Faster access than browser!Similarities between First-order logic and Second-order logic
First-order logic and Second-order logic have 39 things in common (in Unionpedia): Arithmetic, Atomic formula, Branching quantifier, Cardinality, Charles Sanders Peirce, Compactness theorem, Completeness (logic), Computational complexity theory, Countable set, Decidability (logic), Domain of discourse, Formal system, Gödel's completeness theorem, Gödel's incompleteness theorems, George Boolos, Gottlob Frege, Higher-order logic, Löwenheim number, Löwenheim–Skolem theorem, Mathematics, Natural deduction, Non-logical symbol, Nonfirstorderizability, Peano axioms, Plural quantification, Power set, Proof theory, Propositional calculus, Quantifier (logic), Recursively enumerable set, ..., Rule of inference, Second-order arithmetic, Set theory, Skolem's paradox, Springer Science+Business Media, Type theory, Well-formed formula, Willard Van Orman Quine, Zermelo–Fraenkel set theory. Expand index (9 more) »
Arithmetic
Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.
Arithmetic and First-order logic · Arithmetic and Second-order logic ·
Atomic formula
In mathematical logic, an atomic formula (also known simply as an atom) is a formula with no deeper propositional structure, that is, a formula that contains no logical connectives or equivalently a formula that has no strict subformulas.
Atomic formula and First-order logic · Atomic formula and Second-order logic ·
Branching quantifier
In logic a branching quantifier, also called a Henkin quantifier, finite partially ordered quantifier or even nonlinear quantifier, is a partial ordering of quantifiers for Q ∈.
Branching quantifier and First-order logic · Branching quantifier and Second-order logic ·
Cardinality
In mathematics, the cardinality of a set is a measure of the "number of elements of the set".
Cardinality and First-order logic · Cardinality and Second-order logic ·
Charles Sanders Peirce
Charles Sanders Peirce ("purse"; 10 September 1839 – 19 April 1914) was an American philosopher, logician, mathematician, and scientist who is sometimes known as "the father of pragmatism".
Charles Sanders Peirce and First-order logic · Charles Sanders Peirce and Second-order logic ·
Compactness theorem
In mathematical logic, the compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model.
Compactness theorem and First-order logic · Compactness theorem and Second-order logic ·
Completeness (logic)
In mathematical logic and metalogic, a formal system is called complete with respect to a particular property if every formula having the property can be derived using that system, i.e. is one of its theorems; otherwise the system is said to be incomplete.
Completeness (logic) and First-order logic · Completeness (logic) and Second-order logic ·
Computational complexity theory
Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.
Computational complexity theory and First-order logic · Computational complexity theory and Second-order logic ·
Countable set
In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.
Countable set and First-order logic · Countable set and Second-order logic ·
Decidability (logic)
In logic, the term decidable refers to the decision problem, the question of the existence of an effective method for determining membership in a set of formulas, or, more precisely, an algorithm that can and will return a boolean true or false value that is correct (instead of looping indefinitely, crashing, returning "don't know" or returning a wrong answer).
Decidability (logic) and First-order logic · Decidability (logic) and Second-order logic ·
Domain of discourse
In the formal sciences, the domain of discourse, also called the universe of discourse, universal set, or simply universe, is the set of entities over which certain variables of interest in some formal treatment may range.
Domain of discourse and First-order logic · Domain of discourse and Second-order logic ·
Formal system
A formal system is the name of a logic system usually defined in the mathematical way.
First-order logic and Formal system · Formal system and Second-order logic ·
Gödel's completeness theorem
Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic.
First-order logic and Gödel's completeness theorem · Gödel's completeness theorem and Second-order logic ·
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic.
First-order logic and Gödel's incompleteness theorems · Gödel's incompleteness theorems and Second-order logic ·
George Boolos
George Stephen Boolos (September 4, 1940 – May 27, 1996) was an American philosopher and a mathematical logician who taught at the Massachusetts Institute of Technology.
First-order logic and George Boolos · George Boolos and Second-order logic ·
Gottlob Frege
Friedrich Ludwig Gottlob Frege (8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician.
First-order logic and Gottlob Frege · Gottlob Frege and Second-order logic ·
Higher-order logic
In mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics.
First-order logic and Higher-order logic · Higher-order logic and Second-order logic ·
Löwenheim number
In mathematical logic the Löwenheim number of an abstract logic is the smallest cardinal number for which a weak downward Löwenheim–Skolem theorem holds.
