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Logic and Semantics Semantics

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

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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

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

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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)

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

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

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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)

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

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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!

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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))

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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

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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

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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…

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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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CAS LX 502 8a. Formal semantics 10.1-10.4. Truth and meaning The basis of formal semantics: knowing the meaning of a sentence is knowing under what conditions.

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