Abstract
Girard [1] introduced Ludics as an interactive theory aiming at overcoming the distinction between syntax and semantics in logic.
In this paper, we investigate how ludics could serve as a foundation for logic programming, providing a mechanism for interactive proof search, that is proof search by interaction (or proof search by cut-elimination).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Girard, J.Y.: Locus solum. Mathematical Structures in Computer Science 11(3) (2001)
Howard, W.A.: The formulae-as-type notion of construction, 1969. In: Seldin, Hindley (eds.) To H. B. Curry: Essays in Combinatory Logic, Lambda Calculus, and Formalism. Academic Press, New York (1980)
Miller, D., Nadathur, G., Pfenning, F., Scedrov, A.: Uniform proofs as a foundation for logic programming. Annals of Pure and Applied Logic 51 (1991)
Andreoli, J.M.: Logic programming with focusing proofs in linear logic. Journal of Logic and Computation 2(3) (1992)
Girard, J.Y.: Linear logic. Theoretical Computer Science 50 (1987)
Naish, L.: Negation and Control in Prolog. LNCS, vol. 238. Springer, Heidelberg (1986)
Naish, L.: Pruning in logic programming. Technical Report 95/16, Department of Computer Science, University of Melbourne, Australia (1995)
Miller, D.: Sequent calculus and the specification of computation. In: Berger, U., Schwichtenberg, H. (eds.) Computational Logic. Nato ASI Series, vol. 165. Springer, Heidelberg (1999)
Griffin, T.: A formulae-as-types notion of control. In: POPL 1990 (1990)
Parigot, M.: λμ-calculus: an algorithmic interpretation of classical natural deduction. In: Voronkov, A. (ed.) LPAR 1992. LNCS, vol. 624. Springer, Heidelberg (1992)
Faggian, C., Hyland, M.: Designs, disputes and strategies. In: Bradfield, J.C. (ed.) CSL 2002 and EACSL 2002. LNCS, vol. 2471, p. 442. Springer, Heidelberg (2002)
Abramsky, S., Jagadeesan, R.: Games and full completeness for multiplicative linear logic. Journal of Symbolic Logic 59(2) (1994)
Hyland, J.M.E., Ong, C.H.L.: On full abstraction for PCF. Information and Computation 163 (2000)
van Emden, M.H.: Quantitative deduction and its fixpoint theory. Journal of Logic Programming 3(1) (1986)
Cosmo, R.D., Loddo, J.V., Nicolet, S.: A game semantics foundation for logic programming. In: PLILP/ALP (1998)
Loddo, J.V., Cosmo, R.D.: Playing logic programs with the alpha-beta algorithm. In: Parigot, M., Voronkov, A. (eds.) LPAR 2000. LNCS, vol. 1955. Springer, Heidelberg (2000)
Loddo, J.V.: Généralisation des Jeux Combinatoires et Applications aux Langages Logiques. Ph.D thesis, Université Paris VII (2002)
Pym, D., Ritter, E.: Reductive Logic and Proof-search: proof theory, semantics, and control, vol. 45. Oxford Logic Guides, Oxford (2004)
Pym, D., Ritter, E.: A games semantics for reductive logic and proof-search. In: Ghica, D., McCusker, G. (eds.) GaLoP 2005 (2005)
Miller, D., Saurin, A.: A game semantics for proof search: Preliminary results. In: Proceedings of MFPS 2005. ENTCS, vol. 155 (2006)
Delande, O., Miller, D.: A neutral approach to proof and refutation in MALL. In: Pfenning, F. (ed.) LICS 2008. IEEE Computer Society Press, Los Alamitos (2008)
Galanaki, C., Rondogiannis, P., Wadge, W.W.: An infinite-game semantics for well-founded negation in logic programming. Annals of Pure and Applied Logic 151(2) (2008)
Laurent, O.: Étude de la polarisation en logique. Thèse de doctorat, Université Aix-Marseille II (2002)
Faggian, C.: Travelling on designs. In: Bradfield, J.C. (ed.) CSL 2002 and EACSL 2002. LNCS, vol. 2471. Springer, Heidelberg (2002)
Fleury, M.R., Quatrini, M.: First order in ludics. Mathematical Structures in Computer Science 14(2) (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Saurin, A. (2008). Towards Ludics Programming: Interactive Proof Search. In: Garcia de la Banda, M., Pontelli, E. (eds) Logic Programming. ICLP 2008. Lecture Notes in Computer Science, vol 5366. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89982-2_27
Download citation
DOI: https://doi.org/10.1007/978-3-540-89982-2_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-89981-5
Online ISBN: 978-3-540-89982-2
eBook Packages: Computer ScienceComputer Science (R0)