Semantics Logic and Semantics The semiotic triangle logic

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Semantics Logic and Semantics

Semantics Logic and Semantics

The semiotic triangle logic meaning linguistic sign object in the world “referent”

The semiotic triangle logic meaning linguistic sign object in the world “referent”

Logic Predicates • “one place” – – door (x) accountant (x) book (x) run

Logic Predicates • “one place” – – door (x) accountant (x) book (x) run (x) • “two place” – eat (x, y) – chase (x, y) – read (x, y) Connectives ‘and’ : ‘or’: ‘not’: ‘implies’

Logical formulae • “If someone chases someone else then both people run” what predicates?

Logical formulae • “If someone chases someone else then both people run” what predicates? what connectives?

Logical formulae • “If someone chases someone else then both people run” chase (x,

Logical formulae • “If someone chases someone else then both people run” chase (x, y) run (x) run (y) person (x) person (y) chase (x, y) run (x) run (y)

Logic Quantifiers • existence: • for all: All men are mortal. Socrates is a

Logic Quantifiers • existence: • for all: All men are mortal. Socrates is a man. Therefore Socrates is mortal.

Logic Quantifiers • existence: • for all: All men are mortal. Socrates is a

Logic Quantifiers • existence: • for all: All men are mortal. Socrates is a man. Therefore Socrates is mortal.

Logic Quantifiers • existence: • for all: All men are mortal. • x: man

Logic Quantifiers • existence: • for all: All men are mortal. • x: man (x) mortal (x) Socrates is a man. • man (Socrates) Therefore Socrates is mortal (Socrates)

Logic Quantifiers • existence: • for all: All men are mortal. • x: man

Logic Quantifiers • existence: • for all: All men are mortal. • x: man (x) mortal (x) Some man is mortal. • x: man (x) mortal (x)

Logic: Venn diagrams mortal things men mortal things not empty! All men are mortal.

Logic: Venn diagrams mortal things men mortal things not empty! All men are mortal. x: man (x) mortal (x) Some man is mortal x: man (x) mortal (x)

Logical Scope Quantifiers • existence: • for all: All men like some mountain. •

Logical Scope Quantifiers • existence: • for all: All men like some mountain. • x: man (x) like (x, y) • • mountain (y) y: mountain (y) ( x: man (x) like (x, y)) • x: man (x) ( y: mountain (y) like (x, y))

Logical Scope All men like some mountain. higher scope • y: mountain (y) (

Logical Scope All men like some mountain. higher scope • y: mountain (y) ( x: man (x) like (x, y)) lower scope • x: man (x) ( y: mountain (y) like (x, y))

Logic: Venn diagrams mortal things Socrates is a man (Socrates) men the refo All

Logic: Venn diagrams mortal things Socrates is a man (Socrates) men the refo All men are mortal. x: man (x) mortal (x) re Socrates is mortal (Socrates) VALID LOGICAL DEDUCTION

Componential Meanings for verbs… • Dowty… – The door is open. – The door

Componential Meanings for verbs… • Dowty… – The door is open. – The door opens. – John opened the door. open(x) become(open(x)) cause(John, become(open(x))) –Statives, inchoatives, causatives…

Logic: capturing ambiguity 1. Every person in this room speaks two languages. 2. Two

Logic: capturing ambiguity 1. Every person in this room speaks two languages. 2. Two languages are spoken by everyone in this room. what predicates? what connectives? what quantifiers?