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Understanding Predicate Logic: The Role of Categories and Statements

This text delves into the principles of predicate logic, focusing on the use of categories such as "Any," "Some," and "All," and clarifies how these terms influence the interpretation of statements. By examining examples involving cookies in jars and the classification of animals, we shed light on how language can shape logical conclusions and the implications of existential claims. The exploration aims to enhance comprehension of logical structure and reasoning, offering a deeper understanding of how logic functions in everyday language.

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Understanding Predicate Logic: The Role of Categories and Statements

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  1. Any General Some A B All A B No A B -#x(Ax&Bx) $x(Ax>-Bx) #x(Ax&Bx) $x(Ax>Bx) Any A B

  2. Any General Some A B All A B No A B -#x(Ax&Bx) $x(Ax>-Bx) #x(Ax&Bx) $x(Ax>Bx) Any A B All A B $x(Ax>Bx)

  3. Not Any General Some A B All A B No A B -#x(Ax&Bx) $x(Ax>-Bx) #x(Ax&Bx) $x(Ax>Bx) Not any A B

  4. Not Any General Some A B All A B No A B -#x(Ax&Bx) $x(Ax>-Bx) #x(Ax&Bx) $x(Ax>Bx) Not any A B No A B Not some A B

  5. Not Any General Some A B All A B No A B -#x(Ax&Bx) $x(Ax>-Bx) #x(Ax&Bx) $x(Ax>Bx) Not any A B There are not any COOKIES in the JAR.

  6. Not Any General Some A B All A B No A B -#x(Ax&Bx) $x(Ax>-Bx) #x(Ax&Bx) $x(Ax>Bx) Not any A B There are not any COOKIES in the JAR. No COOKIES are in the JAR.

  7. Not Any General Some A B All A B No A B -#x(Ax&Bx) $x(Ax>-Bx) #x(Ax&Bx) $x(Ax>Bx) Not any A B There are not any COOKIES in the JAR. No COOKIES are in the JAR. Not some COOKIES are in the JAR.

  8. Not Any General Some A B All A B No A B -#x(Ax&Bx) $x(Ax>-Bx) #x(Ax&Bx) $x(Ax>Bx) Not any A B There are not any COOKIES in the JAR. No COOKIES are in the JAR. Not some COOKIES are in the JAR. -#x(Cx&Jx) $x(Cx>-Jx)

  9. ‘A’ can mean ‘all’ General Some A B All A B No A B -#x(Ax&Bx) $x(Ax>-Bx) #x(Ax&Bx) $x(Ax>Bx) An A is B A PENCIL is on the DESK. #x(Px&Dx)

  10. ‘A’ can mean ‘all’ General Some A B All A B No A B -#x(Ax&Bx) $x(Ax>-Bx) #x(Ax&Bx) $x(Ax>Bx) An A is B A WHALE is a MAMMAL. $x(Wx>Mx)

  11. ‘The’ can mean ‘all’ General Some A B All A B No A B -#x(Ax&Bx) $x(Ax>-Bx) #x(Ax&Bx) $x(Ax>Bx) The A is B The WHALE is a MAMMAL. $x(Wx>Mx)

  12. As are Bs General Some A B All A B No A B -#x(Ax&Bx) $x(Ax>-Bx) #x(Ax&Bx) $x(Ax>Bx) As are Bs WHALES are MAMMALS. $x(Wx>Mx)

  13. The Road Map General Some A B All A B No A B A road map for predicate logic translation. Is the statement singular? No Yes Pn -#x(Ax&Bx) $x(Ax>-Bx) #x(Ax&Bx) $x(Ax>Bx)

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