Aguado, F., Cabalar, P., Pérez, G. and Vidal, C. 2008. Strongly equivalent temporal logic programs. In Proceedings of the 11th European Conference on Logics in Artificial Intelligence (JELIA 2008), Hölldobler, S., Lutz, C., and Wansing, H., Eds. LNCS, vol. 5293. Springer, Berlin, 8–20.

Arieli, O. and Denecker, M. 2003. Reducing preferential paraconsistent reasoning to classical entailment. Journal of Logic and Computation 13 (4), 557–580.

Baral, C. 2003. Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, Cambridge.

Ben-Eliyahu, R. and Dechter, R. 1994. Propositional semantics for disjunctive logic programs. Annals of Mathematics and Artificial Intelligence 12, 53–87.

Besnard, P., Schaub, T., Tompits, H. and Woltran, S. 2005. Representing paraconsistent reasoning via quantified propositional logic. In Inconsistency Tolerance, Bertossi, L., Hunter, A. and Schaub, T., Eds. LNCS, vol. 3300. Springer, Berlin, 84–118.

Biere, A. 2005. Resolve and expand. In Proceedings of the 7th International Conference on Theory and Applications of Satisfiability Testing (SAT 2004), Hoos, H. H. and Mitchell, D. G., Eds. LNCS, vol. 3542. Springer, Berlin, 59–70.

Brewka, G. 2002. Logic programming with ordered disjunction. In Proceedings of the 18th National Conference on Artificial Intelligence (AAAI 2002). AAAI Press, Menlo Park, CA, 100–105.

Brewka, G., Niemelä, I. and Syrjänen, T. 2004. Logic programs with ordered disjunctions. Computational Intelligence 20 (2), 335–357.

Cabalar, P. and Ferraris, P. 2007. Propositional theories are strongly equivalent to logic programs. Theory and Practice of Logic Programming 7, 6, 745–759.

Cabalar, P., Pearce, D. and Valverde, A. 2005. Reducing propositional theories in equilibrium logic to logic programs. In Proceedings of the 12th Portuguese Conference on Artificial Intelligence (EPIA 2005), Bento, C., Cardoso, A. and Dias, G., Eds. LNCS, vol. 3808. Springer, Berlin, 4–17.

Cabalar, P., Pearce, D. and Valverde, A. 2007. Minimal logic programs. In Proceedings of the 23rd International Conference on Logic Programming (ICLP 2007), Dahl, V. and Niemelä, I., Eds. LNCS, vol. 4670. Springer, Berlin, 104–118.

Cabalar, P. and Pérez Vega, G. 2007. Temporal equilibrium logic: A first approach. In Proceedings of the 11th International Conference on Computer Aided Systems Theory (EUROCAST 2007), Moreno-Díaz, R., Pichler, F. and Quesada-Arencibia, A., Eds. LNCS, vol. 4739. Springer, Berlin, 241–248.

Chen, J. 1993. Minimal knowledge + negation as failure = only knowing (sometimes). In Proceedings of the 2nd International Workshop on Logic Programming and Nonmonotonic Reasoning (LPNMR '93), Pereira, L. M. and Nerode, A., Eds. MIT Press, Cambridge, MA, 132–150.

Chen, Y., Lin, F. and Li, L. 2005. SELP - A system for studying strong equivalence between logic programs. In Proceedings of the 8th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR 2005), Baral, C., Greco, G., Leone, N. and Terracina, G., Eds. LNCS, vol. 3662. Springer, Berlin, 442–446.

Church, A. 1956. Introduction to Mathematical Logic, Volume I. Princeton University Press, Princeton, NJ.

Clark, K. L. 1978. Negation as failure. In Logic and Data Bases, Gallaire, H. and Minker, J., Eds. Plenum Press, New York, NY, 127–138.

de Bruijn, J., Eiter, T., Polleres, A. and Tompits, H. 2007. Embedding non-ground logic programs into autoepistemic logic for knowledge-base combination. In Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI 2007), Veloso, M., Ed. AAAI Press, Menlo Park, CA, 304–309.

de Jongh, D. and Hendriks, L. 2003. Characterizations of strongly equivalent logic programs in intermediate logics Theory and Practice of Logic Programming 3 (3), 259–270.

