Turing's Halting Problem

What was the decision problem posed by mathematicians in the early 20th century?

Who was among the first to prove that first-order logic is not decidable?

What concept was difficult in Turing's proof about first-order logic?

What did Turing propose as a 'black box' in his idea of a program?

What did Turing show to be similar to the logical problem of determining if premises entail a conclusion?

What did Turing prove is impossible for any machine to solve?

In the early 20th century, mathematicians posed the decision problem in logic: Is there an automatic way to determine if given premises entail a conclusion in first-order logic?
Alan Turing was among the first to prove that first-order logic is not decidable.
Turing's proof was conceptually difficult because it required showing no possible program could provide the answer.
Turing proposed the idea of a program as a "black box" that takes inputs and gives outputs.
A new question arose: Given a program and input, will it halt and provide an answer or run indefinitely without halting?
Turing showed that the logical problem of determining if premises entail a conclusion is similar to the halting problem.
Turing proved it's impossible for any machine to solve the halting problem.
He achieved this by creating a machine "h+" that would loop forever if given a yes answer and halt with a no answer.
He then asked the question "Does h+ halt when given h+ as input?" which resulted in a paradox.
Thus, Turing proved that no machine or program can solve the halting problem.

Test your knowledge about Alan Turing's proof that no machine or program can solve the halting problem, and its connection to first-order logic and the decision problem. Learn about the conceptual difficulty of proving the impossibility of determining if a program will halt and provide an answer or run indefinitely.