Midterm study materials Flashcards
Behaviorism
- Previously, human behavior viewed as mind, animal behavior viewed as instinct
- Obvserved human behavior from introspection
- Behavioralism rejected unobservable data, only observable was scientific study
- Confined to studying stimulus and response elicited
Structuralism
- Immediate constituency analysis
- Bloomfeld
Ethology
- Study of animal behavior from zoology
- Innate vs learned fixed action patterns
- Model- experience-> innate endowment->capacity
Kazimierz Ajdukiewicz
-devised in order to give a mathematical characterization of the notation of classical quantificational logic.
Yehoshua Bar-Hillel
-Better exploration of how categorical grammar might apply to natural language
Leonard Bloomfield
- Paninis bitch
- syntax in addition to paninis morph and phonology
- Viewed study of language (linguistics) as special branch of psychology
- Sought to make linguistics scientific by recasting it as behavioral psychology
- Structuralism
Noam Chomsky
-Anti-behavioralism, new moderl based on language acquisition device
Zellig Harris
-Furthered Bloomfield’s work
Charles Hockett
-Furthered Bloomfield’s work
Joachim Lambek
-Calculus- explains recursive expressions of natural language and is a generalization of categorical grammar
Panini
-First generative grammar for sanskrit 500 BCE
Ferdinand de Saussure
- Beginning of 20th century
- Synchronic vs diachronic
B F Skinner
-Behavioral Psychologist
Alfred Tarski
-Model theory
Nikolaas Tinbergen
- Zoologist
- Ethology grew out of his work
John Watson
-Behavioralism
Rulon Wells
-Furthered bloomfield’s work
Wilhelm Wundt
-Established psychology as empirical science, independent of philosophy
Critical period
-The life stage when an animal needs a certain stimulus in order to develop the capacity
Competence vs Performance
Competence- language stored inside mind
Performance- observable production of language
Deprivation experiment
- Deprive animal of stimulus during critical period and see if behavior still happens
- If yes, it’s innate. if no, it’s learned
Diachronic vs synchronic
- Diachronic- change over time
- Synchronic- at specific point in time
Fixed action pattern
- Sequence of actions for example way a bird builds a nest
- Ethology studies innate vs learned
Language acquisition device/ language faculty
- Chomsky
- Experience -> LAD -> grammatical competence
Distinctive properties of human language behavior
- Monkeys- discrete, definite expressions
- Honey bees- dance- indescrete, indefinite
- Humans- discrete, indefinite
Basic insights into language found in Indian grammatical tradition
- 4000 rules
- Phonological features
- Phonological rules (context)
- Theta roles
- First generative grammar
Features of linguistic inquiry (minimal pairs)
-All items in sentences are alike except 1 from each, allows us to compare function of 2 constituents in identical environments
Poverty of the stimulus
- Chomsky
- Hearing stimuli of spoken language is not enough for child to acquire grammatical competence. Must be something innate in humans that allows us to learn language
- Language structure more complex and systematic than sound waves we hear
- Children acquire competence in short time without hearing a lot of spoken lang
- Children hearing different stimuli still arrive at same grammatical competence
- Rules for competence not taught
- Lang acq separate from childs motivation, personality, genetics
Criticism of poverty of stimulus
- No special LAD, part of humans general ability to learn
- Maybe you can learn complex language structure out of acoustic signal
Generative grammar vs grammar
-Generative- finite set of rules that can be used to create every possible expression in the language
Immediate constituency analysis
- Every complex expression can be divided into subexpressions until minimal constituents
- Can more or less mix and match constituents and sentence still acceptable
- Infinite num of expressions from finite set of rules and lexical items
Formation rules
- Figure out how language is put together in your own words
- pay attention to what expressions are allowed and what not allowed- this is conditions for formation rules
- Write formation rule with memorized format- just how lang is put together not what it means
Valuation rule
-Write valuation rule that includes same condition as formation rule but it tells you values/ meanings of expressions
Model theory
- Tarski
- Studies how meanings of constituents makes up meaning of complex expressions
Set
-Collection of members. Always abstract
Members
-Things in the set. members can be concrete or abstract
Ways to define set
- List membership- let set be {a,b,c,d}
- Abstract notation- let set be {x:is a chair in this room}
Terms in set theory
- Capital letters refer to sets
- A,B,C- Sets are fixed names- if refer to A again, same A as first time
- XYZ- sets are variables, X can refer to new set or same set
- Lower case letters sets or not sets
- x,y,z variables, a,b,c fixed
Important sets
N- natural numbers Z- integers Z+- positive integers Z-- negative integers E- is a member of
Cardinality
- The size of a set. How many membrs it has. 2 straight lines show cardinality |{a,b}| = 2.