Delgrande, J., Schaub, T., Tompits, H. and Woltran, S. 2004. On computing solutions to belief change scenarios. Journal of Logic and Computation 14 (6), 801–826.

Dix, J., Gottlob, G. and Marek, V. 1996. Reducing disjunctive to non-disjunctive semantics by shift-operations. Fundamenta Informaticae XXVIII, (1/2), 87–100.

Egly, U., Eiter, T., Tompits, H. and Woltran, S. 2000. Solving advanced reasoning tasks using quantified Boolean formulas. In Proceedings of the 17th National Conference on Artificial Intelligence (AAAI 2000). AAAI Press/MIT Press, Menlo Park, CA, 417–422.

Egly, U., Seidl, M., Tompits, H., Woltran, S. and Zolda, M. 2004. Comparing different prenexing strategies for quantified Boolean formulas. In Proceedings of the 6th International Conference on Theory and Applications of Satisfiability Testing (SAT 2003). Selected Revised Papers, Giunchiglia, E. and Tacchella, A., Eds. LNCS, vol. 2919. Springer, Berlin, 214–228.

Egly, U., Seidl, M. and Woltran, S. 2006. A solver for QBFs in nonprenex form. In Proceedings of the 17th European Conference on Artificial Intelligence (ECAI 2006), Brewka, G., Coradeschi, S., Perini, A., and Traverso, P., Eds. IOS Press, Amsterdam, 477–481.

Eiter, T., Faber, W. and Traxler, P. 2005a. Testing strong equivalence of nonmonotonic datalog programs – implementation and examples. In Proceedings of the 8th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR 2005), Baral, C., Greco, G., Leone, N. and Terracina, G., Eds. LNCS, vol. 3662. Springer, Berlin, 437–441.

Eiter, T. and Fink, M. 2003. Uniform equivalence of logic programs under the stable model semantics. In Proceedings of the 19th International Conference on Logic Programming (ICLP 2003), Palamidessi, C., Ed. LNCS, vol. 2916. Springer, Berlin, 224–238.

Eiter, T., Fink, M., Tompits, H. and Woltran, S. 2004a. On eliminating disjunctions in stable logic programming. In Proceedings of the 9th International Conference on Principles of Knowledge Representation and Reasoning (KR 2004), Dubois, D., Welty, C. A. and Williams, M.-A., Eds. AAAI Press, Menlo Park, CA, 447–458.

Eiter, T., Fink, M., Tompits, H. and Woltran, S. 2004b. Simplifying logic programs under uniform and strong equivalence. In Proceedings of the 7th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR 2004), Lifschitz, V. and Niemelä, I., Eds. LNCS, vol. 2923. Springer, Berlin, 87–99.

Eiter, T., Fink, M. and Woltran, S. 2007. Semantical characterizations and complexity of equivalences in answer set programming. ACM Transactions on Computational Logic 8 (3), 1–53.

Eiter, T. and Gottlob, G. 1995. On the computational cost of disjunctive logic programming: Propositional case. Annals of Mathematics and Artificial Intelligence 15 (3–4), 289–323.

Eiter, T., Gottlob, G. and Mannila, H. 1997. Disjunctive datalog. ACM Transactions on Database Systems 22 (3), 364–418.

Eiter, T., Klotz, V., Tompits, H. and Woltran, S. 2002. Modal nonmonotonic logics revisited: Efficient encodings for the basic reasoning tasks. In Proceedings of the 11th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2002), Egly, U. and Fermüller, C., Eds. LNCS, vol. 2381. Springer, Berlin, 100–114.

Eiter, T., Tompits, H. and Woltran, S. 2005b. On solution correspondences in answer set programming. In Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI 2005), Kaelbling, L. Pack and Saffiotti, A., Eds. Professional Book Center, Denver, CO, 97–102.

