Semantics Notes - ryan's website



Semantics Notes Disclaimer: The notes below are fully/partially NOT created by myself. They are from slides and/or wikipedia and/or textbook. The purpose of this post is simply to learn and review for the course. If you think something is inappropriate, please contact me at “ryan_yrs [at] hotmail [dot] com” immediately and I will remove it as soon as possible.

Truth-Condition To know meaning of a declarative sentence is to know conditions in which it is true.

Entailment p entails q iff every situation in which p is true is a situation in which q is true. p => q Note: Even if p entails q, there may be situations in which q is true and p is false.

Contradiction When 2 sentences cannot be true in same situation, they contradict each other. p entails q iff p & ¬q are contradictory.

# It indicates following sentence is semantically unacceptable.

Literal & Non-Literal Meaning 2 forms of non-literal meaning of a sentence are: Implicature Metaphor Not same as truth-conditions, which can have both literal and non-literal meaning.

Implicature Non-literal meaning. A type of inference. Conclusion reached by reasoning about literal meaning of a sentence. Can be denied without creating a contradiction.

Metaphor Literal meaning of a phrase is used as a symbol for something else.

Presupposition Sometimes, when speakers utter certain sentences, they make presuppositions. A piece of info that is presented as taken for granted when a speaker utters a sentence. It behaves differently in NON-VERIDICAL env. When putting a clause in a non-veridical env, its entailments are trapped in there. They are not entailments of whole sentence. Projected over scope of negation. Presuppositions of a sentence are also entailments. But it may NOT.

Negation Non-veridical If negating a sentence, it loses its entailments, but not PRESUPPOSITION, which is projected over scope of negation. e.g. - Did he stop smoking? - He used to smoke.

Speech Act Assertion Present sentence as being a true and relevant piece of info. Give orders Ask questions Make promises

Set: Basic ({}) A collection of objects {…} Using curly braces List notation for sets List notation is called an extensional definition Heterogeneous ORDER does not matter. {a, b} = {b, a} REPETITION does not matter. {a, b, b} = {a ,b}

Set: Membership (Î, Ï) A relation between a set and something that is a member of this set. Symbol: Î (“is a member of”) e.g. 3 Î {1, 2, 3} Symbol: Ï (“is not a member of”) e.g. 4 Ï {1, 2, 3}

Set: Predicate (:) {x: x is a natural number} Set of all natural numbers Set of every x such that x is a natural number {x: 3 is a natural number} Set of everything {x: pi is a natural number} Set has no members. {x is a natural number} Only member of set is formula “x is a natural number”.

Set: Identity (=) 2 sets are identical iff they have same members e.g. {1, 2} = {2, 1} {1, 2} = {1, 2}

Set: Inclusion (Í, , Ì) Let S_1 & S_2 be 2 sets S_1 is included in S_2 iff EVERY member of S_1 is a member of S_2. If S_1 is included in S_2, then S_1 is a subset of S_2. Note: if A = B, then A Í B. Note: A = B iff (A Í B and B Í A) If A is included in B but A is not identical to B, then A is PROPERLY INCLUDED (Ì) in B. If A Í B, then A is a subset of B. B is a superset of A. If A Ì B, then A is a PROPER subset of B. B is a PROPER superset of A.

Set: Union () Union of 2 sets A and B is set that contains every element that is either in A OR B, or both. AB = {x: x ÎA or xÎB} e.g. A = {1,2,3} B = {3,4,5} then AB = {1,2,3,4,5}

Set: Intersection () Intersection fo 2 sets A and B is set that contains every element that is both in A AND B. AB = {x: x ÎA and xÎB} e.g. A = {1,2,3} B = {3,4,5} AB = {3}

Set: Difference (-) Diff btw a set A and B is set that contains ANY element in A that is NOT in B. A - B = {X: xÎA and xÏB} e.g. A = {1,2,3} B = {3,4,5} A - B = {1,2}

Set: Empty (Æ) Empty set is set that hes no member IMPORTANT: empty is NOT “nothing”, it is a set. Æ = {}

Meaning of Expression () Meaning of common nouns dog = {x: x is a dog} dog = set of all dogs Meaning of modifiers cute = {x: x is cute} who smokes = {x: x smokes} e.g. cute dog = cute dog = {x: x is cute} {x: x is a dog} = {x: x is cute and x is a dog} linguist who smokes = linguist who smokes = {x: x is a linguist} {x: x smokes} = {x: x is a linguist and x smokes} IMPORTANT: It does not work for ANTI-INTERSECTIVE (PRIVATIVE) adjectives.

