logic system
- PROPOSITIONAL
- Quantifiers:
Lectures 7-9
- SET THEORY
- Sets - collections of things
Set theory - algebras of set
things
- Notation
- 1. A=B: A is identical to B 2. A⊂B: A is a proper subset of B 3. A⊆B: A is a subset of B
4. |A|=2: The cardinality of A is 2; A has 2 members 5. |B>A|: B has more members
than A 6. |B∩A|: The cardinality of the intersection of B and A is two 7.
|B-A|>|A∩B|: The number of members in B that are not also in A is greater than
the number of elements in both
- 1. A=B: A is identical to B 2. A⊂B: A is a proper subset of B 3. A⊆B: A is a subset of B
4. |A|=2: The cardinality of A is 2; A has 2 members 5. |B>A|: B has more members
than A 6. |B∩A|: The cardinality of the intersection of B and A is two 7.
|B-A|>|A∩B|: The number of members in B that are not also in A is greater than
the number of elements in both
- Asymmetric
Quantifiers
- Most, few, every
- Asymmetric quantifiers describe
what proportion of the nominal
restriction is in the intersection
- Most circles are red ≠ Most red things
are circles
- PROPORTIONAL QUANTIFIERS
- Most, few, every
- Symmetric
Quantifiers
- Numbers
- Symmetric quantifiers
just count subsets
- CARDINAL QUANTIFIERS (do
not come with an existence
presupposition)
- Numbers
- Sets - collections of things
Set theory - algebras of set
things
- NEGATIVE POLARITY ITEMS
- Words that seem to need to be in the
scope of a negative element e.g. ever and anything
- NPIs are licensed in non-negative
sentences with PROPORTIONAL
quantifiers that have downward entailments
- CARDINAL quantifiers
do not license NPIs at all
- No: downward entailing on restriction and
main predicate so NPIs licensed in both
positions = neg + NPI
- Every: downward
entailing only on
restriction, only
licenses NPIs here
- Three: not downward
entailing on either
argument, so NPIs not
licensed anywhere
- Words that seem to need to be in the
scope of a negative element e.g. ever and anything
- EXISTENTIAL SENTENCES
- THERE+BE+NP
- Only some quantifiers can
be in the subject of such
sentences, e.g. some,
many, four
- Proportional quantifiers resist these positions because
they presuppose the existence of a background set, and
it would sound odd to use them in an existential
sentence, because existence is already ASSERTED by the quantifiers
- THERE+BE+NP
- SET THEORY
- Presuppositions, Definites &
Opacity: Lectures 9-11
- PRESUPPOSITIONS
- Only propositions can give
rise to entailments, but
lexical items can give rise to
presuppositions
- Tests
- Negation test: presuppositions are
retained under negation, but
entailments are not
- Interruption test: "I didn't know
P" is an appropriate interruption
- Negation test: presuppositions are
retained under negation, but
entailments are not
- Kinds of presuppositions
- Existential: presupposes
the existence of a given
identity
- Factive: presupposes the
truth of a following
proposition
- Counterfactual:
presupposes the falsity of
a following proposition
- Lexical/aspectual: presupposes another
concept with the use of a given
expression, typically related to structured
sequence of events
- Existential: presupposes
the existence of a given
identity
- Only propositions can give
rise to entailments, but
lexical items can give rise to
presuppositions
- DEFINITE DESCRIPTIONS
- Refer to a single individual in the actual
world, but definite descriptions are not rigid
designators, because the intension of a
definite description is richer than the name
- Russell's proposal
- Definite descriptions assert existence (there
must be an individual accurately described by
the expression), and uniqueness (there must be
exactly one individual satisfying the
descriptions)
- Formula in classical predicate logic, using ∃ for
existence and ∀ for uniqueness e.g.