Erdem, E. and Lifschitz, V. 2001. Fages' theorem for programs with nested expressions. In Proceedings of the 18th International Conference on Logic Programming (ICLP 2001), Codognet, P., Ed. LNCS, vol. 2237. Springer, Berlin, 242–254.

Erdem, E. and Lifschitz, V. 2003. Tight logic programs. Theory and Practice of Logic Programming 3 (4–5), 499–518.

Faber, W. and Konczak, K. 2005. Strong equivalence for logic programs with preferences. In Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI 2005), Kaelbling, L. Pack and Saffiotti, A., Eds. Professional Book Center, Denver, CO, 430–435.

Faber, W., Tompits, H. and Woltran, S. 2008. Notions of strong equivalence for logic programs with ordered disjunction. In Proceedings of the 11th International Conference on Principles of Knowledge Representation and Reasoning (KR 2008), Brewka, G. and Lang, J., Eds. AAAI Press, Menlo Park, CA, 433–443.

Fages, F. 1994. Consistency of Clark's completion and existence of stable models. Methods of Logic in Computer Science 1, 51–60.

Ferraris, P. 2005. Answer sets for propositional theories. In Proceedings of the 8th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR 2005), Baral, C., Greco, G., Leone, N. and Terracina, G., Eds. LNCS, vol. 3662. Springer, Berlin, 119–131.

Ferraris, P., Lee, J. and Lifschitz, V. 2006. A generalization of the Lin-Zhao theorem. Annals of Mathematics and Artificial Intelligence 47, 1–2, 79–101.

Ferraris, P., Lee, J., and Lifschitz, V. 2007. A new perspective on stable models. In Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI 2007), Veloso, M., Ed. AAAI Press, Menlo Park, CA, 372–379.

Fink, M. 2008. Equivalences in answer-set programming by countermodels in the logic of here-and-there. In Proceedings of the 24th International Conference on Logic Programming (ICLP 2008), de la Banda, M. G. and Pontelli, E., Eds. LNCS, vol. 5366. Springer, Berlin, 99–113.

Garey, M. R. and Johnson, D. S. 1979. Computers and Intractability. W. H. Freeman, New York, NY.

Gebser, M., Lee, J. and Lierler, Y. 2006. Elementary sets for logic programs. In Proceedings of the 21st National Conference on Artificial Intelligence (AAAI 2006). AAAI Press, Menlo Park, CA, 244–249.

Gebser, M., Schaub, T., Tompits, H. and Woltran, S. 2008. Alternative characterizations for program equivalence under answer-set semantics based on unfounded sets. In Proceedings of the 5th International Symposium on Foundations of Information and Knowledge Systems (FoIKS 2008), Hartmann, S. and Kern-Isberner, G., Eds. LNCS, vol. 4932. Springer, Berlin, 24–41.

Gelfond, M. 1987. On stratified autoepistemic theories. In Proceedings of 6th National Conference on Artificial Intelligence (AAAI '87), Forbus, K. and Shrobe, H. E., Eds. AAAI Press/MIT Press, Menlo Park, CA, 207–211.

Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9 (3–4), 365–385.

Gelfond, M., Lifschitz, V., Przymusinska, H. and Schwarz, G. 1994. Autoepistemic logic and introspective circumscription. In Proceedings of the 5th Conference on Theoretical Aspects of Reasoning about Knowledge (TARK '94), Fagin, R., Ed. Morgan Kaufmann, San Mateo, CA, 197–207.

Gelfond, M., Lifschitz, V., Przymusinska, H. and Truszczyński, M. 1991. Disjunctive defaults. In Proceedings of the 2nd Conference on Principles of Knowledge Representation and Reasoning (KR '91), Allen, J., Fikes, R. and Sandewall, B., Eds. Morgan Kaufmann, San Mateo, CA, 230–237.

Gelfond, M., Przymusinska, H. and Przymusinski, T. C. 1989. On the relationship between circumscription and negation as failure. Artificial Intelligence 38 (1), 75–94.

