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**Connecting many-sorted theories.**
*(English)*
Zbl 1136.03012

The authors develop an interesting and useful approach for merging families of decision procedures in complex logical systems. E.g., good use is made of the well-known Presburger-type procedures/algorithms for arithmetical systems of logic. Indeed, their approach seems to work for merging the several different kinds of algorithms/procedures used to prove the polynomial-time solvability of linear programming problems. They propose a novel scheme for merging many-sorted theories and show under what conditions decidability of the “universal fragment” of the component theories transfers to their combination. If their approach carries over to the situation wherein undecidability of the “universal fragment” of the component theories transfers to their combination then important new results would be available for a better understanding of (1) undecidable theories and (2) recursively enumerable degrees of unsolvability. The authors’ paper will be especially valuable for classical logicians interested in deep problems of artificial intelligence.

Reviewer: Albert A. Mullin (Madison)

### MSC:

03B25 | Decidability of theories and sets of sentences |

03B35 | Mechanization of proofs and logical operations |

03B45 | Modal logic (including the logic of norms) |

03D40 | Word problems, etc. in computability and recursion theory |

68T27 | Logic in artificial intelligence |

### Keywords:

many-sorted theories; automated deduction; artificial intelligence; modal logic; word problems of logic
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\textit{F. Baader} and \textit{S. Ghilardi}, J. Symb. Log. 72, No. 2, 535--583 (2007; Zbl 1136.03012)

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