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 |
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| SubjectTerms | Inductive inference Logical queries Oracles inference degrees Turing degrees |
| Title | Learning via queries and oracles |
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