Gelfond, M., Przymusinska, H. and Przymusinski, T. C. 1990. On the relationship between CWA, minimal model, and minimal Herbrand model semantics. International Journal of Intelligent Systems 5, 549–564.

Giunchiglia, E., Narizzano, M. and Tacchella, A. 2003. Backjumping for quantified Boolean logic satisfiability. Artificial Intelligence 145, 99–120.

Gödel, K. 1932. Zum intuitionistischen Aussagenkalkül. *Anzeiger der Akademie der Wissenschaften in Wien*, 65–66.

Gurevich, Y. 1977. Intuitionistic logic with strong negation. Studia Logica 36 (1–2), 49–59.

Heyting, A. 1930. Die formalen Regeln der intuitionistischen Logik. Sitzungsberichte der Preussischen Akademie der Wissenschaften, 42–56. Reprint in *Logik-Texte: Kommentierte Auswahl zur Geschichte der Modernen Logik*, Akademie-Verlag, Berlin, 1986.

Inoue, K. and Sakama, C. 1998. Negation as failure in the head. Journal of Logic Programming 35, 1, 39–78.

Inoue, K. and Sakama, C. 2004. Equivalence of logic programs under updates. In Proceedings of the 9th European Conference on Logics in Artificial Intelligence (JELIA 2004), Alferes, J. J. and Leite, J. A., Eds. LNCS, vol. 3229. Springer, Berlin, 174–186.

Janhunen, T. 2001. On the effect of default negation on the expressiveness of disjunctive rules. In Proceedings of the 6th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR 2001), Eiter, T., Faber, W. and Truszczyński, M., Eds. LNCS, vol. 2173. Springer, Berlin, 93–106.

Janhunen, T. 2004. Representing normal programs with clauses. In Proceedings of the 16th European Conference on Artificial Intelligence (ECAI 2004), de Mántaras, R. L. and Saitta, L., Eds. IOS Press, Amsterdam, 358–362.

Janhunen, T. and Oikarinen, E. 2002. Testing the equivalence of logic programs under stable model semantics. In Proceedings of the 8th European Conference on Logics in Artificial Intelligence (JELIA 2002), Flesca, S., Greco, S., Leone, N. and Ianni, G., Eds. LNCS, vol. 2424. Springer, Berlin, 493–504.

Kowalski, V. 1968. The calculus of the weak “law of excluded middle”. Mathematics of the USSR 8, 648–658.

Lee, J. 2005. A model-theoretic counterpart of loop formulas. In Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI 2005), Kaelbling, L. Pack and Saffiotti, A., Eds. Professional Book Center, Denver, CO, 503–508.

Lee, J. and Lifschitz, V. 2003. Loop formulas for disjunctive logic programs. In Proceedings of the 19th International Conference on Logic Programming (ICLP 2003), Palamidessi, C., Ed. LNCS, vol. 2916. Springer, Berlin, 451–465.

Lee, J., Lifschitz, V. and Palla, R. 2008. A reductive semantics for counting and choice in answer set programming. In Proceedings of the 23rd National Conference on Artificial Intelligence (AAAI 2008), Fox, D. and Gomes, C. P., Eds. AAAI Press, Menlo Park, CA, 472–479.

Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S. and Scarcello, F. 2006. The DLV system for knowledge representation and reasoning. ACM Transactions on Computational Logic 7 (3), 499–562.

Leśniewski, S. 1929. Grundzüge eines neuen Systems der Grundlagen der Mathematik. Fundamenta Mathematica 14, 1–81.

Letz, R. 2002. Lemma and model caching in decision procedures for quantified Boolean formulas. In Proceedings of the 11th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2002), Egly, U. and Fermüller, C., Eds. LNCS, vol. 2381. Springer, Berlin, 160–175.

Lierler, Y. 2005. Disjunctive answer set programming via satisfiability. In Proceedings of the 8th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR 2005), Baral, C., Greco, G., Leone, N. and Terracina, G., Eds. LNCS, vol. 3662. Springer, Berlin, 447–451.

