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What we are given here as input is a proposition in the propositional calculus and we have to decide whether it has a satisfying truth assignment.
Their goal was to try to solve with this algorithm an instance of satisfiability deciding whether a proposition in the propositional calculus has a satisfying truth assignment which is one of the most famous NP-complete problems (Cook 1971).
Since the things a term stands for are not established a priori but dependent on propositional context, the analysis of the structure of a proposition in terms of the identity relation requires a correspondence theory of truth.
In order to transfer the relations between ideas to propositions, Bolzano has to resort to the method of variation: to the referring relation between an idea and its object will then correspond the verifying relation between an idea and a propositional form (or, in the fundamental idiom, between one or more ideas and a proposition in which one or more ideas are considered variable).
As a proposition in political philosophy, there is no doubt much to be said for this view.
When young, lovely Isabella goes to Angelo to beg for her brother's life, Angelo makes her a proposition, in every sense.
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According to Lehrer, a person is justified in accepting a proposition just in case that proposition coheres with the relevant part of her cognitive system.
Toulon should find Leinster a different proposition in a fortnight.
That presents a scary proposition in a country with almost no antivenin stocks.
"Boston Marriage" is a different proposition in a couple of ways.
Officials would be required to disregard court orders: a terrible proposition in a country that prides itself on adherence to law.
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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