CA 208 Logic Ex5

1
CA 208 Logic Ex5

• Given our definition of the syntax of first order
  predicate logic (FOPL), which of the following
  are well-formed formulas (WWFs) and which are not
  (and why)? Assume that all constant and variable
  symbols are defined and that is a 2-place
  predicate symbol and student is a 1-place
  predicate symbol.
• For those that are WWFs of FOLP, translate them
  into English (assume that j refers to John, k to
  Kate etc).
  
• like(j,k)
• like(j,k) ? like(k,j)
• (like(j,k) ? like(k,j))
• like(j,k) ? ?like(k,j)
• (like(j,k) ? ?like(k,j))
• ?x like(k,x)
• ?y like(k,y)
• ?x like(x,k)
• ?x like(x,x)
• ?y like(k,y)
• ?x ?y like(x,y)
• ?y ?x like(x,y)
• like(j,k) ? j
• k ? j
• like(j ? k)

2
CA 208 Logic Ex5

• Translate (i.e. formalise) the following English
  sentences into (in) FOPL (use female(_), male(_),
  sister(_,_), brother(_,_), mother(_,_),
  father(_,_) as one and two-place predicate
  symbols. Let the meaning of sister(x,y) be that x
  is a sister of y, etc. )
• Kate is female
• John is male
• Kate is a sister of John
• John is a brother of Kate
• Anne is the mother of Kate
• Ted is the father of Kate
• Charlie is the father of Ted
• Mary is the mother of Ted
• Formalise the following statements about family
  relations in FOPL (use sibling(_,_) and
  ancestor(_,_) in addition to the predicate
  symbols from above)
• If x is a brother of y, then x is a sibling of y
• If x is a sister of y, then x is a sibling of y
• If x is a sibling of y, then y is a sibling of x
• If x is a mother of y, then x is an ancestor of
  y
  
• If x is a father of y, then x is an ancestor of
  y