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- Judgment_(mathematical_logic) abstract "In mathematical logic, a judgment can be an assertion about occurrence of a free variable in an expression of the object language, or about provability of a proposition (either as a tautology or from a given context), but judgments can be also other inductively definable assertions in the metatheory. Judgments are used for example in formalizing deduction systems: a logical axiom expresses a judgment, premises of a rule of inference are formed as a sequence of judgments, and their conclusion is a judgment as well. Also the result of a proof expresses a judgment, and the used hypotheses are formed as a sequence of judgments.A characteristic feature of the variants of Hilbert-style deduction systems is that the context is not changed in any of their rules of inference, while both natural deduction and sequent calculus contain some context-changing rules. Thus, if we are interested only in the derivability of tautologies, not hypothetical judgments, then we can formalize the Hilbert-style deduction system in such a way that its rules of inference contain only judgments of a rather simple form. The same cannot be done with the other two deductions systems: as context is changed in some of their rules of inferences, they cannot be formalized so that hypothetical judgments could be avoided—not even if we want to use them just for proving derivability of tautologies.This basic diversity among the various calculi allows such difference, that the same basic thought (e.g. deduction theorem) must be proven as a metatheorem in Hilbert-style deduction system, while it can be declared explicitly as a rule of inference in natural deduction.In type theory, some analogous notions are used as in mathematical logic (giving rise to connections between the two fields, e.g. Curry-Howard correspondence). The abstraction in the notion of judgment in mathematical logic can be exploited also in foundation of type theory as well.".
- Judgment_(mathematical_logic) wikiPageExternalLink martin.html.
- Judgment_(mathematical_logic) wikiPageExternalLink index.pl?node=Judgment.
- Judgment_(mathematical_logic) wikiPageExternalLink ch2-natded.pdf.
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- Judgment_(mathematical_logic) wikiPageWikiLink Axiom.
- Judgment_(mathematical_logic) wikiPageWikiLink Category:Concepts_in_logic.
- Judgment_(mathematical_logic) wikiPageWikiLink Category:Logical_calculi.
- Judgment_(mathematical_logic) wikiPageWikiLink Category:Proof_theory.
- Judgment_(mathematical_logic) wikiPageWikiLink Curry-Howard_correspondence.
- Judgment_(mathematical_logic) wikiPageWikiLink Curry–Howard_correspondence.
- Judgment_(mathematical_logic) wikiPageWikiLink Deduction_theorem.
- Judgment_(mathematical_logic) wikiPageWikiLink Free_variable.
- Judgment_(mathematical_logic) wikiPageWikiLink Free_variables_and_bound_variables.
- Judgment_(mathematical_logic) wikiPageWikiLink Hilbert-style_deduction_system.
- Judgment_(mathematical_logic) wikiPageWikiLink Hilbert_system.
- Judgment_(mathematical_logic) wikiPageWikiLink Logical_axiom.
- Judgment_(mathematical_logic) wikiPageWikiLink Mathematical_logic.
- Judgment_(mathematical_logic) wikiPageWikiLink Metatheorem.
- Judgment_(mathematical_logic) wikiPageWikiLink Metatheory.
- Judgment_(mathematical_logic) wikiPageWikiLink Natural_deduction.
- Judgment_(mathematical_logic) wikiPageWikiLink Proposition.
- Judgment_(mathematical_logic) wikiPageWikiLink Rule_of_inference.
- Judgment_(mathematical_logic) wikiPageWikiLink Sequent_calculus.
- Judgment_(mathematical_logic) wikiPageWikiLink Simply_typed_lambda_calculus.
- Judgment_(mathematical_logic) wikiPageWikiLink Tautology_(logic).
- Judgment_(mathematical_logic) wikiPageWikiLink Type_theory.
- Judgment_(mathematical_logic) wikiPageWikiLinkText "Judgment (mathematical logic)".
- Judgment_(mathematical_logic) wikiPageWikiLinkText "judgement".
- Judgment_(mathematical_logic) wikiPageWikiLinkText "judgment".
- Judgment_(mathematical_logic) wikiPageWikiLinkText "judgments".
- Judgment_(mathematical_logic) wikiPageWikiLinkText "typing judgment".
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- Judgment_(mathematical_logic) wikiPageUsesTemplate Template:Mathlogic-stub.
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- Judgment_(mathematical_logic) wikiPageUsesTemplate Template:Other_uses.
- Judgment_(mathematical_logic) subject Category:Concepts_in_logic.
- Judgment_(mathematical_logic) subject Category:Logical_calculi.
- Judgment_(mathematical_logic) subject Category:Proof_theory.
- Judgment_(mathematical_logic) comment "In mathematical logic, a judgment can be an assertion about occurrence of a free variable in an expression of the object language, or about provability of a proposition (either as a tautology or from a given context), but judgments can be also other inductively definable assertions in the metatheory.".
- Judgment_(mathematical_logic) label "Judgment (mathematical logic)".
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- Judgment_(mathematical_logic) sameAs Urteil_(Logik).
- Judgment_(mathematical_logic) sameAs Juicio_(pensamiento).
- Judgment_(mathematical_logic) sameAs Arvostelma.
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- Judgment_(mathematical_logic) sameAs Q1720612.
- Judgment_(mathematical_logic) sameAs Q1720612.
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