tautology is a system to check if a boolean
expression is a tautology. Here the formulae are boolean
expressions and a formula is valid if it is a tautology
and it is provable if tautology return
Valid for it.
Therefore, tautology is sound
if whenever tautology returns Valid
its input was a tautology. tautology is complete
if tautology returns Valid for
all boolean expressions which are tautologies.
Question
Give a (trivial) system to check if a boolean expression is a tautology which is sound (but not complete). Give a (trivial) system to check if a boolean expression is a tautology which is complete (but not sound).
Exercise 2.11 of the text
Questions 1, 2, 7, 8, 9 from Chapter 1 of