Consider the language that contains the predicates of symbols degree, student, pass, test, goodscore, and subscribe, all of arty 0. Given the following knowledge base built from this language: degree ← student ∧ pass. pass ← test ∧ goodscore. test ← subscribe. student. subscribe. a) How many interpretations exist for this propositional language? b) Consider the following interpretations:   π(student) π(subscribe) π(test) π(goodscore) π(pass) π(degree) I1 F T T F F F I2 T T F T F T I3 T T T T F F I4 T T T T T T I5 T T T T F F Which interpretations are models of the knowledge-base? Which are not? Why (not)? c) Give all logical consequences of the knowledge-base.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Consider the language that contains the predicates of symbols degree, student, pass, test, goodscore, and subscribe, all of arty 0. Given the following knowledge base built from this language:

degree ← student ∧ pass.

pass ← test ∧ goodscore.

test ← subscribe. student.

subscribe.

a) How many interpretations exist for this propositional language?

b) Consider the following interpretations:

 

π(student)

π(subscribe)

π(test)

π(goodscore)

π(pass)

π(degree)

I1 F T T F F F
I2 T T F T F T
I3 T T T T F F
I4 T T T T T T
I5 T T T T F F

Which interpretations are models of the knowledge-base? Which are not? Why (not)?

c) Give all logical consequences of the knowledge-base.

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