“non-normal”的概念、定义、翻译、参考文献-科学参考

non-normal

Logic

1. A property holding of any deductive system with a modal operator $□$ that is not normal, that is, a modal logic for which either rule necessitation fails or an instance of the axiom scheme:
- • $□ (φ \to ψ) \to (□ φ \to □ ψ)$
fails.
2. In Kripke semantics for modal logics, describes a type of world $w$ at which formulae are evaluated in an unusual (and perhaps counterintuitive) fashion. Normal worlds are defined as possible worlds at which formulae of the form $□ φ$ receive the familiar, Leibnizian truth condition:
- • $□ φ$ is true at $w$ if for all worlds $w^{'}$ accessible from $w$ , $φ$ is true at $w^{'}$ .
Modal formulae have different truth conditions at non-normal worlds. Thus, in the semantics for the Lewis systems $S 2$ and $S 3$ a non-normal world $w$ is one at which formulae of the form $□ φ$ are evaluated by the truth condition:
- • $□ φ$ is not true at $w$ .
Non-normal worlds are employed in semantics for non-normal modal logics, explaining their pathological nature. Semantics for many non-normal logics $L$ must provide models serving as counterexamples to rule necessitation. Hence, the possible worlds framework requires a type of world at which $□ φ$ can fail for some $L$ -theorem $φ$ . Other deductive systems require further deviations from the evaluation of formulae at normal worlds; hence, other related devices, such as impossible worlds and the absurd world, are often referred to as ‘non-normal’.

单词	non-normal
释义	non-normal Logic 1. A property holding of any deductive system with a modal operator $□$ that is not normal, that is, a modal logic for which either rule necessitation fails or an instance of the axiom scheme: • $□ (φ \to ψ) \to (□ φ \to □ ψ)$ fails. 2. In Kripke semantics for modal logics, describes a type of world $w$ at which formulae are evaluated in an unusual (and perhaps counterintuitive) fashion. Normal worlds are defined as possible worlds at which formulae of the form $□ φ$ receive the familiar, Leibnizian truth condition: • $□ φ$ is true at $w$ if for all worlds $w^{'}$ accessible from $w$ , $φ$ is true at $w^{'}$ . Modal formulae have different truth conditions at non-normal worlds. Thus, in the semantics for the Lewis systems $S 2$ and $S 3$ a non-normal world $w$ is one at which formulae of the form $□ φ$ are evaluated by the truth condition: • $□ φ$ is not true at $w$ . Non-normal worlds are employed in semantics for non-normal modal logics, explaining their pathological nature. Semantics for many non-normal logics $L$ must provide models serving as counterexamples to rule necessitation. Hence, the possible worlds framework requires a type of world at which $□ φ$ can fail for some $L$ -theorem $φ$ . Other deductive systems require further deviations from the evaluation of formulae at normal worlds; hence, other related devices, such as impossible worlds and the absurd world, are often referred to as ‘non-normal’.
随便看	domestic space dome–crescent–mushroom domichnia dominance dominance hierarchy dominant dominant dead time process dominant discharge dominant firm dominant mode dominant strategy dominated convergence theorem dominator Dominian Reef Dominica, Commonwealth of Dominican Republic Dominic, St (1170–1221) dominion Dominion Astrophysical Observatory Dominion Radio Astrophysical Observatory domino effect Donahoe, John (1806–30) Donaldson, Simon (1957–) Donatello Donati, Comet