Provability: meaning, definitions and examples
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provability
[ prəˈvuːəbəlɪti ]
mathematics logic
Provability refers to the property of a statement being able to be proven within a given formal system. In mathematical logic, a statement is considered provable if there exists a formal proof demonstrating its truth based on the axioms and rules of inference of that system. Provability is a critical concept in various branches of mathematics, including set theory and proof theory. It also plays a key role in computer science, particularly in automated theorem proving.
Synonyms
confirmation, demonstrability, establishability.
Examples of usage
- The provability of the theorem was established by multiple mathematicians.
- In our discussion, we examined the provability of several propositions.
- The topic of provability is central to Gödel's incompleteness theorems.
- Hello, I am studying the provability in logic.
Translations
Translations of the word "provability" in other languages:
🇵🇹 provabilidade
🇮🇳 प्रमाणिकता
🇩🇪 Beweisbarkeit
🇮🇩 kemampuan untuk dibuktikan
🇺🇦 доводимість
🇵🇱 dowodliwość
🇯🇵 証明可能性
🇫🇷 prouvabilité
🇪🇸 demostrabilidad
🇹🇷 kanıtlanabilirlik
🇰🇷 증명 가능성
🇸🇦 قابل الإثبات
🇨🇿 dokazatelnost
🇸🇰 dôkazateľnosť
🇨🇳 可证明性
🇸🇮 dokazljivost
🇮🇸 sönnunargildi
🇰🇿 дәлелдеуге болатындық
🇬🇪 დადასტურებადობა
🇦🇿 sübut edilə bilənlik
🇲🇽 probabilidad de prueba
Etymology
The term 'provability' is derived from the verb 'prove', which originates from the Latin word 'probare', meaning 'to test, to try, to prove'. The suffix '-ability' indicates a quality of being able to be achieved. The concept has evolved significantly since its early usage in formal logic and mathematics. The use of provability in formal systems became prominent in the early 20th century, especially with the advent of mathematical logic and the formalization of axiomatic systems. During this period, researchers like Kurt Gödel explored the limitations and capabilities of provability, leading to important discoveries such as the incompleteness theorems. Since then, the term 'provability' has been essential in discussions surrounding the foundations of mathematics, logic, and even computer science. Today, it continues to be relevant, particularly in fields involving algorithms and computational logic.