martin emma jenny tony olivia william john christopher steve david michael dorothy sophia PARENT(olivia, william). PARENT(olivia, emma). PARENT (tony, martin). PARENT (tony,olivia). PARENT (john, olivia). PARENT (john, steve). PARENT (jenny, tony). PARENT (david, tony). PARENT (michael, john). PARENT (dorothy, john). PARENT (sophia, jenny). PARENT (christopher, michael). (b) State a new rule named as SIBLING(X, Y) and construct a proof theoretic interpretation of this rule to find all siblings. (c) State a new rule named as DESCENDANT(X, Y) and construct a proof theoretic interpretation of this rule to find all descendants of Martin. Note DESCENDANT(X, Y) means Y is a descendant of X.

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Consider that a database contains the following relations  PARENT(X, Y), and a relation BIRTH(X, B), where B is the birthdate of a person X. The following information is used for question (b), (c)  that we have the following family tree
martin
emma
jenny
tony
olivia
william
john
christopher
steve
david michael dorothy
sophia
PARENT(olivia, william).
PARENT(olivia, emma).
PARENT (tony, martin).
PARENT (tony,olivia).
PARENT (john, olivia).
PARENT (john, steve).
PARENT (jenny, tony).
PARENT (david, tony).
PARENT (michael, john).
PARENT (dorothy, john).
PARENT (sophia, jenny).
PARENT (christopher, michael).
(b) State a new rule named as SIBLING(X, Y) and construct a proof theoretic interpretation of this rule to find all siblings.
(c) State a new rule named as DESCENDANT(X, Y) and construct a proof theoretic interpretation of this rule to find all
descendants of Martin. Note DESCENDANT(X, Y) means Y is a descendant of X.
Transcribed Image Text:martin emma jenny tony olivia william john christopher steve david michael dorothy sophia PARENT(olivia, william). PARENT(olivia, emma). PARENT (tony, martin). PARENT (tony,olivia). PARENT (john, olivia). PARENT (john, steve). PARENT (jenny, tony). PARENT (david, tony). PARENT (michael, john). PARENT (dorothy, john). PARENT (sophia, jenny). PARENT (christopher, michael). (b) State a new rule named as SIBLING(X, Y) and construct a proof theoretic interpretation of this rule to find all siblings. (c) State a new rule named as DESCENDANT(X, Y) and construct a proof theoretic interpretation of this rule to find all descendants of Martin. Note DESCENDANT(X, Y) means Y is a descendant of X.
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