By Franz Baader

ISBN-10: 3540405593

ISBN-13: 9783540405597

The refereed lawsuits of the nineteenth foreign convention on automatic Deduction, CADE 2003, held in Miami seashore, FL, united states in July 2003. The 29 revised complete papers and seven method description papers offered including an invited paper and three abstracts of invited talks have been conscientiously reviewed and chosen from eighty three submissions. All present elements of computerized deduction are mentioned, starting from theoretical and methodological matters to the presentation of latest theorem provers and platforms.

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**Additional resources for Automated deduction, CADE-19: 19th International Conference on Automated Deduction, Miami Beach, FL, USA, July 28-August 2, 2003 : proceedings**

**Example text**

A. Robinson & A. ), Handbook of Automated Reasoning, Vol. 1, pages 845–911, 2001. 7. H. B. Enderton. A Mathematical Introduction to Logic. 2nd edition, Harcourt/ Academic Press, 2001. 8. J. Giesl & D. Kapur. Decidable Classes of Inductive Theorems. Proc. IJCAR ’01, LNAI 2083, pages 469–484, 2001. 9. J. Giesl & D. Kapur. Deciding Inductive Validity of Equations. Technical Report AIB-2003-03, 2003. de 10. D. Kapur & H. Zhang. An Overview of Rewrite Rule Laboratory (RRL). Journal of Computer and Mathematics with Applications, 29:91–114, 1995.

Here, ti and sj are replaced by fresh variables and identical terms are replaced by the same variable. This generalized equation is an equation over FT and thus, its (inductive) validity can be decided by a decision procedure for T . In general, however, inductive validity of the generalized equation implies inductive validity of the original equation, but not vice versa. We deﬁne a no-theory condition which ensures that this generalization is safe in the theory of free constructors or Presburger Arithmetic3 .

The constraints are unsatisﬁable iﬀ f satisﬁes the no-theory condition. For “∗” in Ex. 2, we assume that x ∗ y =TP A a0 + a1 · x + a2 · y. The mapping τ is now applied to both deﬁning equations of “∗”. , a0 + a2 y = a0 . , a0 + a1 + a1 x + a2 y = a0 + a1 x + (a2 + 1)y. Since polynomials are only considered equal if the corresponding coeﬃcients are equal, the resulting set of constraints is {a2 = 0, a0 + a1 = a0 , a2 = a2 + 1} (plus trivial constraints). It is easy to detect their unsatisﬁability and thus, “∗” satisﬁes the no-theory condition.

### Automated deduction, CADE-19: 19th International Conference on Automated Deduction, Miami Beach, FL, USA, July 28-August 2, 2003 : proceedings by Franz Baader

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