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Translating English to Propositional Logic

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Janet Stemwedel
Janet Stemwedel
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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]
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]
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. ,[object Object],[object Object],[object Object],[object Object],[object Object]
Translating material conditionals. ,[object Object],[object Object],[object Object],[object Object],[object Object]
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]
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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Translating English to Propositional Logic

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  • 18. 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 )
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