Translating English to Propositional Logic

Translating English to Propositional Logic Phil 57 section 3 San Jose State University Fall 2010

Does order always matter? ,[object Object],[object Object],[object Object],[object Object],[object Object]

Conjunction and disjunction are commutative. ,[object Object],P Q (P  Q) (Q  P) T T T T T F F F F T F F F F F F

Conjunction and disjunction are commutative. ,[object Object],P Q (P  Q) (Q  P) T T T T T F T T F T T T F F F F

Conjunction and disjunction are also associative. ,[object Object],[object Object]

With mixed operators, order does matter. ,[object Object],[object Object],[object Object],[object Object]

Translating material conditionals. ,[object Object],[object Object],[object Object],[object Object]

Material conditionals and necessary conditions. ,[object Object],[object Object],[object Object],[object Object],[object Object]

Material conditionals and necessary conditions. ,[object Object],[object Object],[object Object],P Q Q  P T T T T F T F T F F F T

Material conditionals and sufficient conditions. ,[object Object],[object Object],[object Object],[object Object],[object Object]

Material conditionals and sufficient conditions. ,[object Object],[object Object],[object Object],P Q P  Q T T T T F F F T T F F T

Translating material conditionals. ,[object Object],[object Object],[object Object],[object Object],[object Object]

Translating material conditionals. Construction Translation If P, then Q (P  Q ) P, if Q ( Q  P ) P only if Q (P  Q ) Only if P, Q ( Q  P )

Translating biconditionals. ,[object Object],[object Object],[object Object],[object Object],[object Object]

A biconditional is the conjunction of two material conditionals. ,[object Object],[object Object],[object Object],[object Object]

Biconditionals are commutative. ,[object Object],[object Object],[object Object],[object Object]

Biconditionals are associative. ,[object Object],[object Object],[object Object],[object Object],[object Object]

Order matters translating conditionals. ,[object Object],[object Object],[object Object],[object Object]

Order matters translating conditionals. ,[object Object],[object Object],P Q (P  Q) (Q  P) T T T T T F F T F T T F F F T T

Translating English to PL. ,[object Object],[object Object],[object Object]

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