Final study cards Flashcards
Cotext
text which comes before or after utterance
Circumstances of utterance
-physical circumstances in which expression is uttered
exophor
expression whose full understanding requires knowledge of the setting in which they are uttered (your and my)
- character- invariant aspect
- person, time,spacial
content
-meaning of utterance when it is filled out by a suitable knowledge of the setting in which it is used
Endophora
-dependence- third person personal pronoun
-endophor/ proform- words exhibiting this dependence
“He was driving it today”
-demonstrative, “one”, it, he/she/they, “the bastard”, “so”, “there”, “such”
-Can be any constituent, antecedent can be anything,
-Most common- third person pronoun
Ellipsis
-dependence
-“Ed a porsche”
=Not a full constituent
-Varies with what preceding clause presents
-Fails to convey a proposition unless in the presence of another constituent
Antecedent
-relevant portion of the cotext necessary for full understanding
Gapping
-Ellipsis
- two constituents, neither of which is a constituent of the other
-correspond to first and final constituents of sentence before
“Peter saw the movie and susan ___ the play”
Interrogative ellipses
-Ellipses
-Antecedent entire clause,
-Ellipses for interrogative constituent, standing for ind clause
“Ed bought a mercedes”
“Where ____”
Verb phrase ellipses
- ellipses
- VP is antecedent
- The man who promised to bring wine will.
- to do can be used
Copular complement ellipses
-ellipses
-verb to be in context
“Bill is fond of cheese and mary is ____ too”
Appended coordination
- Ellipses
- One or two phrases appended, often introduced by a coordinating conjunction (and, but)
- Fred goes to the cinema but __ seldom __ with his friends
Nominal ellipses
Antecedent noun phrase, defective expression is one containing constituent that is a sister to the noun
“Colleen ate two large cookies and evan ate three”
Ambiguity
use of alternate truth value judgement to determine ambiguity relies on fixed state of affairs and fixed setting, while use of alternate truth judgement to determine exophora relies on a change in setting and cotext
Implicature
- “i have a cat” implies i do not have 20 cats
- enrichment which is obtained on the basis of utterances literal meaning as well as beliefs about maxims
Entailment
- relation between a set of statements and a single statement- “all men are mortal socrates is a man” entails “socrates is mortal”
- Can be once sentence “wellington was taller than napoleon” entials “napoleon was shorter than wellington”
Cooperation
- maxim
- one should make ones contribution such as is required, by the accepted purpose or direction of the conversation
Quality
- Maxim
- One should have adequate evidence for what one says, should not say what one believes is false
Quantity
-Maxim, One should contribute as much information as is required for purpose of conversation
Relevance
-ones remarks should be relevant
Manner
-One should be perspicuous- brief orderly, clear, unambiguous
Non-conventionality
- Conversational implicatures not conventional
- Can have implicature in some situations, not in others
- Not same as idioms
Non-detachability
- implicatures invariant under paraphrase
- Ex. sarcastic “bill is genius” same implicature as sarcastic “bill is mental prodigy”
Derivability
-Implicatures Can by characterized by form of reasoning
Cancellability
-Implicatures can be undone or cancelled by further information
Implicature ambiguity
-When ambiguity is solved by additional sentence, literal meaning not changed but implicatures can be
presupposition
-supposes previous information to make sense- did you quit smoking presupposes that you used to smoke
Triggers of presupposition
- again, even, still, too
- various verbs - continue, desire, admit, return
- cleft
- if
- when/ since
valid arguement
truth of premisses guarantees truth of conclusion
denial of the antecedent
fallacy- if p then q, it is not the case that p, then not q
modus tollens
if p then q, not q, then not p
syncategorematic defintion of set of formulae
