Learning via queries and oracles
Inductive inference considers two types of queries: Queries to a teacher about the function to be learned and queries to a non-recursive oracle. This paper combines these two types — it considers three basic models of queries to a teacher (QEX[Succ], QEX[<] and QEX[+]) together with membership qu...
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| Vydáno v: | Annals of pure and applied logic Ročník 94; číslo 1; s. 273 - 296 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier B.V
05.10.1998
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| ISSN: | 0168-0072 |
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| Abstract | Inductive inference considers two types of queries: Queries to a teacher about the function to be learned and queries to a non-recursive oracle. This paper combines these two types — it considers three basic models of queries to a teacher (QEX[Succ], QEX[<] and QEX[+]) together with membership queries to some oracle.
The results for each of these three models of query-inference are the same: If an oracle is omniscient for query-inference then it is already omniscient for EX. There is an oracle of trivial EX-degree, which allows nontrivial query-inference. Furthermore, queries to a teacher cannot overcome differences between oracles and the query-inference degrees are a proper refinement of the EX-degrees.
In the case of finite learning, the query-inference degrees coincide with the Turing degrees. Furthermore oracles can not close the gap between the different types of queries to a teacher. |
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| AbstractList | Inductive inference considers two types of queries: Queries to a teacher about the function to be learned and queries to a non-recursive oracle. This paper combines these two types — it considers three basic models of queries to a teacher (QEX[Succ], QEX[<] and QEX[+]) together with membership queries to some oracle.
The results for each of these three models of query-inference are the same: If an oracle is omniscient for query-inference then it is already omniscient for EX. There is an oracle of trivial EX-degree, which allows nontrivial query-inference. Furthermore, queries to a teacher cannot overcome differences between oracles and the query-inference degrees are a proper refinement of the EX-degrees.
In the case of finite learning, the query-inference degrees coincide with the Turing degrees. Furthermore oracles can not close the gap between the different types of queries to a teacher. |
| Author | Stephan, Frank |
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| Cites_doi | 10.2307/2273221 10.1006/inco.1993.1014 10.1016/0890-5401(87)90052-6 10.1016/S0019-9958(67)91165-5 10.2307/2275058 10.1145/146637.146670 10.1016/0304-3975(83)90061-0 10.1006/jcss.1996.0018 10.1016/0168-0072(94)90035-3 10.2307/2275176 |
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| Keywords | Inductive inference 03D30 03D80 Oracles inference degrees 03D25 Logical queries Turing degrees |
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| References | Adleman, Blum (BIB1) 1991; 56 Fortnow, Gasarch, Jain, Kinber, Kummer, Kurtz, Pleszkoch, Slaman, Solovay, Stephan (BIB5) 1994; 66 Gasarch, Smith (BIB8) 1992; 39 Slaman, Solovay (BIB15) 1991 Jockusch (BIB10) 1981; vol. 45 Stephan (BIB17) 1995 Gasarch, Pleszkoch (BIB6) 1989 Soare (BIB16) 1987 Posner, Robinson (BIB12) 1981; 46 Gold (BIB9) 1967; 10 Case, Smith (BIB4) 1983; 25 Osherson, Stob, Weinstein (BIB14) 1986 Odifreddi (BIB13) 1989 Kummer, Stephan, Kummer, Stephan (BIB11) 1996; 52 Beigel, Gasarch, Gill, Owings (BIB3) 1993; 103 Angluin (BIB2) 1987; 75 Gasarch, Pleszkoch, Solovay (BIB7) 1992; 57 Posner (10.1016/S0168-0072(97)00077-8_BIB12) 1981; 46 Gasarch (10.1016/S0168-0072(97)00077-8_BIB6) 1989 Gasarch (10.1016/S0168-0072(97)00077-8_BIB7) 1992; 57 Gold (10.1016/S0168-0072(97)00077-8_BIB9) 1967; 10 Jockusch (10.1016/S0168-0072(97)00077-8_BIB10) 1981; vol. 45 Soare (10.1016/S0168-0072(97)00077-8_BIB16) 1987 Angluin (10.1016/S0168-0072(97)00077-8_BIB2) 1987; 75 Fortnow (10.1016/S0168-0072(97)00077-8_BIB5) 1994; 66 Gasarch (10.1016/S0168-0072(97)00077-8_BIB8) 1992; 39 Kummer (10.1016/S0168-0072(97)00077-8_BIB11_2) 1993 Osherson (10.1016/S0168-0072(97)00077-8_BIB14) 1986 Beigel (10.1016/S0168-0072(97)00077-8_BIB3) 1993; 103 Adleman (10.1016/S0168-0072(97)00077-8_BIB1) 1991; 56 Case (10.1016/S0168-0072(97)00077-8_BIB4) 1983; 25 Kummer (10.1016/S0168-0072(97)00077-8_BIB11_1) 1996; 52 Stephan (10.1016/S0168-0072(97)00077-8_BIB17) 1995 Odifreddi (10.1016/S0168-0072(97)00077-8_BIB13) 1989 Slaman (10.1016/S0168-0072(97)00077-8_BIB15) 1991 |
