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