Computational Thinking (CO2412) Tutorial 4.1: Week 17

4.1 Parse tree data structure for statements in propositional logic

The propositional logic statements notebook defines a data structure, the class Propositional, that represents a logical statement by a tree (this is also known as a parse tree).

1. Have a look at the code and the examples. Raise anything that is unclear for discussion during the tutorial.
2. Create a Propositional object for the statement ((p ∨ q) ∧ (¬p ∨ ¬q)) and print its truth table.
3. What would be the correct truth table for the statement ((p ∧ q) ↔ (q ∧ r))?
4. In the method evaluate(self, valuation) of the class Propositional, the implementation of logical equivalence (operator ↔, also called biconditionality) is missing. Add an implementation for this and check that it works correctly, e.g., by printing the truth table of the Propositional object statement_R that represents the propositional logic statement ((p ∧ q) ↔ (q ∧ r)).
5. Create a Propositional object that generates the following truth table:

   False(p)    False(q)    False(r)    <>    False
   False(p)    False(q)     True(r)    <>    False
   False(p)     True(q)    False(r)    <>    False
   False(p)     True(q)     True(r)    <>    True
    True(p)    False(q)    False(r)    <>    True
    True(p)    False(q)     True(r)    <>    True
    True(p)     True(q)    False(r)    <>    True
    True(p)     True(q)     True(r)    <>    True

Submission deadline: 12^th February 2022; discussion planned for 8^th March 2022. Group work by up to four people is welcome.