See undecidable on Wiktionary
{ "antonyms": [ { "word": "decidable" } ], "etymology_templates": [ { "args": { "1": "en", "2": "un", "3": "decidable" }, "expansion": "un- + decidable", "name": "prefix" } ], "etymology_text": "From un- + decidable.", "head_templates": [ { "args": { "1": "-" }, "expansion": "undecidable (not comparable)", "name": "en-adj" } ], "lang": "English", "lang_code": "en", "pos": "adj", "related": [ { "_dis1": "0 0", "word": "noncomputable" } ], "senses": [ { "categories": [ { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Theory of computing", "orig": "en:Theory of computing", "parents": [ "Computer science", "Computing", "Sciences", "Technology", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "51 49", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "49 51", "kind": "other", "name": "English terms prefixed with un-", "parents": [], "source": "w+disamb" }, { "_dis": "55 45", "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w+disamb" }, { "_dis": "47 53", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "47 53", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" }, { "_dis": "51 49", "kind": "other", "name": "Terms with Czech translations", "parents": [], "source": "w+disamb" }, { "_dis": "48 52", "kind": "other", "name": "Terms with Finnish translations", "parents": [], "source": "w+disamb" }, { "_dis": "49 51", "kind": "other", "name": "Terms with German translations", "parents": [], "source": "w+disamb" }, { "_dis": "50 50", "kind": "other", "name": "Terms with Hebrew translations", "parents": [], "source": "w+disamb" }, { "_dis": "51 49", "kind": "other", "name": "Terms with Polish translations", "parents": [], "source": "w+disamb" }, { "_dis": "48 52", "kind": "other", "name": "Terms with Romanian translations", "parents": [], "source": "w+disamb" }, { "_dis": "51 49", "kind": "other", "name": "Terms with Serbo-Croatian translations", "parents": [], "source": "w+disamb" }, { "_dis": "50 50", "kind": "other", "name": "Terms with Spanish translations", "parents": [], "source": "w+disamb" } ], "examples": [ { "ref": "1982, Wolfgang Bibel, Automated Theorem Proving, Braunschweig: Friedr. Vieweg & Sohn, →ISBN, page 83:", "text": "The first-order procedure SP differs from the proposi-\n tional procedure CP°₁ in an essential feature. Namely, CP°₁\n always terminates while SP may run forever as we have seen with\n the example immediately after (3.7). This is not a specific\n defect of SP. Rather it is known that first-order logic is an\n undecidable theory while propositional logic is a decidable\n theory. This means that for the latter there are decision pro-\n cedures which for any formula decide whether it is valid or\n not — and CP°₁ in fact is such a decision procedure — while\n for the former such decision procedures do not exist in princi-\n ple. Thus SP, according to these results for which the reader\n is referred to any logic texts such as [End], [DrG] or [Lew],\n is of the kind which we may expect, it is a semi-decision\n procedure which confirms if a formula is valid but may run\n forever for invalid formulas. Therefore, termination by running\n out of time or space after any finite number of steps will\n leave the question for the validity of a formula unsettled. [...]", "type": "quote" } ], "glosses": [ "Incapable of being algorithmically decided in finite time. For example, a set of strings is undecidable if it is impossible to program a computer (even one with infinite memory) to determine whether or not specified strings are included." ], "id": "en-undecidable-en-adj-Cc4G40e4", "links": [ [ "mathematics", "mathematics" ], [ "computing", "computing#Noun" ], [ "theory", "theory" ], [ "algorithm", "algorithm" ], [ "finite", "finite" ], [ "string", "string" ], [ "computer", "computer" ], [ "memory", "memory" ] ], "raw_glosses": [ "(mathematics, computing theory) Incapable of being algorithmically decided in finite time. For example, a set of strings is undecidable if it is impossible to program a computer (even one with infinite memory) to determine whether or not specified strings are included." ], "tags": [ "not-comparable" ], "topics": [ "computing", "computing-theory", "engineering", "mathematics", "natural-sciences", "physical-sciences", "sciences" ], "translations": [ { "_dis1": "80 20", "code": "cs", "lang": "Czech", "sense": "incapable of being algorithmically decided", "tags": [ "masculine" ], "word": "nerozhodnutelný" }, { "_dis1": "80 20", "code": "fi", "lang": "Finnish", "sense": "incapable of being algorithmically