“Löb’s axiom”的概念、定义、翻译、参考文献-科学参考

Löb’s axiom

Logic

In modal logic, the axiom scheme named after mathematician Martin Löb (1921–2006):
- • $□ (□ φ \to φ) \to □ φ$
When $□$ is interpreted as a provability operator, i.e., when $□ φ$ is read ‘ $φ$ is provable’, Löb’s axiom aligns with Löb’s theorem in arithmetic:
- • If $PA ⊢ Prv (⌜ φ ⌝) \to φ$ then $PA ⊢ φ$
From a semantic perspective, Löb’s axiom corresponds to transitive and converse well-founded Kripke frames. That is, the accessibility relation, $R$ , is such that if $x R y$ and $y R z$ then $x R z$ , and there is no infinite sequence of worlds such that $w_{1} R w_{2} R w_{3} R . . .$ .

单词	Löb’s axiom
释义	Löb’s axiom Logic In modal logic, the axiom scheme named after mathematician Martin Löb (1921–2006): • $□ (□ φ \to φ) \to □ φ$ When $□$ is interpreted as a provability operator, i.e., when $□ φ$ is read ‘ $φ$ is provable’, Löb’s axiom aligns with Löb’s theorem in arithmetic: • If $PA ⊢ Prv (⌜ φ ⌝) \to φ$ then $PA ⊢ φ$ From a semantic perspective, Löb’s axiom corresponds to transitive and converse well-founded Kripke frames. That is, the accessibility relation, $R$ , is such that if $x R y$ and $y R z$ then $x R z$ , and there is no infinite sequence of worlds such that $w_{1} R w_{2} R w_{3} R . . .$ .
随便看	recurrent state recurrent-surge oscilloscope recurring decimal recursion recursion theorem recursion theory recursive recursive descent parsing recursive doubling recursive filters recursive function recursive list recursively axiomatizable recursively decidable problem recursively enumerable set recursively solvable problem recursively undecidable recursive model recursive real number recursive relation recursive set recursive subroutine recusants recycle recycled pulsar