“accessibility relation”的概念、定义、翻译、参考文献-科学参考

accessibility relation

Logic

A binary relation $R$ holding between possible worlds in frames for intuitionistic and modal logic. When for two worlds $w$ , $w^{'}$ , $w R w^{'}$ holds in a model, $w^{'}$ is said to be ‘accessible from’ $w$ . Accessibility provides a basis for the typical truth condition for a formula $□ φ$ where $□$ is a necessity operator:
- • $□ φ$ is true at $w$ if for all $w^{'}$ such that $w R w^{'}$ (i.e., at all accessible worlds $w^{'}$ ) $φ$ is true at $w^{'}$ .
One natural application of accessibility is found in tense logic, in which the interpretation of $R$ is that $w R w^{'}$ whenever $w^{'}$ represents a state in the future of $w$ . Generalizations of the accessibility relation are common. In many semantics for conditional logic, there exists an accessibility relation corresponding to each formula $φ$ in the language so that $w R_{φ} w^{'}$ is often interpreted as representing that $w^{'}$ is among the most similar worlds to $w$ at which $φ$ is true. In semantics for relevant logics, a ternary relation $R$ between possible worlds (or set-ups), provides the apparatus for the truth condition for relevant conditionals:
- • $φ \to ψ$ is true at $w$ if for all $w^{'}$ and $w^{″}$ such that $R w w^{'} w^{″}$ , if $φ$ is true at $w^{'}$ , then $ψ$ is true at $w^{″}$ .

Philosophy

See modal logic, possible worlds.

单词	accessibility relation
释义	accessibility relation Logic A binary relation $R$ holding between possible worlds in frames for intuitionistic and modal logic. When for two worlds $w$ , $w^{'}$ , $w R w^{'}$ holds in a model, $w^{'}$ is said to be ‘accessible from’ $w$ . Accessibility provides a basis for the typical truth condition for a formula $□ φ$ where $□$ is a necessity operator: • $□ φ$ is true at $w$ if for all $w^{'}$ such that $w R w^{'}$ (i.e., at all accessible worlds $w^{'}$ ) $φ$ is true at $w^{'}$ . One natural application of accessibility is found in tense logic, in which the interpretation of $R$ is that $w R w^{'}$ whenever $w^{'}$ represents a state in the future of $w$ . Generalizations of the accessibility relation are common. In many semantics for conditional logic, there exists an accessibility relation corresponding to each formula $φ$ in the language so that $w R_{φ} w^{'}$ is often interpreted as representing that $w^{'}$ is among the most similar worlds to $w$ at which $φ$ is true. In semantics for relevant logics, a ternary relation $R$ between possible worlds (or set-ups), provides the apparatus for the truth condition for relevant conditionals: • $φ \to ψ$ is true at $w$ if for all $w^{'}$ and $w^{″}$ such that $R w w^{'} w^{″}$ , if $φ$ is true at $w^{'}$ , then $ψ$ is true at $w^{″}$ . Philosophy See modal logic, possible worlds.
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