decided", "word": "ratkeamaton" }, { "_dis1": "80 20", "code": "de", "lang": "German", "sense": "incapable of being algorithmically decided", "word": "unentscheidbar" }, { "_dis1": "80 20", "code": "he", "lang": "Hebrew", "roman": "í-karí'a", "sense": "incapable of being algorithmically decided", "word": "אי-כריע" }, { "_dis1": "80 20", "code": "pl", "lang": "Polish", "sense": "incapable of being algorithmically decided", "tags": [ "masculine" ], "word": "nierozstrzygalny" }, { "_dis1": "80 20", "code": "ro", "lang": "Romanian", "sense": "incapable of being algorithmically decided", "word": "nedecidabil" }, { "_dis1": "80 20", "code": "sh", "lang": "Serbo-Croatian", "sense": "incapable of being algorithmically decided", "word": "neodlučiv" }, { "_dis1": "80 20", "code": "es", "lang": "Spanish", "sense": "incapable of being algorithmically decided", "word": "indecidible" } ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "51 49", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "49 51", "kind": "other", "name": "English terms prefixed with un-", "parents": [], "source": "w+disamb" }, { "_dis": "55 45", "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w+disamb" }, { "_dis": "47 53", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "47 53", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" }, { "_dis": "51 49", "kind": "other", "name": "Terms with Czech translations", "parents": [], "source": "w+disamb" }, { "_dis": "48 52", "kind": "other", "name": "Terms with Finnish translations", "parents": [], "source": "w+disamb" }, { "_dis": "49 51", "kind": "other", "name": "Terms with German translations", "parents": [], "source": "w+disamb" }, { "_dis": "50 50", "kind": "other", "name": "Terms with Hebrew translations", "parents": [], "source": "w+disamb" }, { "_dis": "51 49", "kind": "other", "name": "Terms with Polish translations", "parents": [], "source": "w+disamb" }, { "_dis": "48 52", "kind": "other", "name": "Terms with Romanian translations", "parents": [], "source": "w+disamb" }, { "_dis": "51 49", "kind": "other", "name": "Terms with Serbo-Croatian translations", "parents": [], "source": "w+disamb" }, { "_dis": "50 50", "kind": "other", "name": "Terms with Spanish translations", "parents": [], "source": "w+disamb" } ], "glosses": [ "(of a WFF) logically independent from the axioms of a given theory; i.e., that it can never be either proved or disproved (i.e., have its negation proved) on the basis of the axioms of the given theory. (Note: this latter definition is independent of any time bounds or computability issues, i.e., more Platonic.)" ], "id": "en-undecidable-en-adj-7RhXqDqc", "links": [ [ "mathematics", "mathematics" ], [ "WFF", "WFF" ], [ "logically independent", "logically independent" ], [ "axiom", "axiom" ] ], "raw_glosses": [ "(mathematics) (of a WFF) logically independent from the axioms of a given theory; i.e., that it can never be either proved or disproved (i.e., have its negation proved) on the basis of the axioms of the given theory. (Note: this latter definition is independent of any time bounds or computability issues, i.e., more Platonic.)" ], "tags": [ "not-comparable" ], "topics": [ "mathematics", "sciences" ] } ], "sounds": [ { "audio": "en-us-undecidable.ogg", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/5/5d/En-us-undecidable.ogg/En-us-undecidable.ogg.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/5/5d/En-us-undecidable.ogg" } ], "wikipedia": [ "undecidable" ], "word": "undecidable" }
{ "antonyms": [ { "word": "decidable" } ], "categories": [ "English adjectives", "English entries with incorrect language header", "English lemmas", "English terms prefixed with un-", "English uncomparable adjectives", "Entries with translation boxes", "Pages with 1 entry", "Pages with entries", "Terms with Czech translations", "Terms with Finnish translations", "Terms with German translations", "Terms with Hebrew translations", "Terms with Polish translations", "Terms with Romanian translations", "Terms with Serbo-Croatian translations", "Terms with Spanish translations" ], "etymology_templates": [ { "args": { "1": "en", "2": "un", "3": "decidable" }, "expansion": "un- + decidable", "name": "prefix" } ], "etymology_text": "From un- + decidable.", "head_templates": [ { "args": { "1": "-" }, "expansion": "undecidable (not comparable)", "name": "en-adj" } ], "lang": "English", "lang_code": "en", "pos": "adj", "related": [ { "word": "noncomputable" } ], "senses": [ { "categories": [ "English terms with quotations", "en:Mathematics", "en:Theory of