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First-order logic —also called predicate logic, predicate calculus, quantificational logic —is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables.
A predicate is a generalization of a propositional variable. Recalling Section 12.10, suppose that we have three propositions: r (“It is raining”), u (“Joe takes his umbrella”), and w (“Joe gets wet”).
28 Φεβ 2021 · The text is divided into 6 chapters: basic logical concepts; symbolization in propositional logic; truth table; symbolization in predicate logic; semantic theory for predicate logic; proofs.
18 Μαρ 2000 · One major difference between Aristotle’s understanding of predication and modern (i.e., post-Fregean) logic is that Aristotle treats individual predications and general predications as similar in logical form: he gives the same analysis to “Socrates is an animal” and “Humans are animals”.
17 Νοε 2018 · As a philosophical matter, the logicist project aimed to show that “mathematics can be reduced to logic”: and they conceived of the entire hierarchy of types as constituting logic. And then, as a mathematical matter, second-order logic was necessary to their construction of the integers.
19 Οκτ 1999 · Appeals to logical form arose in the context of attempts to say more about this intuitive distinction between impeccable inferences, which invite metaphors of security, and inferences that involve some risk of slipping from truth to falsity.
18 Ιαν 2021 · The symbols ∼, ⊃, ∀ are the logical constants of L q. ∼ and ⊃ stand respectively for ‘not’ and ‘if’, as in a propositional language, and behave truth-functionally. For example, ‘If Othello loves Desdemona, Socrates is not a philosopher’ is formalized as follows: Lod ⊃ ∼Ps.