First-order logic and Löwenheim number · Löwenheim number and Second-order logic ·
Löwenheim–Skolem theorem
In mathematical logic, the Löwenheim–Skolem theorem, named for Leopold Löwenheim and Thoralf Skolem, states that if a countable first-order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ. The result implies that first-order theories are unable to control the cardinality of their infinite models, and that no first-order theory with an infinite model can have a unique model up to isomorphism.
First-order logic and Löwenheim–Skolem theorem · Löwenheim–Skolem theorem and Second-order logic ·
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
First-order logic and Mathematics · Mathematics and Second-order logic ·
Natural deduction
In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning.
First-order logic and Natural deduction · Natural deduction and Second-order logic ·
Non-logical symbol
In logic, the formal languages used to create expressions consist of symbols, which can be broadly divided into constants and variables.
First-order logic and Non-logical symbol · Non-logical symbol and Second-order logic ·
Nonfirstorderizability
In formal logic, nonfirstorderizability is the inability of an expression to be adequately captured in particular theories in first-order logic.
First-order logic and Nonfirstorderizability · Nonfirstorderizability and Second-order logic ·
Peano axioms
In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano.
First-order logic and Peano axioms · Peano axioms and Second-order logic ·
Plural quantification
In mathematics and logic, plural quantification is the theory that an individual variable x may take on plural, as well as singular, values.
First-order logic and Plural quantification · Plural quantification and Second-order logic ·
Power set
In mathematics, the power set (or powerset) of any set is the set of all subsets of, including the empty set and itself, variously denoted as, 𝒫(), ℘() (using the "Weierstrass p"),,, or, identifying the powerset of with the set of all functions from to a given set of two elements,.
First-order logic and Power set · Power set and Second-order logic ·
Proof theory
Proof theory is a major branchAccording to Wang (1981), pp.
First-order logic and Proof theory · Proof theory and Second-order logic ·
Propositional calculus
Propositional calculus is a branch of logic.
First-order logic and Propositional calculus · Propositional calculus and Second-order logic ·
Quantifier (logic)
In logic, quantification specifies the quantity of specimens in the domain of discourse that satisfy an open formula.
First-order logic and Quantifier (logic) · Quantifier (logic) and Second-order logic ·
Recursively enumerable set
In computability theory, traditionally called recursion theory, a set S of natural numbers is called recursively enumerable, computably enumerable, semidecidable, provable or Turing-recognizable if.
First-order logic and Recursively enumerable set · Recursively enumerable set and Second-order logic ·
Rule of inference
In logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions).
First-order logic and Rule of inference · Rule of inference and Second-order logic ·
Second-order arithmetic
In mathematical logic, second-order arithmetic is a collection of axiomatic systems that formalize the natural numbers and their subsets.
First-order logic and Second-order arithmetic · Second-order arithmetic and Second-order logic ·
Set theory
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.
First-order logic and Set theory · Second-order logic and Set theory ·
Skolem's paradox
In mathematical logic and philosophy, Skolem's paradox is a seeming contradiction that arises from the downward Löwenheim–Skolem theorem.
First-order logic and Skolem's paradox · Second-order logic and Skolem's paradox ·
Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
First-order logic and Springer Science+Business Media · Second-order logic and Springer Science+Business Media ·
Type theory
In mathematics, logic, and computer science, a type theory is any of a class of formal systems, some of which can serve as alternatives to set theory as a foundation for all mathematics.
First-order logic and Type theory · Second-order logic and Type theory ·
Well-formed formula
In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language.
First-order logic and Well-formed formula · Second-order logic and Well-formed formula ·
Willard Van Orman Quine
Willard Van Orman Quine (known to intimates as "Van"; June 25, 1908 – December 25, 2000) was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century." From 1930 until his death 70 years later, Quine was continually affiliated with Harvard University in one way or another, first as a student, then as a professor of philosophy and a teacher of logic and set theory, and finally as a professor emeritus who published or revised several books in retirement.
First-order logic and Willard Van Orman Quine · Second-order logic and Willard Van Orman Quine ·
Zermelo–Fraenkel set theory
In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox.
First-order logic and Zermelo–Fraenkel set theory · Second-order logic and Zermelo–Fraenkel set theory ·
The list above answers the following questions
- What First-order logic and Second-order logic have in common
- What are the similarities between First-order logic and Second-order logic
First-order logic and Second-order logic Comparison
First-order logic has 207 relations, while Second-order logic has 83. As they have in common 39, the Jaccard index is 13.45% = 39 / (207 + 83).
References
This article shows the relationship between First-order logic and Second-order logic. To access each article from which the information was extracted, please visit:
