Y. Matijacevic. Enumerable sets are diophantine. Soviet Math. Doklady, 11:354-- 357, 1970. English translation. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Extensions of Terminological Knowledge Representation Languages.. - Baader (1996) (1 citation) (Correct)
.... (see e.g. Weispfenning,1988 ] and in the quantifier free linear case one even has incremental methods for deciding satisfiability [ Jaakola,1990; Jaffar et al. 1992 ] The concrete domain Z is not admissible since Hilbert s Tenth Problem one of the most prominent undecidable problems [ Matijacevic,1970; Davis,1973 ] is a special case of its satisfiability problem. In [ Baader and Hanschke,1991 ] it is shown how the tableau based reasoning algorithm for ALC can be extended to ALC(D) provided that D is admissible. Theorem 3.4 If D is an admissible concrete domain, then the subsumption ....
Y. Matijacevic. Enumerable sets are diophantine. Soviet Math. Doklady, 11:354-- 357, 1970. English translation.
A Scheme for Integrating Concrete Domains into Concept Languages - Baader, Hanschke (1991) (120 citations) (Correct)
.... (where the polynomials in the equalities and inequalities have to be linear) there exist more efficient methods (see e.g. Weispfenning, 1988; Loos and Weispfenning, 1990 ] The concrete domain Z is not admissible since Hilbert s Tenth Problem one of the most prominent undecidable problems [ Matijacevic, 1970; Davis, 1973 ] is a special case of its satisfiability problem. Sometimes the adequate modeling of a problem domain could be facilitated if reference to more than one concrete domain would be possible in a terminology. Therefore, we show how two disjoint admissible concrete domains D 1 and D 2 ....
Y. Matijacevic. Enumerable sets are diophantine. Soviet Math. Doklady, 11:354--357, 1970. English translation.
A New Method for Undecidability Proofs of First Order Theories - Treinen (1992) (21 citations) (Correct)
....(Example (F) Quine (1946) showed already the undecidability of the theory of concatenation. He gives a translation of number theory to the theory of concatenation that yields a Sigma 6 sentence for an instance of Hilbert s Tenth Problem, using the undecidability of Hilbert s Tenth Problem (Matijacevic (1970)) this proves the undecidability of the Sigma 6 fragment of the theory of concatenation. On the other hand (Example (F) shows the undecidability of the Sigma 2 fragment of the theory of a ground term algebra modulo associativity. A unification algorithm for this theory (without free function ....
....these results (see Section 5) The undecidability of the Sigma 2 fragment of complete number theory (Example (G) is of course by no means a new result; it is presented here merely for demonstrating some aspects of the method proposed. The undecidability of the Sigma 1 fragment has been shown in Matijacevic (1970). The separation of Post s Correspondence Problem into two datatypes induces the structure of the paper: After a survey of the mathematical framework in Section 2 the simulation of the data type strings is discussed in Section 3. In the applications this part will always be the trivial one. ....
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Matijacevic, Y. (1970). Enumerable sets are diophantine. Dokl. Akad. Nauk. SSSR, 191:279--282.
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