- all propositional variabls are formulae
- any formula with not is a formula and a pair of formulae with connector and enclosed with parenthesis is a formula
- nothing else is a formula
categorematic definition of set of formulae
- adds category of UC (unary connective like not), and BC binary connective
- otherwise same as syncategorematic
atomic formulae (AF) vs composite formulae (CF) vs basic formulae (BF)
- Atomic- just PV
- CF- more complex
- BF- atomic + negations
immediate subformula
-one formula is immediate subformula if it can either be prefixed by negation or paired with another formula and BC +parenthesis to form the second
proper subformula
-immediate subformula or immediate subformula of immediate subformula etc
subformula
- proper subformula or the whole equation
scope of propositional connective
scope of occurance of prop connective is subformula which contains the prop connective but whose subformulae do not
parenthesis abbreviation
- omit for whole formula
- omit for conjuncts of conjunct, adjuncts of adjuncts
truth value assignment
function from domain (PV) to codomain including {T,F}
-bivalent assignment- truth value assignment whose co domain is only t and fvaluation
any function where domain is FM and codomain includes T and F
-classical valuation- valuation that conforms to connective true and false values
extention to a classical valuation (syncategorematic)
a bivalent assignment classically extends to a unique classical valuation
extention to a classical valuation( categorematic
o sub not, o sub V, o sub ^ etc,
satisfaction
bivalent assignment a and each formula x, a satisfies x iff va(x) = T
for a and set of formulae y, a satisfies y iff for each xEy, va(y) = T
- for bivalent ass. a, and formula y, a satisfies y iff a satisfies {y}
- bivalent assignment satisfies empty set
tautology
-formula is tautology iff each bivalent assignment satisfies it
contradiction
-formula is a contradiction iff each bivalent assignment doesnt satisfy it
contingency
a formula is a contingency iff some bivalent assignment satisfies it, some does not
satisfiability
- formula satisfiable if some bivalent assignment satisfies it
- formuale set satisfiable if some bivalent ass satisfies it
- y satisfieable if {y} satisfiable
- each subset of satisfiable set is satisfiable
- empty is satisfiable
unsatisfiability
formula is unsatisfiable if no biv ass satisfies it, set same
y is unsatis. iff {y} is unsatis.
each superset of unsatisfiable set forms unsatis. set
FM is unsatisfiable
semantic equivelence
set of formula or formula is sem. equivalent if each biv ass satisfies former and latter
- all tautologies are sem equiv
- all tautologies are sem equiv to empty set
- all contr. and sets of contr. are sem equiv
- all contr and sets of contr are sem equiv to FM
entailment (formula)
a and b are formulae, x and y are sets
if a E x then x entails a
if c subs y and x entails a, y entails a
x U {a} entails b iff x entails a then b
x entails a and b iff x entails a and x entails b
Coordinators vs Subordinators
C S intrusion N N connect verb phrases Y N admits gapping Y N may iterate N Y initial in compound clause N Y
syndetic vs asyndetic coordination
-syndetic uses “and” while asyndetic uses none
CPDL
-classical predicate logic
=basic expressions are predicates (relational symbols) (constants) and idividual symbols rather than PV
-
CPDL notation
- Adicity- CPDL term for number of places relational symbol has (transitivity)
- IS- individual symbols
- RS- relational symbols
CPDL Signature
let (IS, RS, ad) be a sig for CPDL iff IS and RS are disjoint sets and ad is a function from RS into Z+
Atomic formula of CPDL
n place relational symbol followed by n occurences of individual symbols
Formula of CPDL
- Atomic formula
- if a E FM and b E FM then ab E FM
- if a, b E FM and c E BC, a c b E FM
Other CPDL terms
-Basic formula, immediate subformula, proper subformula, scope definition all same as CPL
problems with english and and ^ comparisson
- Mary does too and peter owns a car bad, flipped is good.
