On decidability of the decomposability problem for finite theories (Q630293)
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scientific article; zbMATH DE number 5867023
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On decidability of the decomposability problem for finite theories |
scientific article; zbMATH DE number 5867023 |
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On decidability of the decomposability problem for finite theories (English)
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17 March 2011
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The authors consider the problem of nontrivial representation of a theory as a union of two (or several) theories in disjoint signatures. They prove that for a number of finite signatures this problem is \(\Sigma_1^0\)-complete and, thus, undecidable. This is true already for finite universal Horn theories (theories axiomatized by a finite set of quasi-identities). These theories correspond to the class of logic programs. But if the signature consists only of monadic predicates and constants, the decomposability problem is decidable.
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decomposition of a theory
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Horn theory
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logic programming
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decomposable theory
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monadic logic
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