Logical symbols · Truth constants: T, V, or ⊤ for "true" and F, O, or ⊥ for "false" (V and O are from Polish notation). · Additional logical connectives such as ... Second-order logic · Higher-order · Quantifier (logic) · Predicate (mathematical logic) |
First-order logic will involve expressions built from symbols of our lan- guage together with additional symbols: • Infinitely many first-order variables, x0,x1 ... |
| Логика первого порядка |  |
Логика первого порядка — формальное исчисление, допускающее высказывания относительно переменных, фиксированных функций и предикатов. Расширяет логику высказываний.
Помимо логики первого порядка существуют также логики высших порядков, в которых... Википедия
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Logic alphabet · Double turnstile · Turnstile (symbol) · Metalanguage |
The symbol ∀ is called the universal quantifier. The formula ∀xH is read “for all x, H”. A general first-order formula is built up from atomic formulas. |
Definition. A first-order signature consists of two disjoint sets F and P of func- tion symbols, respectively, predicate symbols, together with an arity ... |
Numbers are not “built in” to first-order logic. They're constant symbols just like “You” and “a” above. |
2 Quantifiers, variable symbols, relation symbols. First order formulas are made up of. •. quantifiers ∀ and ∃ ,. •. the logical connectives ¬ , ∧ , ∨ , ⟹ and ... |
Expressions of first-order logic are built up from a basic vocabulary containing variables, constant symbols, predicate symbols and sometimes function symbols. |
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