In logic and computer science:
* Decidable problem: A problem for which there exists an algorithm that can always determine whether a given input is a "yes" or "no" instance of the problem. In other words, the algorithm always produces a definite answer, and it does so in a finite amount of time.
* Decidable language: A language where every string is recognized by a Turing machine (a theoretical model of computation). In other words, there is an algorithm that can decide whether any given string belongs to the language or not.
In general usage:
* Decidable issue: Something that can be resolved or settled. This could be a dispute, a question, or a problem. For example, "The issue of climate change is highly debatable but it's a very decidable topic in the sense that we need to come to a solution."
* Decidable question: A question that has a clear and definitive answer, even if it's difficult to find. For example, "Is the Earth flat?" is a decidable question, even though it's not a simple question to answer.
In mathematics:
* Decidable theory: A theory in which every sentence is either provable or disprovable. This means that there is a procedure to determine whether any given sentence is true or false.
Key points to remember:
* "Decidable" usually implies there's a definite answer or solution.
* The concept of decidability is often linked to the idea of algorithms and computability.
* In certain fields, "decidable" might have a slightly different nuance, so it's always good to consider the context.
I hope this explanation helps clarify the meaning of "decidable" for you!