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First-order Answer Set Programming as Constructive Proof Search

Published online by Cambridge University Press:  10 August 2018

ALEKSY SCHUBERT  and
PAWEŁ URZYCZYN
ALEKSY SCHUBERT
Affiliation:
University of Warsaw, Poland (e-mail: alx@mimuw.edu.pl, urzy@mimuw.edu.pl)
PAWEŁ URZYCZYN
Affiliation:
University of Warsaw, Poland (e-mail: alx@mimuw.edu.pl, urzy@mimuw.edu.pl)
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Abstract

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We propose an interpretation of the first-order answer set programming (FOASP) in terms of intuitionistic proof theory. It is obtained by two polynomial translations between FOASP and the bounded-arity fragment of the Σ1 level of the Mints hierarchy in first-order intuitionistic logic. It follows that Σ1 formulas using predicates of fixed arity (in particular unary) is of the same strength as FOASP. Our construction reveals a close similarity between constructive provability and stable entailment, or equivalently, between the construction of an answer set and an intuitionistic refutation. This paper is under consideration for publication in Theory and Practice of Logic Programming

Keywords

Answer set programmingintuitionistic logicproof termslambda calculus
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 18 , Special Issue 3-4: 34th International Conference on Logic Programming , July 2018 , pp. 673 - 690
Copyright
Copyright © Cambridge University Press 2018 

References

Brewka, G., Eiter, T. and Truszczyński, M. 2011. Answer set programming at a glance. Commun. ACM 54, 12 (Dec.), 92–103.Google Scholar
Dantsin, E., Eiter, T., Gottlob, G., and Voronkov, A. 2001. Complexity and expressive power of logic programming. ACM Comput. Surv. 33, 3, 374–425.Google Scholar
Fu, P. and Komendantskaya, E. 2017. Operational semantics of resolution and productivity in Horn clause logic. Formal Asp. Comput. 29, 3, 453–474.Google Scholar
Kolaitis, P. G. and Papadimitriou, C. H. 1988. Why not negation by fixpoint? In Proceedings of the Seventh ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems. PODS'88. ACM, New York, NY, USA, 231–239.Google Scholar
Lifschitz, V. 2008. What is answer set programming? In Proceedings of the 23rd National Conference on Artificial Intelligence - Volume 3. AAAI'08. AAAI Press, 1594–1597.Google Scholar
Marek, W. and Truszczyński, M. 1991. Autoepistemic logic. J. ACM 38, 3 (July), 587–618.Google Scholar
Osorio, M., Navarro, J. A., and Arrazola, J. 2004. Applications of intuitionistic logic in answer set programming. Theory Pract. Log. Program. 4, 3 (May), 325–354.Google Scholar
Pearce, D. 1999. Stable inference as intuitionistic validity. The Journal of Logic Programming 38, 1, 79–91.Google Scholar
Pearce, D. 2006. Equilibrium logic. Annals of Mathematics and Artificial Intelligence 47, 1–2, 3–41.Google Scholar
Schubert, A. and Urzyczyn, P. 2018. Answer set programming in intuitionistic logic. Indagationes Mathematicae 29, 1, 276–292. L.E.J. Brouwer, fifty years later.Google Scholar
Schubert, A., Urzyczyn, P. and Walukiewicz-Chrząszcz, D. 2015. Restricted positive quantification is not elementary. In Proc. TYPES 2014, Herbelin, H., Letouzey, P., and Sozeau, M., Eds. LIPIcs, vol. 39. Schloss Dagstuhl–Leibniz-Zentrum für Informatik, 251–273.Google Scholar
Schubert, A., Urzyczyn, P., and Zdanowski, K. 2016. On the Mints hierarchy in first-order intuitionistic logic. Logical Methods in Computer Science 12, 4.Google Scholar