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.
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
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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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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