Lifschitz, V. 1989. Between circumscription and autoepistemic logic. In Proceedings of the 1st International Conference on Principles of Knowledge Representation and Reasoning (KR '89), Brachman, R., Levesque, H. and Reiter, R., Eds. Morgan Kaufmann, San Mateo, CA, 235–244.

Lifschitz, V. 1994. Circumscription. In Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3: Nonmonotonic Reasoning and Uncertain Reasoning, Gabbay, D. M., Hogger, C. J. and Robinson, J. A., Eds. Clarendon Press, Oxford, 297–352.

Lifschitz, V., Pearce, D. and Valverde, A. 2001. Strongly equivalent logic programs. ACM Transactions on Computational Logic 2 (4), 526–541.

Lifschitz, V., Pearce, D. and Valverde, A. 2007. A characterization of strong equivalence for logic programs with variables. In Proceedings of the 9th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR 2007), Baral, C., Brewka, G. and Schlipf, J. S., Eds. LNCS, vol. 4483. Springer, Berlin, 188–200.

Lifschitz, V. and Schwarz, G. 1993. Extended logic programs as autoepistemic theories. In Proceedings of the 2nd International Workshop on Logic Programming and Nonmonotonic Reasoning (LPNMR '93), Pereira, L. M. and Nerode, A., Eds. MIT Press, Cambridge, MA, 101–114.

Lifschitz, V., Tang, L. and Turner, H. 1999. Nested expressions in logic programs. Annals of Mathematics and Artificial Intelligence 25 (3–4), 369–389.

Lifschitz, V. and Turner, H. 1994. Splitting a logic program. In Proceedings of the 11th International Conference on Logic Programming (ICLP '94). MIT Press, Cambridge, MA, 23–38.

Lin, F. 1991. *A Study of Nonmonotonic Reasoning*. Ph.D. thesis, Stanford University, California.

Lin, F. 2002. Reducing strong equivalence of logic programs to entailment in classical propositional logic. In Proceedings of the 8th International Conference on Principles of Knowledge Representation and Reasoning (KR 2002), Fensel, D., Giunchiglia, F., McGuinness, D., and Williams, M.-A., Eds. Morgan Kaufmann, San Mateo, CA, 170–176.

Lin, F. and Zhao, Y. 2002. ASSAT: Computing answer sets of a logic program by SAT solvers. In Proceedings of the 18th National Conference on Artificial Intelligence (AAAI 2002). AAAI Press/MIT Press, Menlo Park, CA, 112–117.

Linke, T., Tompits, H. and Woltran, S. 2004. On acyclic and head-cycle free nested logic programs. In Proceedings of the 20th International Conference on Logic Programming (ICLP 2004), Demoen, B. and Lifschitz, V., Eds. LNCS, vol. 3132. Springer, Berlin, 225–239.

Liu, L. and Truszczyński, M. 2005. Properties of programs with monotone and convex constraints. In Proceedings of the 20th National Conference on Artificial Intelligence (AAAI 2005), Veloso, M. and Kambhampati, S., Eds. AAAI Press, Menlo Park, CA, 701–706.

Łukasiewicz, J. and Tarski, A. 1930. Untersuchungen über den Aussagenkalkül. Comptes Rendus Séances Société des Sciences et Lettres Varsovie 23, Cl. III, 30–50.

Maher, M. J. 1988. Equivalence of logic programs. In Foundations of Deductive Databases and Logic Programming, Minker, J., Ed. Morgan Kaufmann, San Mateo, CA, 627–658.

Marek, V. W. and Truszczyński, M. 1993. Reflexive autoepistemic logic and logic programming. In Proceedings of the 2nd International Workshop on Logic Programming and Nonmonotonic Reasoning (LPNMR '93), Pereira, L. M. and Nerode, A., Eds. MIT Press, Cambridge, MA, 115–131.

McCarthy, J. 1980. Circumscription – a form of nonmonotonic reasoning. Artificial Intelligence 13, 27–39.