Anti-Intersective Adjective aka Privative Adjective If A is an anti-intersective adjective and N is a noun Æ

then A N N = e.g.

fake diamond diamond =


counterfeit Rembrandt Rembrandt =


Adjs like “fake” and “counterfeit” are anti-intersective.

Subset & Superset Inferences e.g. 1. If Mary bought chocolate, it is in the freezer. 2. If Mary bought milk chocolate, it is in the freezer. 3. 1 entails 2, but not opposite (To subset). Antecedent. e.g. If Mary went shopping, she bought chocolate. If Mary went shopping, she bought milk chocolate. 1. 2 entails 1, but not opposite (To superset). Consequent.

Downward & Upward Entailments DE (Downward Entailing) Antecedent of a conditional is a DE env. An env X_Y is DE iff: If A Í B, then XBY entails XAY. (To subset)

UE (Upward Entailing) Consequent of a conditional is an UE env. An env X_Y is UE iff: If A Í B, then XAY entails XBY. (To superset)

Word Analysis: “Any” Grammatical in: Negative clause There isn’t anyone to talk to. Antecedents of conditionals If we talk to anyone, they will discover our secret. Complements of “doubt” I doubt that there is anyone to talk to. Ungrammatical in: Unembedded positive clauses *There is anyone to talk to. Consequents of conditional * If we go home, there is anyone to talk to. Complements of “believe” I believe that there is anyone to talk to.

DE-ness & UE-ness Distribution of “any” if sensitive to DE-ness of its env. DE-ness is a logical property of envs. Grammar is sensitive to logical properties of sentences. This supports our use of truth-conditions and logical concepts like entailments in our study of natural lnaguage semantics. “Exactly 1” is neither UE or DE.

Ambiguity Lexical Police begin campaign to run down jaywalker. run down knock down chase Safety experts say school bus passengers should be belted. belted secured with a belt beaten with a belt Bank Drive-in Window Blocked by Board. board committee piece of wood Bar trying to help alcoholic laywers. bar tribunal drinking establishment Structural Teacher strikes idle kids. (Teacher strikes)//S idle//V kids//O. Teacher//S strikes//V (idle//ADJ kids//N)O. Squad helps dog bite victim. (Squad helps dog) bite victim. Squad helps (dog-bite victim). Bill hit the man with the hammer. Bill (hit the man) with the hammer.


Bill hit (the man with the hammer). Syntactic (Beyond modification) John told the girl that Bill liked the story. John told (the girl that Bill liked) the story.

Just something small and tiny.

John told the girl that (Bill liked the story). Every student read a book. For every student, there is a book that this student read.

Held by Ryan Ruoshui

There is a book that all of the students read.

Yan. Last Updated: 2017-08-15

Principle of Modification If an expression X (constituent or word) modifies an expression Y, then X must c-

Here is the world of a nerdy guy. Visited:

command Y.

C-Command (Constituent Command) Node A c-commands node B if every node dominating A also dominates B, and neither A

nor B dominates the other.

Test of Ambiguity

Type Not ambiguous but context dependent I am hungry. Diff contexts, diff speakers. Not ambiguous but (lexical) under-specification I am going to visit my aunt. My aunt: My father’s sister, or my mother’s sister. Not ambiguous but vague John is bald. How much hair loss counts as baldness? Test Truth-Conditions If a sentence can both be true and false in same situation, it is AMBIGUOUS. John hit the man with the hammer. Situation: hammer was used as an instrument. Sentence is true in 1 reading, false in another. Thus AMBIGUOUS. I am hungry No matter who speaker is, I refers to speaker. Thus NOT AMBIGUOUS. Ellipsis (?) An elided expression must hae same meaning as its antecedent. If an elided expression and its antecedent can have diff meanings, diff in meaning is not a case of ambiguity.

SDCH (Scope/Domain Correspondence Hypothesis) Semantic scope of a linguistic operator in a sentence corresponds to its c-command domain in some syntactic representation of sentence.

Scope Ambiguity John didn’t leave because he was sick. Meaning John didn’t leave, because he was sick. John didn’t (leave because he was sick). Expression Negation Subordinating conjunction “because” We need single men or women. Meaning We need (single men) or women. We need single (men or women).

DetQ (Determiner Quantifier) Determiner quantifiers are expressions like Type every Every cat is cute T iff cat Í cute some Some cats are cute T iff cat cute ≠ Æ most all e.g. Every child read some book. Meaning 1. For every child, there is some book that this child read. (Surface Scope) 2. There is some book such that every child read this book. (Inverse Scope) Situations

1. is true in abc 1. is true in bc only

LF (Logical Form) In order to keep a strict correspondence between c-command and scope, we assume that there is a level of syntactic representation where quantifiers can be moved according to their scope. This level of syntactic representation is called Logical Form.

