Exercise 8.17 [kinship-exercise]

Write axioms describing the predicates ${Grandchild}$, ${Greatgrandparent}$, ${Ancestor}$, ${Brother}$, ${Sister}$, ${Daughter}$, ${Son}$, ${FirstCousin}$, ${BrotherInLaw}$, ${SisterInLaw}$, ${Aunt}$, and ${Uncle}$. Find out the proper definition of $m$th cousin $n$ times removed, and write the definition in first-order logic. Now write down the basic facts depicted in the family tree in Figure family1-figure. Using a suitable logical reasoning system, it all the sentences you have written down, and it who are Elizabeth’s grandchildren, Diana’s brothers-in-law, Zara’s great-grandparents, and Eugenie’s ancestors.

Figure [family1-figure] A typical family tree. The symbol $\bowtie$ connects spouses and arrows point to children.