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First-order logic and Isabelle (proof assistant)

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between First-order logic and Isabelle (proof assistant)

First-order logic vs. Isabelle (proof assistant)

First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. The Isabelle theorem prover is an interactive theorem prover, a Higher Order Logic (HOL) theorem prover.

Similarities between First-order logic and Isabelle (proof assistant)

First-order logic and Isabelle (proof assistant) have 10 things in common (in Unionpedia): Axiom of choice, Gödel's completeness theorem, Higher-order logic, Metamath, Method of analytic tableaux, Prime number theorem, Proof assistant, Resolution (logic), Type theory, Zermelo–Fraenkel set theory.

Axiom of choice

In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that the Cartesian product of a collection of non-empty sets is non-empty.

Axiom of choice and First-order logic · Axiom of choice and Isabelle (proof assistant) · See more »

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 Isabelle (proof assistant) · See more »

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 Isabelle (proof assistant) · See more »

Metamath

Metamath is a language for developing strictly formalized mathematical definitions and proofs accompanied by a proof checker for this language and a growing database of thousands of proved theorems covering conventional results in logic, set theory, number theory, group theory, algebra, analysis, and topology, as well as topics in Hilbert spaces and quantum logic.

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Method of analytic tableaux

In proof theory, the semantic tableau (plural: tableaux, also called 'truth tree') is a decision procedure for sentential and related logics, and a proof procedure for formulae of first-order logic.

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Prime number theorem

In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers.

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Proof assistant

In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration.

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Resolution (logic)

In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation theorem-proving technique for sentences in propositional logic and first-order logic.

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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.

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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 · Isabelle (proof assistant) and Zermelo–Fraenkel set theory · See more »

The list above answers the following questions

First-order logic and Isabelle (proof assistant) Comparison

First-order logic has 207 relations, while Isabelle (proof assistant) has 37. As they have in common 10, the Jaccard index is 4.10% = 10 / (207 + 37).

References

This article shows the relationship between First-order logic and Isabelle (proof assistant). To access each article from which the information was extracted, please visit:

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