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In essence, he defined a proof to be any finite sequence of statements such that each statement in the sequence either is an axiom or follows from previous members by a valid rule of inference.
Hart's own view is that an overweening deference to law consorts more easily with theories that imbue it with moral ideals, permitting "an enormous overvaluation of the importance of the bare fact that a rule may be said to be a valid rule of law, as if this, once declared, was conclusive of the final moral question: 'Ought this law to be obeyed?" (Hart 1958, p. 75).
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The repeated lack of support for Bergmann's rule in ectotherms suggests that this model should be recognized as a valid rule exclusively for endotherms.
Instances of deductive inferences are justified by showing that they are inferences in accordance with valid rules of inference.
In standard truth-functional propositional logic, commutation, or commutativity refer to two valid rules of replacement.
The goal was to find valid rules of inference and forms of proof to help people find their way in life.
It's illegal — it's a very valid rule about protecting the horses.
The example of importation shows that not every valid rule has a justification consisting of elementary reductions only.
There is also an arithmetical formula M x, y, z) which is true exactly if one has a valid application of the rule of inference modus ponens for some formulas A and B with x = ⌈A⌉, y = ⌈A → B⌉ and z = ⌈B⌉; etc.
The security of individual records is guaranteed via de-identified data collection and the system meets all valid rules on the protection of personal data.
Analogously in Zsyntax we start with reactants and, by using empirically and logically valid rules, we reach the product of the reaction, i.e. we have deductions where the premises represent the reactants (the initial aggregate) and the conclusion represents the (aggregate of the) products.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com