- Count number of objects named not just symbols (if a is twice, only count once)
- ø or{} means empty set
Types of sets
-Singleton sets- 1 number
-Doubleton sets- have 2 numbers
-Sets can have sets as members {N,Z-,Z+}
V= universe of discourse
A⊆B
-A is Subset of or equal to B
Subject transitivity
if x⊆y and y⊆z then x⊆z
-R is transitive iff x,y,x ED, xRy, yRz, then xEz
Antisymmetry
ƒ
-R is antisymmetric iff for every x, yE D iff xRy and yRx then x = y
Reflexivity
X⊆X
Logical truth
Disjointedness
- X is disjointed from Y if there is no member that belongs to X and Y
- X∩Y=ø
Set union
-∪
Member x is member of X ∪ Y iff x is a member of x or a member of y
-Like adding together
Difference
x is a member of X-Y iff x is a member of X but not Y
Complementation
-Complement- everything in V besides the thing
Cartesian product
- Binary operation on sets
- result is set of ordered pairs
- {a,b}x{1,2} = {<a>,<b>}</b></a>
- AXB not same as BXA</b></a>
Family of sets
-Set where sets are members
Power set operation
- Takes set, makes family of sets
- Collets into 1 set possible subsets of set
- Pow{1,2} = {ø,{1},{2},{1,2}}
- Every set is a member of own power set
- Empty set is member of every power set
Binary operations
- Take to sets, yield a set
- Operations of families of sets- take family, yield a set
Generalized Union
- Uz= {x:xEY for some YEZ}
- UZ contains all members of subsets that are contained within Z
Generalized intersection
- ∩z ={x:xEY for each YEZ}
- ∩z only contains those elements which are a member of every subset within z
Generalized cartesian product X
-Applies to family of sets and makes set of ordered pairs or triples or n-tuples
Relations
- Contains a number of instances, not same thing as instances
- Binary relation- has pairs as instances, triple relation has triples as instances
Graph
- Relations graphs is the set of all instances
- Relations domain is background set from which the members of graph are drawn
- Relation on a set is relation seen against background of set
2 ways to show relations visually
- Matrix
- Directed graph
Reflexivity relation
- Relation R is reflexive iff for every XED, xRx
- is a member of the set
Irreflexivity
R is irreflexive iff there is no XED , xRx
- is not member of set
Symmetry
R is symmetric iff for every x, yED if xRy then yRx
Asymmetry
-For every x, yED if xRy then not yRx
Intransitivity
-R is intransitive iff for every x,y,z ED, if xRy and yRz then it is not true that xRz
Connectedness
- R is connected iff for every x,y E D, where x =/=z, then either xRy or yRx
- Is less than
Binary relations from set to a set
- Domain- set of things related to co-domain- domain member = argument = pre-image
- Co-domain- set of things related to domain - codomain member = value = image
- Graph- actual pairings between domain and codomain
Left totality
- Each member of domain bears some relation to some member of codomain
- Existence
Right totality
- Each member of codomain has some relation to domain
- Surjection
Left monogamy
- All of domain has only one relation to something on codomain
- Uniqueness
Right monogamy
- All of codomain has only one relation to something on domain
- Injections
Function
- Binary relation which is both left total and left monogamous
- Fuction f:X->Y
- 3 ways to display function with finite graph
- Bipartite graph
- Table
- Vertical list
Rule of association
-Calculate any ordered pair in function, shown with arrow
Bijection
-Right total and right monogamous
Constant functions
-Every element in domain maps to same one element in codomain
Partial functions
-Not necessarily functions because they are left monogamous but not left total
Extension of a function
- Original domain, codomain, and graph are subsets of new function’s domain, codomain, graph
- Opposite is a restriction- new domain etc is the subset
Near variant function
- One function is near variant of another iff they have same domain and codomain, graphs differ from one another by max 1 ordered pair
- f sub 1 ↦2
Characteristic functions (Chr)
- Function that describes contents of each subset of a power set
- Domain of chr is all the things in the subsets
- Codomain is 0,1 0 means not present, 1 means present
Product functions
- Makes two functions work in tandem
- Delta assigns each natural number to a number twice itself
- Sigma assigns every letter of alphabet letter after itself
- Product of delta and sigma is
- Work in tandem on ordered pair of elements, where first is from the domain of delta and second is domain of sigma
- From example above, <5,b> gives <10,c>
English Nouns
-Grammatical number, case (nominative, objective, posessive- mostly personal pronouns), gender
Copular verbs
-Verbs like to be and to become
Predicate nominatives
Nouns which follow copular verbs (Soccer is A SPORT)
Apposition
-A noun that further specifies another noun is in apposition to the first noun (Paul, my brother)
Objective complement
- We consider them OUR FRIENDS
- Our friends not apposition
- Also adjectives- bill considers the house large.
