Default Negation as Explicit Negation plus Update
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27.05.2021
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Abstract
We argue that under the stable model semantics default negation can be read as explicit negation with update. We show that dynamic logic programming which is based on default negation, even in the heads, can be interpreted in a variant of updates with explicit negation only. As corollaries, we get an easy description of default negation in generalized and normal logic programming where initially negated literals are updated. These results are discussed with respect to the understanding of negation in logic.
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How to Cite
Kahle R. Default Negation as Explicit Negation plus Update // Logicheskie Issledovaniya / Logical Investigations. 2021. VOL. 27. № 1. C. 64-81.
Section
Papers
References
Alferes et al., 2000 – Alferes, J.J., Leite, J.A., Pereira, L.M., Przymusinska, H. and Przymusinski, T.C. “Dynamic Updates of Non-Monotonic Knowledge Bases”, The Journal of Logic Programming, 2000, Vol. 45, No. 1–2, pp. 43–70.
Banti et al., 2004 – Banti, F., Alferes, J.J. and Brogi, A. “Well Founded Semantics for Logic Program Updates”, in: Advances in Artificial Intelligence – IBERAMIA 2004, Volume 3315 of Lecture Notes in Computer Science, ed. by Chr. Lema1tre, C.A. Reyes, and J.A. Gonz´alez. Springer, 2004, pp. 397–407.
Bidoit and Froidevaux, 1991 – Bidoit, N., and Froidevaux, C. “General logic databases and programs: Default logic semantics and stratification”, Information and Computation, 1991, Vol. 91, No. 1, pp. 15–54.
Buccafurri et al., 1999 – Buccafurri, F., Faber, W. and Leone, N. “Disjunctive Logic Programs with Inheritance”, in: Proceedings of the 1999 International Conference on Logic Programming (ICLP-99), ed. by D. De Schreye. Cambridge: MIT Press, 1999, pp. 79–93.
Clark, 1978 – Clark, K.L. “Negation as failure”, in: Logic and Data Bases, ed. by H. Gallaire and J. Minker. Plenum, 1978, pp. 293–322.
Dam´asio and Pereira, 1996 – Dam´asio, C.V., and Pereira, L.M. “Default Negation in the heads: Why not?”, in: Extensions of Logic Programming, ELP’96, ed. by R. Dyckhoff, H. Herre, and P. Schroeder-Heister, Volume 1050 of Lecture Notes in Artificial Intelligence. Springer, 1996, pp. 103–117.
Eiter et al., 2002 – Eiter, Th., Fink, M., Sabbatini, G. and Tompits, H. “On properties of update sequences based on causal rejection”, Theory and Practice of Logic Programming, 2002, Vol. 2, No. 6, pp. 711–767.
Eshghi and Kowalski, 1989 – Eshghi, K., and Kowalski, R.A. “Abduction compared with negation as failure”, in: Proc. 6th International Conference on Logic Programming, ed. by G. Levi and M. Martelli. MIT Press, 1989, pp. 234–255.
Gelder, et al., 1991 – Gelder, A. Van, Ross, K.A. and Schlipf, J.S. “The well-founded semantics for general logic programs”, Journal of the ACM, 1991, Vol. 38, No. 3, pp. 620–650.
Gelfond and Lifschitz, 1988 – Gelfond, M., and Lifschitz, V. “The Stable Model Semantics for Logic Programming”, in: 5th International Conference on Logic Programming, ed. by R. Kowalski and K. A. Bowen. MIT Press, 1988, pp. 1070–1080.
Gelfond and Lifschitz, 1998 – Gelfond, M., and Lifschitz, V. “Action Languages”, Electronic Transactions on Artificial Intelligence, 1998, Vol. 2, pp. 193–210.
Gelfond and Lifschitz, 1991 – Gelfond, M., and Lifschitz, V. “Classical negation in logic programs and disjunctive databases”, New Generation Computing, 1991, Vol. 9, No. 3–4, pp. 365–385.
Inoue and Sakama, 1998 – Inoue, K., and Sakama, C. “Negation as failure in the head”, Journal of Logic Programming, 1998, Vol. 35, pp. 39–78.
