By Gonzalo A. Aranda-Corral, Jacques Calmet, Francisco J. Martín-Mateos

This booklet constitutes the refereed lawsuits of the twelfth foreign convention on synthetic Intelligence and Symbolic Computation, AISC 2014, held in Seville, Spain, in December 2014. The 15 complete papers awarded including 2 invited papers have been rigorously reviewed and chosen from 22 submissions. The targets have been on one part to bind mathematical domain names corresponding to algebraic topology or algebraic geometry to AI but in addition to hyperlink AI to domain names outdoor natural algorithmic computing. The papers handle all present elements within the zone of symbolic computing and AI: simple suggestions of computability and new Turing machines; logics together with non-classical ones; reasoning; studying; determination aid platforms; and computer intelligence and epistemology and philosophy of symbolic mathematical computing.

**Read Online or Download Artificial Intelligence and Symbolic Computation: 12th International Conference, AISC 2014, Seville, Spain, December 11-13, 2014. Proceedings PDF**

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**Extra resources for Artificial Intelligence and Symbolic Computation: 12th International Conference, AISC 2014, Seville, Spain, December 11-13, 2014. Proceedings**

**Sample text**

The essence of the proof is captured in this transformation, showing the adequacy of our contribution. The organization of the paper is as follows. Our general framework to interoperate is brieﬂy described in Section 2. Section 3 is devoted to comment on the Isabelle/HOL theory developed and the translation process, while Section 4 deals with the completion of the ACL2 speciﬁcation until a proof of a fragment of the theory is obtained. The paper ends with conclusions, further work and the Obtaining an ACL2 Speciﬁcation from an Isabelle/HOL Theory 51 bibliography.

This work was partially supported by the research project TIN2012–32482 (Government of Spain). We would like to express our gratitude to Julio Rodr´ıguez–Costa, MD, President of the Sociedad Espa˜ nola de Citolog´ıa (SEC) and Head of the Servicio de Anatom´ıa Patol´ ogica of the Hospital General Universitario Gregorio Mara˜ n´ on (Madrid) for providing the microphotographies in this article and for his most valuable comments. The authors would also like to thank the anonymous reviewers for their valuable comments which helped to improve the manuscript.

N. Pn is a basis of Pn ; this is a consequence of the following. Theorem 3. Let P = {P0 , . . , Pn } be a set of n + 1 polynomials such that P0 ∈ R − {0} and deg(Pi ) = i for all 1 ≤ i ≤ n. Then, P is a basis of Pn (x). Note that Pn+1 = Pn ∪ Pn+1 (x). Proposition 4 (Number of Parameters in the Basis). Given n ∈ N, the number N (n) of parameters in Pn is given by N (0) = 0 and N (n) = N (n − 1) + n n2 n2 −1 otherwise. 2 for n > 0. Furthermore, N (n) = 4 if n is even and 4 26 S. Lucas We prove that Pn characterizes Psd ([0, +∞)) and Pd ([0, +∞)).