- and can be “and then”
- all issues with and also happen without and in ; sentences- more issues with maxims, presupposition, etc.
coordination of nondeclarative clauses by and/ or/ if
- no truth value to question or command, but and still works for them, so and is different than ^
- hard to explain what and means in this context, but imperative compliance conditions and interrogative answerhood conditions can be seen as like truth values
- c-entailment (compliance) allows for entailment relation without declarative truth value (same with a-entailment)
coordination of an imperative and a declarative by and / or/ if(or NP and declarative)
- paraphrase of if then statement
- –> instead of ^
Problems with or/V
- apparent exclusivity of or
- exclusivity is an implicature (can be cancelled by follow up sentence
- can also be explained by 2 meanings of or
- apparent non-commutability- can be solved with “or rather” or “or else”
apparent synonymity of or and and
-either you may have coffee or you may have tea does entail both parts (may just be implicatures)
conditional clauses
-if sentences
=protasis (subordinate)
=apodosis (main clause)
-more or less corresponds to –>
prolems with if/–>
- negation of conditionals0 it is not the case that, if god is dead, everything is permitted doesn’t ential god is dead
- non-declaratives
- subjenctuve conditionals- counterfactual (would have)
- austinian conditionals- if it snows, tehre is a shovel in the trunk.
adjunctive vs disjuctive subordinator
-adjunctive- cleft, pseudo-cleft, form a single clause answer, can be immediately preceded by focus adverb, may form question, can be immediately preceded by not
not syntax
- it is not the case that same as UC not
- not is often adverb
- more restricted in finite than infinite clauses, except with to be
- can be used as implicature, to deny presupposition
CQL
-quantificational logic
-CPDL but with variables, A, E
=binding
-closed (no unbound) vs open
-alphabetical variants- terms with quantifiers same regardless of variable, not true with un-quantified
syncategorematic definitions of valuation of CQL
- medieval valuations - each corresponds with and while some corresponds with or. everything must be finite and named individually, if repeats it doesnt work. valuation departs from the synthesis tree of a formula once truth value has to be assigned a subformula whose main LC is a quantifier
- marcus valuations- finite universes- Universally A formula is true iff each substitution instance is true in it. E formula is true iff a substitution works
- fregean valuations- to see if AxPx is true, substitute every possible value of a for a, check them all
- Tarski- variable assignment and defined truth in a structure at variable assignment, only one where domain s the set of all formulae, open and closed
Satisfaction
- (M,g) satisfies a iff [a]M,g = T
- true with set
- (M,g) satisfies Ø, (M,g) satisfies a iff (M,g) satisfies {a}
Properties of CQL
-tautology, contradiction, contingency, satisfiability, unsatisfiability, semantic equivelence
Minimal clause
clause in declarative mood with smallest number of minimal constituents.
-Constituent has a head and complements
complement polyvalence
-many verbs with a complement admit different syntactic categories as the complement (appeared for ex)
complement permutation
- verb that admits complement permutation- for alice has to become an NP (just alice) to switch the order in “bill bought alice a dog”
- or alternation like Alice blamed bill FOR the accident, alice blamed the accident ON bill
Verb phrase
- optional complements
- also reflexive polyadic verbs, reciprocal polyadic verbs
- indefinite polyadic (to read)
- contextual polyadic- when relevant complement is omitted, verb behaves endo/exophorically
- Causative polyadic- melt
- mid
Adj Phrase
- may be modifiers or predicates, some adj can only be one, some can be both
- No compliment like dead
- PP compliment like averse to
- S- unsure where it is raining
- Some polyadic like happy
- reciprocal polyadic adj
- often different meanings of adj w diff adicity
Prepositions
- many take NP compliments, some take S compliments
- optional compliment- in - he ran in
- Polyadic P only contextual
- Complementless- afterwards, downstairs, soon
Nouns
-None, two, three- (two and three generally start with PP) ex. the gift to alice of the book by bill.
Constituency grammar with enriched categories
- basic lexical categories (A Adv N P V S,
- phrasal category is a pair comprising a basic lexical category and empty sequence A:().
- Complement list etiher empty or sequence of categories
- can also be a set (for polyadic)
- 2 sets for permutable
Semantic rule format
Let (U,i) be a structure for an English lexicon.
If e | NP and f | VP then v(ef|S) = true iff v(e|NP) ⊆ v(f|VP)
