Question

Teachers in the middle Ages supposedly tested the real-time propositional logic ability of a student via a technique known as an obligato game. In an obligato game, a number of rounds are set and in each round, the teacher gives the student successive assertions that the student must either accept or reject as they are given. When the student accepts an assertion, it is added as a commitment; when the student rejects an assertion its negation is added as a commitment. The student passes the test if the consistency of all commitments is maintained throughout the test.

Explain why every obligato game has a winning strategy.

Short answer

It is explained why every obligato game has a winning strategy.

Step-by-step solution

Negation of statement

The opposite of the given mathematical statement is the negation of a statement in mathematics. If "\(P\)" is a statement, then "\( \sim P\)" is the statement's negation.

Explain why every obligato game has a winning strategy

P, Q, R, S, and T are variables found in the commitments. When we give each variable a truth value (T = true and F = false), a commitment is either true T or false F for each combination of the variable truth values.

The system of commitments will then be consistent if the truth values are used in this order for the commitment. Assuming, for instance, that all variables are true. If so, the commitments have the following truth values in ascending order: F, F, T, F, T, F, etc.

Then the student passes the test if the student accepts the commitments with truth value T and rejects commitments with truth value F.

So, in both cases, the student passes the test.

Hence, every obligato game has a winning strategy.