∃x(KING-OF-FRANCE(x) & ∀y(KING-OF-FRANCE(y) ->
y=x) & BALD (x)))
- Definite descriptions assert existence (there
must be an individual accurately described by
the expression), and uniqueness (there must be
exactly one individual satisfying the
descriptions)
- Alternative: GQT + Benefits
- Makes 'the' a
proportional
quantifier,
ensures it comes
with an existence
presupposition
- Accounts for
familiarity effect
with 'the'
- Easily
amended to
account for
plural
definites
- Makes 'the' a
proportional
quantifier,
ensures it comes
with an existence
presupposition
- Refer to a single individual in the actual
world, but definite descriptions are not rigid
designators, because the intension of a
definite description is richer than the name
- OPACITY
- Principle of
Substitutivity
- Identical expressions have the
same truth value
- Does not hold opaque
sentences like "often
been an Italian"
- Identical expressions have the
same truth value
- Opaque contexts: modalized sentences; the
complement of propositional attitude
predicates like 'want'
- Adverbs
- Adverbs like often are not just
simple adjuncts, they are
propositional operators that take
scope, the issue is the scope of the
adverb with respect to the definite
expression
- Weird scope reading: One
individual cannot have a property
like Italian-ness on and off, it's an
individual level predicate which
must hold through all contexts
- Adverbs like often are not just
simple adjuncts, they are
propositional operators that take
scope, the issue is the scope of the
adverb with respect to the definite
expression
- Principle of
Substitutivity
- INDEFINITES
- Specific reading: a
particular individual
- Non-specific reading:
any individual
- Specific reading: a
particular individual
- PRESUPPOSITIONS
- Modality:
Lectures 11-13
- Modal expressions: auxiliaries, adverbs,
adjectives, constructions
- LOGICAL MODALITY
- 4 logical states of modality:
necessarily true/false ◻
(non-contingent) & possibly
true/false ⋄ (contingent)
- 4 logical states of modality:
necessarily true/false ◻
(non-contingent) & possibly
true/false ⋄ (contingent)
- EPISTEMIC MODALITY
- What is necessary/possible, given
WHAT IS KNOWN (context-dependent).
Involves quantification over worlds
which are compatible with what we
know (epistemically possible worlds)
- Necessary
- Must/can't
- ∀we
- Must/can't
- Possible
- Might/could be
- ∃we
- Might/could be
- What is necessary/possible, given
WHAT IS KNOWN (context-dependent).
Involves quantification over worlds
which are compatible with what we
know (epistemically possible worlds)
- DEONTIC MODALITY
- What is MORALLY/LEGALLY necessary/possible, according to
some set of rules (contextually given). Involves quantification
over the set of worlds in which the relevant codes of behaviour
are adhered to (perfect obedience worlds)
- Necessary
- Must/required to
- ∀wpo
- Must/required to
- Possible
- Can/may/allowed to
- ∃wpo
- Can/may/allowed to
- What is MORALLY/LEGALLY necessary/possible, according to
some set of rules (contextually given). Involves quantification
over the set of worlds in which the relevant codes of behaviour
are adhered to (perfect obedience worlds)
- POSSIBLE WORLDS
- Modalized sentences don't
assert that the core proposition
is true in the actual world, they
say something about the set if
worlds in which it would be true
- Possible to quantify over these worlds
using ∀w - all possible worlds & ∃w - at
least one possible world
- Modalized sentences don't
assert that the core proposition
is true in the actual world, they
say something about the set if
worlds in which it would be true
- RESTRICTION
- If modals quantify over possible
worlds, the modal flavour is a
restriction of this quantification.
This is know as the modal base
- Modal base is characterised as being accessible to
the actual word, the restriction is specifying an
accessible relation between the actual world and the
set of possible worlds (epistemically/deontically
accessible).
- Approaches
- VARIABLE STRENGTH APPROACH:
different strengths require
different quantifications over
possible worlds. Stronger the modal
- the more accessible the world is
- VARIABLE RESTRICTION APPROACH:
concentrating on different worlds. The
narrower the restriction, the more
accessible
- VARIABLE STRENGTH APPROACH:
different strengths require
different quantifications over
possible worlds. Stronger the modal
- the more accessible the world is
- Pragmatics
- Modal "must" cannot be used when we
have direct evidence, because it comes
with an evidential presupposition.
- Ambiguities in specific/non-specific
interpretations
- Modal "must" cannot be used when we
have direct evidence, because it comes
with an evidential presupposition.
- If modals quantify over possible
worlds, the modal flavour is a
restriction of this quantification.
This is know as the modal base
- Modal expressions: auxiliaries, adverbs,
adjectives, constructions
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