Pronouns
- Personal (I,we,you)
- Relative (who, which, that)
- Interrogative pronouns (what, who)
- Demonstrative (this, that, those)
- Indefinite (anyone, somebody)
- Reflexive (-self)
- Reciprocal pronouns (each other, one another)
Types of adjectives
- Modifier (large apple)
- Predicate (apple is large)
- Objective complement (Considers the house large)
- Comparative and superlatives (some periphrastic- more attractive)
- Pronominal adj- same categories as pronouns
Limitations of traditional English grammar
- Nothing attempts to characterize recursive structure of English
- Nothing attempts to show how meaning of smaller expressions contribute to meaning of larger expressions
- o clear and systematic criteria whereby it characterizes its fundamental concepts
Constituency analysis rules
-Bill laughed vs The guest laughed
NP1: NP-> N(p)
NP2: NP->Dt N(c)
N(c)->AP N(c)
Definition of constituency grammar
- Non-empty, finite set of expressions
- Non-empty, finite set of categories
- Non-empty, finite set of ordered pairs (category, item)
- Non-empty finite set of synthesis rules
Constituents of a language rules
- Each lexical entry is a constituent
- If C1…Cn->C is a rule, and e1|C1 …. en|Cn are constituents, then e1….en|C is in CSG
- Nothing else in CS
Amphiboly
-When an expression accommodates more than one constituency analysis
Issue with number agreement
- Constituency grammars do not accommodate agreement in grammatical number
- Need to double categories to accommodate for sing. and plural for Nouns and verbs
- Need to double rules as well
- Complex category label in form of ordered pair dogs (Nc,p)
- Adapted notation: dogs|Nc;p
- Add x to synthesis rules to show that agreement is necessary
Issue with subcategorization
- Use subscripts to denote subcategories
- Need to distinguish verbs by what kind of complement they require
Issue with phrasal and lexical categories
-In formal rules A->B etc., nothing shows connection between first and second part of the rule (in informal the connection can be seen)
Acceptability vs grammaticality
- the car walked- grammatical but unacceptable - acceptability determined by speakers
- animality vs not doesnt work (complex)
Types of discontiguity
- English verbs associated with adverbs (to wake up, to wake someone up)
- Wrapping- head of modifier on one side, complement of modifier on other side. (a good enough job to pass inspection)
- Extraposition- modifier appears at end of clause (an article appeared in the newspaper about malaria)
- preposing- entire verb phrase precedes subject and aux verb- ben promised to finish his paper and finish his paper he will
- PPpreposing (near the door colleen saw a spider)- PP at beginning of clause
- Topicalization- (the new painting by picasso bill thinks alice likes very much)
- Easy or tough movement- (that theory was thought to be easy to prove)
- Wh movement
Transformational rules
- More powerful than constituency rules
- Set of expressions generated by CR proper subset of TR
- In same sentences- a review of bleak house appeared vs a review appeared of bleak house, CR does not indicate same meaning
- Deep structure vs surface structure
- Surface structures of these sentences (made by CR) differ, but deep structure made by TR are the same, showing common meaning
- Add in trace coindexed with dislocated constituent
Limits on recursion
- With right embedded recursion, no limit to number of times recursed
- With left embedded recursion, there is a limit.
