Abstract
We define a denotational semantics for Light Affine Logic (LAL) which has the property that denotations of functions are polynomial time computable by construction of the model. This gives a new proof of polytime-soundness of LAL which is considerably simpler than the standard proof based on proof nets and also is entirely semantical in nature. The model construction uses a new instance of a resource monoid; a general method for interpreting variations of linear logic with complexity restrictions introduced earlier by the authors.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Amadio, R.M.: Max-plus quasi-interpretations. In: Proceedings of the 7th International Conference on Typed Lambda Calculi and Applications, pp. 31–45 (2003)
Asperti, A., Roversi, L.: Intuitionistic light affine logic. ACM Transactions on Computational Logic 3(1), 137–175 (2002)
Bellantoni, S., Niggl, K.H., Schwichtenberg, H.: Higher type recursion, ramification and polynomial time. Annals of Pure and Applied Logic 104, 17–30 (2000)
Cook, S., Urquhart, A.: Functional interpretations of feasible constructive arithmetic. Annals of Pure and Applied Logic 63(2), 103–200 (1993)
Coppola, P., Martini, S.: Typing lambda terms in elementary logic with linear constraints. In: Proceedings of the 6th International Conference on Typed Lambda-Calculus and Applications, pp. 76–90 (2001)
Crossley, J., Mathai, G., Seely, R.: A logical calculus for polynomial-time realizability. Journal of Methods of Logic in Computer Science 3, 279–298 (1994)
Lago, U.D., Hofmann, M.: Quantitative models and implicit complexity. In: Proc. Foundations of Software Technology and Theoretical Computer Science, pp. 189–200 (2005)
Girard, J.-Y.: Light linear logic. Information and Computation 143(2), 175–204 (1998)
Hofmann, M.: Linear types and non-size-increasing polynomial time computation. In: Proceedings of the 14th IEEE Syposium on Logic in Computer Science, pp. 464–473 (1999)
Hofmann, M.: Safe recursion with higher types and BCK-algebra. Annals of Pure and Applied Logic 104, 113–166 (2000)
Hofmann, M., Scott, P.: Realizability models for BLL-like languages. Theoretical Computer Science 318(1-2), 121–137 (2004)
Kreisel, G.: Interpretation of analysis by means of constructive functions of finite types. In: Heyting, A. (ed.) Constructiviey in Mathematics, pp. 101–128. North-Holland, Amsterdam (1959)
Lafont, Y.: Soft linear logic and polynomial time. Theoretical Computer Science 318, 163–180 (2004)
Lago, U.D., Martini, S.: Phase semantics and decidability of elementary affine logic. Theor. Comput. Sci. 318(3), 409–433 (2004)
Murawski, A.S., Luke Ong, C.-H.: Discreet games, light affine logic and ptime computation. In: Clote, P.G., Schwichtenberg, H. (eds.) CSL 2000. LNCS, vol. 1862, pp. 427–441. Springer, Heidelberg (2000)
Roversi, L.: A p-time completeness proof for light logics. In: Flum, J., Rodríguez-Artalejo, M. (eds.) CSL 1999. LNCS, vol. 1683, pp. 469–483. Springer, Heidelberg (1999)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lago, U.D., Hofmann, M. (2008). A Semantic Proof of Polytime Soundness of Light Affine Logic. In: Hirsch, E.A., Razborov, A.A., Semenov, A., Slissenko, A. (eds) Computer Science – Theory and Applications. CSR 2008. Lecture Notes in Computer Science, vol 5010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79709-8_16
Download citation
DOI: https://doi.org/10.1007/978-3-540-79709-8_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79708-1
Online ISBN: 978-3-540-79709-8
eBook Packages: Computer ScienceComputer Science (R0)