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29 relations: Antecedent (logic), Assertion (software development), Axiom, Curry–Howard correspondence, Deduction theorem, First-order logic, Formal system, Free variables and bound variables, Hilbert system, Logic, Logical consequence, Loop invariant, Mathematical logic, Metalanguage, Metatheorem, Metatheory, Natural deduction, Premise, Proposition, Rule of inference, Semantics (computer science), Sequence, Sequent, Sequent calculus, Simply typed lambda calculus, Tautology (logic), Turnstile (symbol), Type theory, Well-formed formula.
Antecedent (logic)
An antecedent is the first half of a hypothetical proposition, whenever the if-clause precedes the then-clause.
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Assertion (software development)
In computer programming, an assertion is a statement that a predicate (Boolean-valued function, i.e. a true–false expression) is always true at that point in code execution.
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Axiom
An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.
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Curry–Howard correspondence
In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation) is the direct relationship between computer programs and mathematical proofs.
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Deduction theorem
In mathematical logic, the deduction theorem is a metatheorem of propositional and first-order logic.
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First-order logic
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.
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Formal system
A formal system is the name of a logic system usually defined in the mathematical way.
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Free variables and bound variables
In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation that specifies places in an expression where substitution may take place.
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Hilbert system
In logic, especially mathematical logic, a Hilbert system, sometimes called Hilbert calculus, Hilbert-style deductive system or Hilbert–Ackermann system, is a type of system of formal deduction attributed to Gottlob FregeMáté & Ruzsa 1997:129 and David Hilbert.
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Logic
Logic (from the logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference.
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Logical consequence
Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically follows from one or more statements.
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Loop invariant
In computer science, a loop invariant is a property of a program loop that is true before (and after) each iteration.
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Mathematical logic
Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.
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Metalanguage
Broadly, any metalanguage is language or symbols used when language itself is being discussed or examined.
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Metatheorem
In logic, a metatheorem is a statement about a formal system proven in a metalanguage.
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Metatheory
A metatheory or meta-theory is a theory whose subject matter is some theory.
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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.
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Premise
A premise or premiss is a statement that an argument claims will induce or justify a conclusion.
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Proposition
The term proposition has a broad use in contemporary analytic philosophy.
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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).
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Semantics (computer science)
In programming language theory, semantics is the field concerned with the rigorous mathematical study of the meaning of programming languages.
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Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.
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Sequent
In mathematical logic, a sequent is a very general kind of conditional assertion.
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Sequent calculus
Sequent calculus is, in essence, a style of formal logical argumentation where every line of a proof is a conditional tautology (called a sequent by Gerhard Gentzen) instead of an unconditional tautology.
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Simply typed lambda calculus
The simply typed lambda calculus (\lambda^\to), a form of type theory, is a typed interpretation of the lambda calculus with only one type constructor: \to that builds function types.
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Tautology (logic)
In logic, a tautology (from the Greek word ταυτολογία) is a formula or assertion that is true in every possible interpretation.
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Turnstile (symbol)
In mathematical logic and computer science the symbol \vdash has taken the name turnstile because of its resemblance to a typical turnstile if viewed from above.
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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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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.
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Redirects here:
Judgement (mathematical logic), Logical assertion.
References
[1] https://en.wikipedia.org/wiki/Judgment_(mathematical_logic)
