Abstract
In this paper, we use Girard’s ludics to analyze focalization, a fundamental property of the proof theory of linear logic. In particular, we show how focalization can be realized interactively thanks to suitable section-retraction pairs between semantical types.
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References
Andreoli, J.-M.: Logic Programming with Focusing Proofs in Linear Logic. Journal of Logic and Computation 2(3), 297–347 (1992)
Basaldella, M., Faggian, C.: Ludics with Repetitions (Exponentials, Interactive Types and Completeness). In: LICS (2009)
Basaldella, M., Terui, K.: On the meaning of logical completeness. In: Curien, P.-L. (ed.) TLCA 2009. LNCS, vol. 5608, pp. 50–64. Springer, Heidelberg (2009)
Curien, P.-L.: Introduction to LL and ludics, I & II. In: Advances in Mathematics, China, vol. 34(5), pp. 513–544 (2005); vol. 35(1), pp. 1–44 (2006)
Faggian, C., Piccolo, M.: Ludics is a model for the finitary linear pi-calculus. In: Della Rocca, S.R. (ed.) TLCA 2007. LNCS, vol. 4583, pp. 148–162. Springer, Heidelberg (2007)
Girard, J.-Y.: On the meaning of logical rules I: syntax vs. semantics. In: Berger, U., Schwichtenberg, H. (eds.) Computational Logic, pp. 215–272. Springer, Heidelberg (1999)
Girard, J.-Y.: On the meaning of logical rules II: multiplicatives and additives. In: Berger, Schwichtenberg (eds.) Foundation of Secure Computation, pp. 183–212 (2000)
Girard, J.-Y.: Locus solum: From the rules of logic to the logic of rules. Mathematical Structures in Computer Science 11, 301–506 (2001)
Laurent, O.: Étude de la polarization en logique. PhD thesis, Univ. Aix-Marseille II (2002)
Laurent, O.: A proof of the focalization property of Linear Logic (2004) (unpublished note)
Miller, D., Saurin, A.: From proofs to focused proofs: A modular proof of focalization in linear logic. In: Duparc, J., Henzinger, T.A. (eds.) CSL 2007. LNCS, vol. 4646, pp. 405–419. Springer, Heidelberg (2007)
Terui, K.: Computational ludics. To appear in Theoretical Computer Science (2008)
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Basaldella, M., Saurin, A., Terui, K. (2011). On the Meaning of Focalization. In: Lecomte, A., Tronçon, S. (eds) Ludics, Dialogue and Interaction. Lecture Notes in Computer Science(), vol 6505. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19211-1_5
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DOI: https://doi.org/10.1007/978-3-642-19211-1_5
Publisher Name: Springer, Berlin, Heidelberg
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