computing" ], "examples": [ { "ref": "1982, Wolfgang Bibel, Automated Theorem Proving, Braunschweig: Friedr. Vieweg & Sohn, →ISBN, page 83:", "text": "The first-order procedure SP differs from the proposi-\n tional procedure CP°₁ in an essential feature. Namely, CP°₁\n always terminates while SP may run forever as we have seen with\n the example immediately after (3.7). This is not a specific\n defect of SP. Rather it is known that first-order logic is an\n undecidable theory while propositional logic is a decidable\n theory. This means that for the latter there are decision pro-\n cedures which for any formula decide whether it is valid or\n not — and CP°₁ in fact is such a decision procedure — while\n for the former such decision procedures do not exist in princi-\n ple. Thus SP, according to these results for which the reader\n is referred to any logic texts such as [End], [DrG] or [Lew],\n is of the kind which we may expect, it is a semi-decision\n procedure which confirms if a formula is valid but may run\n forever for invalid formulas. Therefore, termination by running\n out of time or space after any finite number of steps will\n leave the question for the validity of a formula unsettled. [...]", "type": "quote" } ], "glosses": [ "Incapable of being algorithmically decided in finite time. For example, a set of strings is undecidable if it is impossible to program a computer (even one with infinite memory) to determine whether or not specified strings are included." ], "links": [ [ "mathematics", "mathematics" ], [ "computing", "computing#Noun" ], [ "theory", "theory" ], [ "algorithm", "algorithm" ], [ "finite", "finite" ], [ "string", "string" ], [ "computer", "computer" ], [ "memory", "memory" ] ], "raw_glosses": [ "(mathematics, computing theory) Incapable of being algorithmically decided in finite time. For example, a set of strings is undecidable if it is impossible to program a computer (even one with infinite memory) to determine whether or not specified strings are included." ], "tags": [ "not-comparable" ], "topics": [ "computing", "computing-theory", "engineering", "mathematics", "natural-sciences", "physical-sciences", "sciences" ] }, { "categories": [ "en:Mathematics" ], "glosses": [ "(of a WFF) logically independent from the axioms of a given theory; i.e., that it can never be either proved or disproved (i.e., have its negation proved) on the basis of the axioms of the given theory. (Note: this latter definition is independent of any time bounds or computability issues, i.e., more Platonic.)" ], "links": [ [ "mathematics", "mathematics" ], [ "WFF", "WFF" ], [ "logically independent", "logically independent" ], [ "axiom", "axiom" ] ], "raw_glosses": [ "(mathematics) (of a WFF) logically independent from the axioms of a given theory; i.e., that it can never be either proved or disproved (i.e., have its negation proved) on the basis of the axioms of the given theory. (Note: this latter definition is independent of any time bounds or computability issues, i.e., more Platonic.)" ], "tags": [ "not-comparable" ], "topics": [ "mathematics", "sciences" ] } ], "sounds": [ { "audio": "en-us-undecidable.ogg", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/5/5d/En-us-undecidable.ogg/En-us-undecidable.ogg.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/5/5d/En-us-undecidable.ogg" } ], "translations": [ { "code": "cs", "lang": "Czech", "sense": "incapable of being algorithmically decided", "tags": [ "masculine" ], "word": "nerozhodnutelný" }, { "code": "fi", "lang": "Finnish", "sense": "incapable of being algorithmically decided", "word": "ratkeamaton" }, { "code": "de", "lang": "German", "sense": "incapable of being algorithmically decided", "word": "unentscheidbar" }, { "code": "he", "lang": "Hebrew", "roman": "í-karí'a", "sense": "incapable of being algorithmically decided", "word": "אי-כריע" }, { "code": "pl", "lang": "Polish", "sense": "incapable of being algorithmically decided", "tags": [ "masculine" ], "word": "nierozstrzygalny" }, { "code": "ro", "lang": "Romanian", "sense": "incapable of being algorithmically decided", "word": "nedecidabil" }, { "code": "sh", "lang": "Serbo-Croatian", "sense": "incapable of being algorithmically decided", "word": "neodlučiv" }, { "code": "es", "lang": "Spanish", "sense": "incapable of being algorithmically decided", "word": "indecidible" } ], "wikipedia": [ "undecidable" ], "word": "undecidable" }
Download raw JSONL data for undecidable meaning in All languages combined (5.3kB)
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