By Serge Autexier, Jacques Calmet, David Delahaye, P.D.F. Ion, Laurence Rideau, Renaud Rioboo, Alan Sexton

This publication constitutes the joint refereed complaints of the tenth overseas convention on synthetic Intelligence and Symbolic Computation, AISC 2010, the seventeenth Symposium at the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2010, and the ninth foreign convention on Mathematical wisdom administration, MKM 2010. All submissions undergone a rigorous assessment technique. From the 25 papers submitted to AISC 2010, nine have been chosen for presentation on the convention and inclusion within the court cases quantity. a complete of 14 papers have been submitted to Calculemus, of which 7 have been permitted. MKM 2010 obtained 27 submissions, of which sixteen have been authorized for presentation and book. The occasions interested in using AI strategies inside symbolic computation and the applying of symbolic computation to AI challenge fixing; the combo of laptop algebra platforms and automatic deduction structures; and mathematical wisdom administration, respectively.

**Read or Download Intelligent Computer Mathematics: 10th International Conference, AISC 2010, 17th Symposium, Calculemus 2010, and 9th International Conference, MKM 2010, ... PDF**

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**Example text**

The proof is similar to that of the previous case. Theorem 2 (IS refutation completeness). t. IS) unsatisﬁable set of I-clauses contains the empty clause. Proof. The proof is similar to that of Theorem 1. 4 Conclusion The present work is a natural continuation of [5], in which we described the theorem prover dei, an extension of the well-known E-prover [21] devoted to handle I-terms. The present paper focuses on completeness issues. It shows that the resolution calculus (with ordering restrictions and selection functions) is refutationally complete when applied on clauses containing I-terms (in the non equational case).

1. 2. Properties 1, 2, 3 are standard, Property 4 ensures that is compatible with the semantics of I-terms. Given any ordering on terms satisfying the properties 1-3 above, we can extend to an ordering I on I-terms satisfying properties 1-4 as follows: t I s 24 H. Bensaid, R. Caferra, and N. t. the rules →I above and x denotes a variable not occurring in t, s): – t, s are standard terms and t s. – t = f (t1 , . . , tn ), s = f (s1 , . . n], ti si . v and v I s. s{N → 0}. v, u[x] I s and v w[x] and v I w.

The morphism extension package for Isabelle [2] provides implementations of key concepts such as signature and theory morphisms, and seamlessly extends Isabelle’s top-level language Isar with the commands necessary to express these notions; we will use these commands in the following. A crucial property is that any theory morphism τ : T −→ T from a theory T to a theory T ﬁrstly induces the homomorphic extension σ τ of the underlying signature morphism στ to propositions, and secondly the extension τ of τ to proof terms.