# Logic and Semantics Semantics. meaning linguistic sign object in the world referent The semiotic triangle logic.

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Logic and Semantics Semantics

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

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

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, y) run (x) run (y) person (x) person (y) chase (x, y) run (x) run (y)

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

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

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

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

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

Quantifiers Logical Scope 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. y: mountain (y) ( x: man (x) like (x, y)) x: man (x) ( y: mountain (y) like (x, y)) higher scope lower scope

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

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

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?

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