McCluskey, E. J. 1956. Minimization of boolean functions. Bell System Technical Journal 35, 1417–1444.

Meyer, A. R. and Stockmeyer, L. J. 1973. Word problems requiring exponential time. In ACM Symposium on Theory of Computing (STOC '73). ACM Press, New York, NY, 1–9.

Moore, R. C. 1985. Semantical considerations on nonmonotonic logic. Artificial Intelligence 25, 75–94.

Mundici, D. 1987. Satisfiability in many-valued sentential logic is NP-complete. Theoretical Computer Science 52 (1–2), 145–153.

Nelson, D. 1949. Constructible falsity. Journal of Symbolic Logic 14 (2), 16–26.

Oetsch, J., Seidl, M., Tompits, H. and Woltran, S. 2006a. cc⊤: A correspondence-checking tool for logic programs under the answer-set semantics. In Proceedings of the 10th European Conference on Logics in Artificial Intelligence (JELIA 2006), Fisher, M., van der Hoek, W., Konev, B. and Lisitsa, A., Eds. LNCS, vol. 4160. Springer, Berlin, 502–505.

Oetsch, J., Seidl, M., Tompits, H. and Woltran, S. 2006b. cc⊤: A tool for checking advanced correspondence problems in answer-set programming. In Proceedings of the 15th International Conference on Computing (CIC 2006), Gelbukh, A. and Guerra, S. S., Eds. IEEE Computer Society Press, Los Alamitos, CA, 3–10.

Oetsch, J., Seidl, M., Tompits, H. and Woltran, S. 2007a. An extension of the system cc⊤ for testing relativised uniform equivalence under answer-set projection. In Proceedings of the 16th International Conference on Computing (CIC 2007) Gelbukh, A. and Guerra, S. S., Eds. Instituto Politécnico Nacional, Mexico City.

Oetsch, J. and Tompits, H. 2008. Program correspondence under the answer-set semantics: The non-ground case. In Proceedings of the 24th International Conference on Logic Programming (ICLP 2008), de la Banda, M. G. and Pontelli, E., Eds. LNCS, vol. 5366. Springer, Berlin, 591–605.

Oetsch, J., Tompits, H. and Woltran, S. 2007b. Facts do not cease to exist because they are ignored: Relativised uniform equivalence with answer-set projection. In Proceedings of the 22nd National Conference on Artificial Intelligence (AAAI 2007). AAAI Press, Menlo Park, CA, 458–464.

Oikarinen, E. and Janhunen, T. 2004. Verifying the equivalence of logic programs in the disjunctive case. In Proceedings of the 7th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR 2004), Lifschitz, V. and Niemelä, I., Eds. LNCS, vol. 2923. Springer, Berlin, 180–193.

Oikarinen, E. and Janhunen, T. 2006. Modular equivalence for normal logic programs. In Proceedings of the 11th International Workshop on Nonmonotonic Reasoning (NMR 2006), Dix, J. and Hunter, A., Eds. University of Clausthal, Department of Informatics, Technical Report, IfI-06-04, 10–18.

Osorio, M., Navarro, J. A. and Arrazola, J. 2005. Safe beliefs for propositional theories. Annals of Pure and Applied Logic 134 (1), 63–82.

Papadimitriou, C. 1994. Computational Complexity. Addison-Wesley, Reading, MA.

Pearce, D. 1997. A new logical characterisation of stable models and answer sets. In Non-Monotonic Extensions of Logic Programming, Dix, J., Pereira, L. and Przymusinski, T., Eds. LNCS, vol. 1216. Springer, Berlin, 57–70.

Pearce, D. 1999. From here to there: Stable negation in logic programming. In What is Negation?, Gabbay, D. and Wansing, H., Eds. Kluwer, Dordrecht, 161–181.

Pearce, D. 2004. Simplifying logic programs under answer set semantics. In Proceedings of the 20th International Conference on Logic Programming (ICLP 2004), Demoen, B. and Lifschitz, V., Eds. LNCS, vol. 3132. Springer, Berlin, 210–224.