| References_xml | – volume: 56 start-page: 891 year: 1991 end-page: 900 ident: BIB1 article-title: Inductive inference and unsolvability publication-title: J. Symbolic Logic – start-page: 214 year: 1989 end-page: 229 ident: BIB6 article-title: Learning via queries to an oracle publication-title: Proc. 2nd Ann. ACM Conf. on Computational Learning Theory — COLT '89 – volume: 52 start-page: 214 year: 1996 end-page: 238 ident: BIB11 article-title: On the structure of degrees of inferability publication-title: Colt '93 – start-page: 162 year: 1995 end-page: 169 ident: BIB17 article-title: Learning via queries and oracles (a preliminary version of this paper) publication-title: Proc. 8th Ann. ACM Conf. on Computational Learning Theory — COLT '95 – year: 1986 ident: BIB14 article-title: Systems that Learn – volume: 103 start-page: 68 year: 1993 end-page: 85 ident: BIB3 article-title: Terse, superterse, and verbose sets publication-title: Inform. Comput. – volume: 75 start-page: 87 year: 1987 end-page: 106 ident: BIB2 article-title: Learning regular sets from queries and counterexamples publication-title: Inform. Comput. – volume: 25 start-page: 193 year: 1983 end-page: 220 ident: BIB4 article-title: Comparison of identification criteria for machine inductive inference publication-title: Theoret. Comput. Sci. – start-page: 379 year: 1991 end-page: 383 ident: BIB15 article-title: When oracles do not help publication-title: Proc. 4th Ann. ACM Conf. on Computational Learning Theory — COLT '91 – volume: 10 start-page: 447 year: 1967 end-page: 474 ident: BIB9 article-title: Language Identification in the limit publication-title: Inform. Control – volume: 57 start-page: 53 year: 1992 end-page: 81 ident: BIB7 article-title: Learning via Queries in [+, <] publication-title: J. Symbolic Logic – year: 1989 ident: BIB13 article-title: Classical Recursion Theory – year: 1987 ident: BIB16 article-title: Recursively Enumerable Sets and Degrees – volume: vol. 45 start-page: 110 year: 1981 end-page: 139 ident: BIB10 article-title: Degrees of generic sets publication-title: London Mathematical Society Lecture Notes – volume: 39 start-page: 649 year: 1992 end-page: 676 ident: BIB8 article-title: Learning via queries publication-title: J. Assoc. Comput. Mach. – volume: 66 start-page: 231 year: 1994 end-page: 276 ident: BIB5 article-title: Extremes in the degrees of inferability publication-title: Ann. Pure Appl. Logic – volume: 46 start-page: 714 year: 1981 end-page: 722 ident: BIB12 article-title: Degrees joining to 0' publication-title: J. Symbolic Logic – volume: 46 start-page: 714 issue: 4 year: 1981 ident: 10.1016/S0168-0072(97)00077-8_BIB12 article-title: Degrees joining to 0' publication-title: J. Symbolic Logic doi: 10.2307/2273221 – volume: 103 start-page: 68 year: 1993 ident: 10.1016/S0168-0072(97)00077-8_BIB3 article-title: Terse, superterse, and verbose sets publication-title: Inform. Comput. doi: 10.1006/inco.1993.1014 – volume: 75 start-page: 87 year: 1987 ident: 10.1016/S0168-0072(97)00077-8_BIB2 article-title: Learning regular sets from queries and counterexamples publication-title: Inform. Comput. doi: 10.1016/0890-5401(87)90052-6 – volume: 10 start-page: 447 year: 1967 ident: 10.1016/S0168-0072(97)00077-8_BIB9 article-title: Language Identification in the limit publication-title: Inform. Control doi: 10.1016/S0019-9958(67)91165-5 – start-page: 162 year: 1995 ident: 10.1016/S0168-0072(97)00077-8_BIB17 article-title: Learning via queries and oracles (a preliminary version of this paper) – start-page: 117 year: 1993 ident: 10.1016/S0168-0072(97)00077-8_BIB11_2 – year: 1987 ident: 10.1016/S0168-0072(97)00077-8_BIB16 – year: 1989 ident: 10.1016/S0168-0072(97)00077-8_BIB13 – start-page: 379 year: 1991 ident: 10.1016/S0168-0072(97)00077-8_BIB15 article-title: When oracles do not help – volume: 56 start-page: 891 year: 1991 ident: 10.1016/S0168-0072(97)00077-8_BIB1 article-title: Inductive inference and unsolvability publication-title: J. Symbolic Logic doi: 10.2307/2275058 – volume: 39 start-page: 649 issue: 3 year: 1992 ident: 10.1016/S0168-0072(97)00077-8_BIB8 article-title: Learning via queries publication-title: J. Assoc. Comput. Mach. doi: 10.1145/146637.146670 – volume: 25 start-page: 193 year: 1983 ident: 10.1016/S0168-0072(97)00077-8_BIB4 article-title: Comparison of identification criteria for machine inductive inference publication-title: Theoret. Comput. Sci. doi: 10.1016/0304-3975(83)90061-0 – start-page: 214 year: 1989 ident: 10.1016/S0168-0072(97)00077-8_BIB6 article-title: Learning via queries to an oracle – volume: 52 start-page: 214 year: 1996 ident: 10.1016/S0168-0072(97)00077-8_BIB11_1 article-title: On the structure of degrees of inferability publication-title: J. Computer System Sciences doi: 10.1006/jcss.1996.0018 – year: 1986 ident: 10.1016/S0168-0072(97)00077-8_BIB14 – volume: vol. 45 start-page: 110 year: 1981 ident: 10.1016/S0168-0072(97)00077-8_BIB10 article-title: Degrees of generic sets publication-title: London Mathematical Society Lecture Notes – volume: 66 start-page: 231 year: 1994 ident: 10.1016/S0168-0072(97)00077-8_BIB5 article-title: Extremes in the degrees of inferability publication-title: Ann. Pure Appl. Logic doi: 10.1016/0168-0072(94)90035-3 – volume: 57 start-page: 53 issue: 1 year: 1992 ident: 10.1016/S0168-0072(97)00077-8_BIB7 article-title: Learning via Queries in [+, <] publication-title: J. Symbolic Logic doi: 10.2307/2275176 |
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| SubjectTerms | Inductive inference Logical queries Oracles inference degrees Turing degrees |
| Title | Learning via queries and oracles |
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