“modality”的概念、定义、翻译、参考文献-科学参考

modality

Logic

1. In both natural language and formal logic, an operator that acts on a sentence or formula that asserts not only that the sentence is true or false but the way in which the sentence bears its truth value. For example, modalities corresponding to metaphysical notions such as necessity and contingency are used to assert that the truth of a sentence $φ$ is enjoyed with metaphysical necessity or that, whatever the truth value of $φ$ , $φ$ could have enjoyed another truth value.
Distinct modalities arise in many settings—epistemic modalities correspond to whether agents believe or know statements and metaphysical modalities (on, e.g., Leibnizian accounts) correspond to whether statements are true or false in other possible worlds—and frequently they exhibit different behaviour. For example, the epistemic modalities of belief and knowledge differ with respect to whether they satisfy factivity, that is, the statement:
- • If it is true that agent $α$ believes that $φ$ , then $φ$ is true.
is typically treated as false while:
- • If it is true that agent $α$ knows that $φ$ , then $φ$ is true.
tends to be regarded as correct. Modal logics provide formal theories of such modalities by providing rigorous accounts of their behaviour by (for example) providing axioms intended to correspond to common intuitions concerning what can be inferred from the assertion that $φ$ has a particular modality.
2. In a modal logic $L$ with necessity and possibility operators $□$ and $♢$ , respectively, a finite string $σ$ of instances of $□$ , $♢$ , and $\neg$ (negation) (in some presentations, strings of just $□$ and $♢$ ). In tense logic, the modalities correspond to distinct tenses, e.g., $FP φ$ (‘It will be the case that it was the case that $φ$ .’) corresponds to the tense of future perfect. In a modal logic $L$ , two modalities $σ$ and $σ^{'}$ are equivalent if instances of one may be uniformly replaced by the other without loss of generality. The matter of how many distinct modalities (up to equivalence) occur in a given logic has historically been interesting; the modal logic $S 5$ , for example, has six distinct modalities.

Philosophy

The modality of a proposition is the way in which it is true or false. The most important division is between propositions true of necessity, and those true as things are: necessary as opposed to contingent propositions. Other qualifiers sometimes called modal include the tense indicators ‘It will be the case that p’ or ‘It was the case that p’, and there are affinities between the deontic indicators ‘it ought to be the case that p’ or ‘it is permissible that p’, and the logical modalities. See also modal logic.

单词	modality
释义	modality Logic 1. In both natural language and formal logic, an operator that acts on a sentence or formula that asserts not only that the sentence is true or false but the way in which the sentence bears its truth value. For example, modalities corresponding to metaphysical notions such as necessity and contingency are used to assert that the truth of a sentence $φ$ is enjoyed with metaphysical necessity or that, whatever the truth value of $φ$ , $φ$ could have enjoyed another truth value. Distinct modalities arise in many settings—epistemic modalities correspond to whether agents believe or know statements and metaphysical modalities (on, e.g., Leibnizian accounts) correspond to whether statements are true or false in other possible worlds—and frequently they exhibit different behaviour. For example, the epistemic modalities of belief and knowledge differ with respect to whether they satisfy factivity, that is, the statement: • If it is true that agent $α$ believes that $φ$ , then $φ$ is true. is typically treated as false while: • If it is true that agent $α$ knows that $φ$ , then $φ$ is true. tends to be regarded as correct. Modal logics provide formal theories of such modalities by providing rigorous accounts of their behaviour by (for example) providing axioms intended to correspond to common intuitions concerning what can be inferred from the assertion that $φ$ has a particular modality. 2. In a modal logic $L$ with necessity and possibility operators $□$ and $♢$ , respectively, a finite string $σ$ of instances of $□$ , $♢$ , and $\neg$ (negation) (in some presentations, strings of just $□$ and $♢$ ). In tense logic, the modalities correspond to distinct tenses, e.g., $FP φ$ (‘It will be the case that it was the case that $φ$ .’) corresponds to the tense of future perfect. In a modal logic $L$ , two modalities $σ$ and $σ^{'}$ are equivalent if instances of one may be uniformly replaced by the other without loss of generality. The matter of how many distinct modalities (up to equivalence) occur in a given logic has historically been interesting; the modal logic $S 5$ , for example, has six distinct modalities. Philosophy The modality of a proposition is the way in which it is true or false. The most important division is between propositions true of necessity, and those true as things are: necessary as opposed to contingent propositions. Other qualifiers sometimes called modal include the tense indicators ‘It will be the case that p’ or ‘It was the case that p’, and there are affinities between the deontic indicators ‘it ought to be the case that p’ or ‘it is permissible that p’, and the logical modalities. See also modal logic.
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