Pearce, D. 2006. Equilibrium logic. Annals of Mathematics and Artificial Intelligence 47, 3–41.

Pearce, D., de Guzmán, I. and Valverde, A. 2000a. Computing equilibrium models using signed formulas. In Proceedings of the 1st International Conference on Computational Logic (CL 2000), Lloyd, J., 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, Berlin, 688–702.

Pearce, D., de Guzmán, I. and Valverde, A. 2000b. A tableau calculus for equilibrium entailment. In Proceedings of the 9th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2000), Dyckhoff, R., Ed. LNCS, vol. 1847. Springer, Berlin, 352–367.

Pearce, D., Sarsakov, V., Schaub, T., Tompits, H. and Woltran, S. 2002. A polynomial translation of logic programs with nested expressions into disjunctive logic programs: Preliminary report. In Proceedings of the 19th International Conference on Logic Programming (ICLP 2002), Stuckey, P., Ed. LNCS, vol. 2401. Springer, Berlin, 405–420.

Pearce, D., Tompits, H. and Woltran, S. 2001. Encodings for equilibrium logic and logic programs with nested expressions. In Proceedings of the 10th Portuguese Conference on Artificial Intelligence (EPIA 2001), Brazdil, P. and Jorge, A. Eds. LNCS, vol. 2258. Springer, Berlin, 306–320.

Pearce, D. and Valverde, A. 2004a. Synonymous theories in answer set programming and equilibrium logic. In Proceedings 16th European Conference on Artificial Intelligence (ECAI 2004). de Mántaras, R. L. and Saitta, L., Eds. IOS Press, Amsterdam, 388–392.

Pearce, D. and Valverde, A. 2004b. Uniform equivalence for equilibrium logic and logic programs. In Proceedings of the 7th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR 2004), Lifschitz, V. and Niemelä, I., Eds. LNCS, vol. 2923. Springer, Berlin, 194–206.

Pearce, D. and Valverde, A. 2005. A first order nonmonotonic extension of constructive logic. Studia Logica 80 (2–3), 321–346.

Pearce, D. and Valverde, A. 2008. Quantified equilibrium logic and foundations for answer set programs. In Proceedings of the 24th International Conference on Logic Programming (ICLP 2008), de la Banda, M. G. and Pontelli, E., Eds. LNCS, vol. 5366. Springer, Berlin, 546–560.

Pearce, D. and Wagner, G. 1991. Logic programming with strong negation. In Workshop on Extensions of Logic Programming, Proceedings, Schroeder-Heiste, P., Ed. LNAI, vol. 475. Springer, Berlin, 311–326.

Perlis, D. 1988. Autocircumscription. Artificial Intelligence 36, 223–236.

Przymusinski, T. C. 1991. Stable semantics for disjunctive programs. New Generation Computing 9 (3–4), 401–424.

Pührer, J., Tompits, H. and Woltran, S. 2008. Elimination of disjunction and negation in answer-set programs under hyperequivalence. In Proceedings of the 24th International Conference on Logic Programming (ICLP 2008), de la Banda, M. G. and Pontelli, E., Eds. LNCS, vol. 5366. Springer, Berlin, 561–575.

Quine, W. V. O. 1952. The problem of simplifying truth functions. American Mathematical Monthly 59, 521–531.

Rintanen, J. 1999. Constructing conditional plans by a theorem prover. Journal of Artificial Intelligence Research 10, 323–352.

Russell, B. 1906. The theory of implication. American Journal of Mathematics 28 (2), 159–202.

Sagiv, Y. 1988. Optimising datalog programs. In Foundations of Deductive Databases and Logic Programming, Minker, J., Ed. Morgan Kaufmann, San Mateo, CA, 659–698.

Sarsakov, V., Schaub, T., Tompits, H. and Woltran, S. 2004. nlp: A compiler for nested logic programming. In Proceedings of the 7th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR 2004), Lifschitz, V. and Niemelä, I., Eds. LNCS, vol. 2923. Springer, Berlin, 361–364.

