This program solves logic puzzles.
In 1978, logician Raymond Smullyan published “What is the name of this book?”, a book of logical puzzles. Among the puzzles in the book were a class of puzzles that Smullyan called “Knights and Knaves” puzzles.
In a Knights and Knaves puzzle, the following information is given: Each character is either a knight or a knave. A knight will always tell the truth: if knight states a sentence, then that sentence is true. Conversely, a knave will always lie: if a knave states a sentence, then that sentence is false.
The objective of the puzzle is, given a set of sentences spoken by each of the characters, determine, for each character, whether that character is a knight or a knave.
For example, consider a simple puzzle with just a single character named A. A says “I am both a knight and a knave.”
Logically, we might reason that if A were a knight, then that sentence would have to be true. But we know that the sentence cannot possibly be true, because A cannot be both a knight and a knave – we know that each character is either a knight or a knave, but not both. So, we could conclude, A must be a knave.
That puzzle was on the simpler side. With more characters and more sentences, the puzzles can get trickier! The program determines how to represent these puzzles using propositional logic, such that an AI running a model-checking algorithm could solve these puzzles for us.
This file defines several classes for different types of logical connectives. These classes can be composed within each other, so an expression like And(Not(A), Or(B, C)) represents the logical sentence stating that symbol A is not true, and that symbol B or symbol C is true (where “or” here refers to inclusive, not exclusive, or).
logic.py also contains a function model_check. model_check takes a knowledge base and a query. The knowledge base is a single logical sentence: if multiple logical sentences are known, they can be joined together in an And expression. model_check recursively considers all possible models, and returns True if the knowledge base entails the query, and returns False otherwise.
At the top, we’ve defined six propositional symbols. AKnight, for example, represents the sentence that “A is a knight,” while AKnave represents the sentence that “A is a knave.” We’ve similarly defined propositional symbols for characters B and C as well.
What follows are four different knowledge bases, knowledge0, knowledge1, knowledge2, and knowledge3, which will contain the knowledge needed to deduce the solutions to the upcoming Puzzles 0, 1, 2, and 3, respectively. The main function of this puzzle.py loops over all puzzles, and uses model checking to compute, given the knowledge for that puzzle, whether each character is a knight or a knave, printing out any conclusions that the model checking algorithm is able to make.
The program solves the following puzzles.
- Puzzle 0 is the puzzle from the Background. It contains a single character, A.
- A says “I am both a knight and a knave.”
- Puzzle 1 has two characters: A and B.
- A says “We are both knaves.”
- B says nothing.
- Puzzle 2 has two characters: A and B.
- A says “We are the same kind.”
- B says “We are of different kinds.”
- Puzzle 3 has three characters: A, B, and C.
- A says either “I am a knight.” or “I am a knave.”, but you don’t know which.
- B says “A said ‘I am a knave.’”
- B then says “C is a knave.”
- C says “A is a knight.”
In each of the above puzzles, each character is either a knight or a knave. Every sentence spoken by a knight is true, and every sentence spoken by a knave is false.
Run python puzzle.py to see the solution to the puzzle.
