About: Judgment (mathematical logic)

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In mathematical logic, a judgment (or judgement) or assertion is a statement or enunciation in the metalanguage. For example, typical judgments in first-order logic would be that a string is a well-formed formula, or that a proposition is true. Similarly, a judgment may assert the occurrence of a free variable in an expression of the object language, or the provability of a proposition. In general, a judgment may be any inductively definable assertion in the metatheory.

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rdfs:label	Judgment (mathematical logic) (en)
rdfs:comment	In mathematical logic, a judgment (or judgement) or assertion is a statement or enunciation in the metalanguage. For example, typical judgments in first-order logic would be that a string is a well-formed formula, or that a proposition is true. Similarly, a judgment may assert the occurrence of a free variable in an expression of the object language, or the provability of a proposition. In general, a judgment may be any inductively definable assertion in the metatheory. (en)
sameAs	Judgment (mathematical logic) Judgment (mathematical logic)
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Cite_journal dbt:Cite_web dbt:Other_uses dbt:Cite_SEP
Subject	Concepts in logic Proof theory Logical calculi
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Judgment_(mathematical_logic)?oldid=1013764665&ns=0
Wikipage page ID	15014170 (xsd:integer)
page length (characters) of wiki page	3866 (xsd:nonNegativeInteger)
Wikipage revision ID	1013764665 (xsd:integer)
Link from a Wikipage to another Wikipage	Formal system Logical consequence Proposition Well-formed formula Axiom Sequence Sequent calculus Tautology (logic) Concepts in logic Proof theory Free variables and bound variables Logical calculi Hilbert system Metalanguage Metatheorem Metatheory Curry–Howard correspondence Deduction theorem Rule of inference First-order logic Type theory Mathematical logic Natural deduction Simply typed lambda calculus
has abstract	In mathematical logic, a judgment (or judgement) or assertion is a statement or enunciation in the metalanguage. For example, typical judgments in first-order logic would be that a string is a well-formed formula, or that a proposition is true. Similarly, a judgment may assert the occurrence of a free variable in an expression of the object language, or the provability of a proposition. In general, a judgment may be any inductively definable assertion in the metatheory. Judgments are used 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 (thus, hypotheses and conclusions of proofs are 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. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Judgment_(mathematical_logic)
is notableIdea of	Robert Stalnaker
is Wikipage redirect of	Logical assertion Judgement (mathematical logic)
is Link from a Wikipage to another Wikipage of	Logical framework Logical quality Norm (philosophy) Affirming a disjunct Assertion Authentication Glossary of computer science Glossary of rhetorical terms Ai-Fak Dialetheism Hilbert system Hindley–Milner type system Defamation Common ground (linguistics) Conceptual schema History of type theory Ideal speech situation Identity type Index of logic articles Index of philosophy articles (A–C) Inference Invariant (mathematics) Luca Incurvati Loop invariant Natural deduction Logical assertion Judgement (mathematical logic)
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Judgment_(mathematical_logic)

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