Simons, P., Niemelä, I. and Soininen, T. 2002. Extending and implementing the stable model semantics. Artificial Intelligence 138, 181–234.

Srzednicki, J. and Stachniak, Z., Eds. 1998. Lesniewski's Systems Protothetic. Kluwer, Dordrecht.

Stockmeyer, L. J. 1976. The polynomial-time hierarchy. Theoretical Computer Science 3 (1), 1–22.

Tompits, H. 2003. Expressing default abduction problems as quantified Boolean formulas. AI Communications 16 (2), 89–105.

Tompits, H. and Woltran, S. 2005. Towards implementations for advanced equivalence checking in answer-set programming. In Proceedings of the 21st International Conference on Logic Programming (ICLP 2005), Gabbrielli, M. and Gupta, G., Eds. LNCS, vol. 3668. Springer, Berlin, 189–203.

Truszczyński, M. and Woltran, S. 2008. Hyperequivalence of logic programs with respect to supported models. In Proceedings of the 23rd National Conference on Artificial Intelligence (AAAI 2008), Fox, D. and Gomes, C. P., Eds. AAAI Press, Menlo Park, CA, 560–565.

Turner, H. 2001. Strong equivalence for logic programs and default theories (made easy). In Proceedings of the 6th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR 2001), Eiter, T., Faber, W. and Truszczyński, M., Eds. LNCS, vol. 2173. Springer, Berlin, 81–92.

Turner, H. 2003. Strong equivalence made easy: Nested expressions and weight constraints. Theory and Practice of Logic Programming 3 (4–5), 609–622.

Valverde, A. 2004. tabeql: A tableau based suite for equilibrium logic. In Proceedings of the 9th European Conference on Logics in Artificial Intelligence (JELIA 2004), Alferes, J. J. and Leite, J. A., Eds. LNCS, vol. 3229. Springer, Berlin, 734–737.

van Dalen, D. 1986. Intuitionistic logic. In Handbook of Philosophical Logic, Volume III: Alternatives to Classical Logic, Gabbay, D. and Guenthner, F., Eds. Synthese Library, vol. 166. D. Reidel Publishing Co., Dordrecht, Chapter III.4, 225–339.

van Gelder, A., Ross, K. and Schlipf, J. 1991. The well-founded semantics for general logic programs. Journal of the ACM 38 (3), 620–650.

Vorob'ev, N. 1952. A constructive propositional calculus with strong negation (in Russian). Doklady Akademii Nauk SSR 85, 689–692.

Whitehead, A. N. and Russell, B. 1910–1913. Principia Mathematica. vol. 1–3. Cambridge University Press, Cambridge.

Woltran, S. 2003. *Quantified Boolean Formulas – From Theory to Practice*. Ph.D. thesis, Technische Universität Wien, Institut für Informationssysteme.

Woltran, S. 2004. Characterizations for relativized notions of equivalence in answer set programming. In Proceedings of the 9th European Conference on Logics in Artificial Intelligence (JELIA 2004), Alferes, J. J. and Leite, J. A., Eds. LNCS, vol. 3229. Springer, Berlin, 161–173.

Woltran, S. 2008. A common view on strong, uniform, and other notions of equivalence in answer-set programming. Theory and Practice of Logic Programming 8 (2), 217–234.

Wrathall, C. 1976. Complete sets and the polynomial-time hierarchy. Theoretical Computer Science 3 (1), 23–33.

You, J.-H., Yuan, L.-Y. and Mingyi, Z. 2003. On the equivalence between answer sets and models of completion for nested logic programs. In Proceedings of the 18th International Joint Conference on Artificial Intelligence (IJCAI 2003), Gottlob, G. and Walsh, T., Eds. Morgan Kaufmann, San Mateo, CA, 859–865.

Yuan, L.-Y. 1994. Autoepistemic logic of first order and its expressive power. Journal of Automated Reasoning 13 (1), 69–82.