Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-08T00:44:50.890Z Has data issue: false hasContentIssue false
  • English
  • Français

Semantics of templates in a compositional framework for building logics

Published online by Cambridge University Press:  03 September 2015

INGMAR DASSEVILLE ,
MATTHIAS VAN DER HALLEN ,
GERDA JANSSENS  and
MARC DENECKER
INGMAR DASSEVILLE
Affiliation:
KU Leuven (e-mail: [email protected])
MATTHIAS VAN DER HALLEN
Affiliation:
KU Leuven (e-mail: [email protected])
GERDA JANSSENS
Affiliation:
KU Leuven (e-mail: [email protected])
MARC DENECKER
Affiliation:
KU Leuven (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

There is a growing need for abstractions in logic specification languages such as FO(·) and ASP. One technique to achieve these abstractions are templates (sometimes called macros). While the semantics of templates are virtually always described through a syntactical rewriting scheme, we present an alternative view on templates as second order definitions. To extend the existing definition construct of FO(·) to second order, we introduce a powerful compositional framework for defining logics by modular integration of logic constructs specified as pairs of one syntactical and one semantical inductive rule. We use the framework to build a logic of nested second order definitions suitable to express templates. We show that under suitable restrictions, the view of templates as macros is semantically correct and that adding them does not extend the descriptive complexity of the base logic, which is in line with results of existing approaches.

Keywords

compositionalitymodularitytemplatesmacrossemanticssecond order logic
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 15 , Special Issue 4-5: 31st International Conference on Logic Programming , July 2015 , pp. 681 - 695
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramson, H. and Rogers, H. 1989. Meta-programming in Logic Programming. MIT Press.Google Scholar
Baral, C., Dzifcak, J., and Takahashi, H. 2006. Macros, macro calls and use of ensembles in modular answer set programming. In Logic Programming, 22nd International Conference, ICLP 2006, Seattle, WA, USA, August 17-20, 2006, Proceedings, Etalle, S. and Truszczynski, M., Eds. Lecture Notes in Computer Science, vol. 4079. Springer, 376–390.Google Scholar
Chen, W., Kifer, M., and Warren, D. S. 1993. Hilog: A foundation for higher-order logic programming. The Journal of Logic Programming 15, 3, 187–230.Google Scholar
Dao-Tran, M., Eiter, T., Fink, M., and Krennwallner, T. 2009. Modular nonmonotonic logic programming revisited. In Logic Programming, 25th International Conference, ICLP 2009, Pasadena, CA, USA, July 14-17, 2009. Proceedings, Hill, P. M. and Warren, D. S., Eds. Lecture Notes in Computer Science, vol. 5649. Springer, 145–159.Google Scholar
Denecker, M. 2000. Extending classical logic with inductive definitions. In Computational Logic - CL 2000, First International Conference, London, UK, 24-28 July, 2000, Proceedings, Lloyd, J. W., Dahl, V., Furbach, U., Kerber, M., Lau, K.-K., Palamidessi, C., Pereira, L. M., Sagiv, Y., and Stuckey, P. J., Eds. LNCS, vol. 1861. Springer, 703–717.Google Scholar
Denecker, M., Lierler, Y., Truszczyński, M., and Vennekens, J. 2012. A Tarskian informal semantics for answer set programming. In International Conference on Logic Programming (Technical Communications), Dovier, A. and Costa, V. S., Eds. LIPIcs, vol. 17. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 277–289.Google Scholar
Denecker, M. and Ternovska, E. 2008. A logic of nonmonotone inductive definitions. ACM Trans. Comput. Log. 9, 2 (Apr.), 14:1–14:52.Google Scholar
Denecker, M. and Vennekens, J. 2014. The well-founded semantics is the principle of inductive definition, revisited. In Principles of Knowledge Representation and Reasoning: Proceedings of the Fourteenth International Conference, KR 2014, Vienna, Austria, July 20-24, 2014, Baral, C., De Giacomo, G., and Eiter, T., Eds. AAAI Press, 22–31.Google Scholar
Eiter, T., Krennwallner, T., and Redl, C. 2011. Hex-programs with nested program calls. In Applications of Declarative Programming and Knowledge Management - 19th International Conference, INAP 2011, and 25th Workshop on Logic Programming, WLP 2011, Vienna, Austria, September 28-30, 2011, Revised Selected Papers, Tompits, H., Abreu, S., Oetsch, J., Pührer, J., Seipel, D., Umeda, M., and Wolf, A., Eds. Lecture Notes in Computer Science, vol. 7773. Springer, 269–278.Google Scholar
Ianni, G., Ielpa, G., Pietramala, A., Santoro, M. C., and Calimeri, F. 2004. Enhancing answer set programming with templates. In 10th International Workshop on Non-Monotonic Reasoning (NMR 2004), Whistler, Canada, June 6-8, 2004, Proceedings, Delgrande, J. P. and Schaub, T., Eds. 233–239.Google Scholar
IDP 2013. The IDP system. http://dtai.cs.kuleuven.be/krr/software.Google Scholar
Kleene, S. C. 1952. Introduction to Metamathematics. Van Nostrand.Google Scholar
Lifschitz, V. 1999. Answer set planning. In 16th International Conference on Logic Programming, ICLP 1999, Las Cruces, New Mexico, USA, November 29 - December 4, 1999, Proceedings, De Schreye, D., Ed. MIT Press, 23–37.Google Scholar
Musser, D. R., Derge, G. J., and Saini, A. 2009. STL tutorial and reference guide: C++ programming with the standard template library. Addison-Wesley Professional.Google Scholar
Pelov, N., Denecker, M., and Bruynooghe, M. 2007. Well-founded and stable semantics of logic programs with aggregates. Theory Pract. Log. Program. 7, 3, 301–353.CrossRefGoogle Scholar
Shaw, M. 1984. Abstraction techniques in modern programming languages. IEEE Software 1, 4, 10–26.CrossRefGoogle Scholar
Tasharrofi, S. and Ternovska, E. 2011. A semantic account for modularity in multi-language modelling of search problems. In Frontiers of Combining Systems, 8th International Symposium, FroCoS 2011, Saarbrücken, Germany, October 5-7, 2011. Proceedings, Tinelli, C. and Sofronie-Stokkermans, V., Eds. Lecture Notes in Computer Science, vol. 6989. Springer, 259–274.Google Scholar
van Fraassen, B. 1966. Singular terms, truth-value gaps and free logic. Journal of Philosophy 63, 17, 481–495.Google Scholar