Wikipedia describes the first-order vs. second-order logic as follows: First-order logic uses only variables that range over individuals (elements of the domain of discourse); second-order logic ...

1 About the difference between the propositional logic and the (first order) predicate logic-> can you give me one or more remarkable examples which underly the differences and the similarities between the …

Predicate logic is usually used as a synonym for first-order logic, but sometimes it is used to refer to other logics that have similar syntax. Syntactically, first-order logic has the same connectives as …

Oct 4, 2018 · I am struggling to understand how to really negate in first order logic. Take the following examples: "Somebody loves everybody" Negating this would be: "It is not the case that somebody loves

Jun 1, 2019 · Interestingly, while it's generally easy to show that a generalized quantifier isn't first-order definable (usually via compactness), there is a precise sense in which $\ {\forall,\exists\}$ is …

May 22, 2017 · First-order, second-order and third-order logic are all logical languages with universal and existential quantifiers. The difference lies in what quantifiers speak about.

Dec 9, 2016 · Once you know precisely how to interpret every sentence in first-order logic, translating an English sentence into first-order logic becomes very straightforward; you simply construct the desired …

Jan 13, 2021 · In what language? In the language of set theory, ALL undergraduate analysis can be written in first order logic (at least in theory). Indeed, we care about set theory (at least in part) …

Oct 22, 2017 · I am trying to get a grasp about the mechanicly difference between First order logic (FOL) and Second order logic (SOL). From my understanding objects within them can be divided into these …

Much of mathematics can be stated in first order logic and, crucially, some things are distinctively second order. For instance, in number theory, Peano's axioms except for induction are first order, but …