Logical Form Scope Principle At level of LF, an element has scope over iff is in domain of . “Domain” means c-command domain.

Entailments e.g. DE Every DOG is a pet. At most 5 STUDENTS watched the video. At most 5 students WATCHED THE VIDEO. Every cat who ate BANANAS got sick. No CAT got sick. No cat GOT SICK. UE Every dog is A PET. Some cat who ate BANANAS got sick. Neither Exactly one DOG is a pet. The CAT ate the canary.

Ambiguity e.g. Lexical Syntactical Both

Principle of Compositionality Meaning of a composite expression is a function of meaning of its immediate constituents and way these constituents are put together.

Mental Representation Reference The meaning of the expression X as a relation btw this expression and the real object called X. The name X refers to (denotes) the object called X.

Referent (Denotation) The object that is called X is the referent (or denotation) of the name X.

Definite Description Formed by combining a definite determiner with an NP. Possessive phrases are another type of definite descriptions. It describes its denotation, while proper names do not.

CN (Common Noun) Singular common nouns refer to SETS. e.g. CAT refers to set of cats X is cute = 1 iff X \in {x: x is a cute INDIVIDUAL}

Word Analysis: “Every” Every boy is happy = 1 iff boy Í is happy Every NP VP = 1 iff NP Í VP

Word Analysis: “Some” Some NP VP = 1 iff NP VP ≠


Word Analysis: “A(n)” Some NP VP = 1 iff NP VP ≠


Relational Noun A class of nouns that do not refer to sets of individuals e.g. mother friend side owner birthplace

Functional Noun Relations that satisfy the following condition are functions: A 2 place relation R is a function iff \forall x,u,v: if both \in R and \in R, then u=v.

Transitivity 0: Intransitive 1: Transitive 2: Ditransitive

Intransitive Verb Like CNs, they denote sets of individuals smokes = the set of individuals who smoke is sleeping = the set of individuals who are sleeping was sleeping = the set of individuals who were sleeping slept = the set of individuals who slept Predication as set membership A is sleeping = 1 iff A \in is sleeping A is sleeping = 1 iff A \in {x: x is sleeping}

Transitive Verb Similar to that of relational nouns. A likes B. likes = {, , …} Order: A likes B = 1 iff \in likes Not symmetric A likes B but B might not like A.

Ditransitive Verb Have triples in its extensions. A gave B to C 1 iff \in gave gave = {, , …}

Meaning of Expression Extension Intension

Extension Denotation of these (Proper Name, CN, etc.) expressions are called their extensions. Extension of an expression is its denotation. e.g. Extension of sentence “A likes B” is the truth value ‘true’. Extension of sentence “A does not like B” is the truth value ‘false’.

Review for Midterm

- Truth Condition - Entailment - p entails q iff sentence "p and not q" IS contradictory. - Situation: - Test 1. p && q 2. p && !q - If 1 && !2 => p entails q - If 1 && 2 => p does not entail q - If !1 => p and q are contradictory - Implicature - Cancellation Test (.... Indeed, ...) - I saw two elks. I didn't see three elks. => I saw two elks. Indeed, I saw three of - I saw two elks. I saw more than one elk. => \*I saw two elks. Indeed, I didn't see - Presupposition - Projection Test - Non-Verdical Environment - Antecedent of Conditionals - Negation - Complement of "Doubt" - Question - Inclusion - Í: Inclusion - Ì: Proper Inclusion - Union - AÈB = {x: xÎA or xÎB} - Intersection - AÇB = {x: xÎA and xÎB} - Difference - A-B = {x: xÎA and xÎB} - Ambiguity - Test - Truth-Conditions - Ellipsis - Constituent Command - Extension (Set of ...) - Intension (Concept of ...) - Set Theory - \{\{1,2,3,6},{4,5,8\}\} - {4,5,8} = \{\{1,2,3,6},{4,5,8\}\} - \{\{1,2,3,6},{4,5,8\}\} - \{\{4,5,8\}\} = \{\{1,2,3,6\}\} - {1,2,3,4,5,6} - {4,5,8} = {1,2,3,6} - \{\{\{2,6\}\}\} - \{\{8},\{\{2,6\}\}\} - {2,6,{8\}\} = \{\{\{2,6\}\}\} - \{\{8},\{\{2,6\}\}\} - \{\{2,6},{8\}\} = \{\{\{2,6\}\}\} - \{\{8},\{\{2,6\}\}\} - \{\{\{2,6\}\},{8\}\} = empty

Environment of Proposition RECENT

Visual Computing Notes


Matlab Notes

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2017-01-11 •


2017-01-10 •


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Semantics Notes - ryan's website

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