## Frontiers of Combining Systems: Third International Workshop, FroCoS 2000 Nancy, France, March 22-24, 2000 ProceedingsThis volume contains the proceedings of FroCoS2000, the 3rd International WorkshoponFrontiersofCombiningSystems, heldMarch22-24,2000, inNancy, France. Like its predecessors organized in Munich (1996) and in Amsterdam (1998), FroCoS2000 is intended to o?er a common forum for research activities related to the combination and the integration of systems in the areas of logic, automateddeduction, constraintsolving, declarativeprogramming, andarti?cial intelligence. There were 31 submissions of overall high quality, authored by researchers from countries including Australia, Brasil, Belgium, Chili, France, Germany, - pan, Ireland, Italy, Portugal, Spain, Switzerland, The Netherlands, the United Kingdom, and the United States of America. All submissions were thoroughly evaluatedonthebasisofatleastthreerefereereports, andanelectronicprogram committeemeetingwasheldthroughtheInternet.Theprogramcommitteesel- ted 14 research contributions. The topics covered by the selected papers include: combinationoflogics;combinationofconstraintsolvingtechniques, combination of decision procedures; modular properties for theorem proving; combination of deduction systems and computer algebra; integration of decision procedures and other solving processes into constraint programming and deduction systems. We welcomed ?ve invited lectures by Alexander Bockmayr on "Combining Logic and Optimization in Cutting Plane Theory," Gilles Dowek on "Axioms vs. Rewrite Rules: From Completeness to Cut Elimination," Klaus Schulz on "Why Combined Decision Problems Are Often Intractable," Tomas Uribe on "Combinations of Theorem Proving and Model Checking," and Richard Zippel on "Program Composition Techniques for Numerical PDE Codes." Full papers of these lectures, except the last one, are also included in this volume. |

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### Contents

Combining Logic and Optimization in Cutting Plane Theory | 1 |

Towards Cooperative Interval Narrowing | 18 |

Integrating Constraint Solving into Proof Planning | 32 |

Termination of Constraint Contextual Rewriting | 47 |

From Completeness to Cut Elimination | 62 |

Normal Forms and Proofs in Combined Modal and Temporal Logics | 73 |

Structured Sequent Calculi for Combining Intuitionistic and Classical FirstOrder Logic | 88 |

Handling Differential Equations with Constraints for Decision Support | 105 |

Combinations of Model Checking and Theorem Proving | 151 |

Compiling Multiparadigm Declarative Programs into Prolog | 171 |

Modular Redundancy for Theorem Proving | 186 |

Composing and Controlling Search in Reasoning Theories Using Mappings | 200 |

Why Combined Decision Problems Are Often Intractable | 217 |

Congruence Closure Modulo Associativity and Commutativity | 245 |

Combining Equational Theories Sharing NonCollapseFree Constructors | 260 |

Comparing Expressiveness of Set Constructor Symbols | 275 |

Nontrivial Symbolic Computations in Proof Planning | 121 |

Integrating Computer Algebra and Reasoning through the Type System of Aldor | 136 |

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### Common terms and phrases

Aldor algorithm annotated application axioms Boolean bound box consistency clauses combination method complete component computer algebra computer algebra systems Computer Science condition conjunction constraint solver constructors context contextual rewriting cutting plane decision problems decision procedure deduction deﬁned Deﬁnition denote derivation disjunction domains equational theories ERThs eseq eseq1 eseq2 evaluation example expressions extended finite first-order function symbols G1 G given hull-consistency implementation inequalities inference rules input instance instantiated integration interval intuitionistic language Lemma literals LNCS Logic Programming modal logics model checking modulo multiset normal form notion NP-hard NQTHM obtained operations optimization parameters Parents(F polynomial predicate Proc Prolog proof planning properties proposition prover module relation resolution rewrite rules rewrite system satisﬁes Section sequent calculus sequent signature set of formulae solution solving Springer step structure techniques temporal logic theorem proving trajectory transition relation type theory unification variables verification