Jonker, 1994 – Jonker, C. “Constraints and Negations in Logic Programming”, Ph.D. diss., Department of Philosophy, Utrecht University, 1994.
Kakas et al., 1998 – Kakas, A.C., Kowalski, R.A. and Toni, F. “The Role of Abduction”, in: Handbook of Logic in Artificial Intelligence and Logic Programming, ed. by D.M. Gabbay, C.J. Hogger, and J.A. Robinson, Volume 5: Logic Programming. Oxford, 1998, pp. 235–324.
Leite, 1997 – Leite, J.A. “Logic Program Updates”, Master’s thesis, Dept. de Inform´atica, Faculdade de Ciˆencias e Tecnologia, Universidade Nova de Lisboa, 1997.
Leite, 2003 – Leite, J.A. Evolving Knowledge Bases. Volume 81 of Frontiers in Artificial Intelligence and Applications. IOS Press, 2003.
Leite, 2004 – Leite, J.A. “On Some Differences Between Semantics of Logic Program Updates”, Advances in Artificial Intelligence – IBERAMIA 2004, Volume 3315 of Lecture Notes in Computer Science, ed. by Chr. Lema1tre, C.A. Reyes, and J.A. Gonz´alez. Springer, 2004, pp. 375–385.
Leite and Pereira, 1998a – Leite, J.A., and Pereira, L.M. “Generalizing updates: from models to programs”, LPKR’97: ILPS’97 workshop on Logic Programming and Knowledge Representation. Springer, 1998. pp. 224–246.
Leite and Pereira, 1998b – Leite, J.A., and Pereira, L.M. “Iterated Logic Program Updates”, in: Proceedings of the 1998 Joint International Conference and Symposium on Logic Programming (JICSLP-98), ed. by J. Jaffar. Cambridge: MIT Press, 1998, pp. 265–278.
Lifschitz, 1996 – Lifschitz, V. “Foundations of logic programming”, in: Principles of Knowledge Representation, ed. by G. Brewka. Stanford, California: CSLI, 1996, pp. 69–128.
Lifschitz et al., 2001 – Lifschitz, V., Pearce, D. and Valverde, A. “Strongly equivalent logic programs”, ACM Transactions on Computational Logic, 2001, Vol. 2, pp. 526–541.
Lifschitz and Woo, 1992 – Lifschitz, V., and Woo, T. “Answer sets in general nonmonotonic reasoning (Preliminary report)”, in: Principles of Knowledge Representation and Reasoning (KR92), ed. by B. Nebel, C. Rich, and W. Swartout. Morgan-Kaufmann, 1992, pp. 603–614.
Minker, 1994 – Minker, J. “Overview of disjunctive logic progamming”, Annals of Mathematics and Artificial Intelligence, 1994, Vol. 12, pp. 1–24.
Odintsov and Pearce, 2005 – Odintsov, S., and Pearce, D. “Routley Semantics for Answer Sets”, in: Logic Programming and Nonmonotonic Reasoning, ed. by Ch. Baral, G. Greco, N. Leone, and G. Terracina, Volume 3662 of Lecture Notes in Artificial Intelligence. Springer, 2005, pp. 343–355.
Pearce, 1997 – Pearce, D. “A new logical characterization of stable models and answer sets”, in: Non-Monotonic Extensions of Logic Programming, ed. by J. Dix, L.M. Pereira, and T. Przymusinski, Volume 1216 of Lecture Notes in Computer Science. Springer, 1997, pp. 57–70.
Pearce, 1999 – Pearce, D. “From here to there: Stable negation in logic programming”, in: What is Negation?, ed. by D. Gabbay and H. Wansing. Kluwer, 1999, pp. 161–181.
Pearce, 2006 – Pearce, D. “Equilibrium logic”, Annals of Mathematics and Artificial Intelligence, 2006, Vol. 47, pp. 3–41.
Poole, 1994 – Poole, D. “Default Logic”, in: Handbook of Logic in Artificial Intelligence and Logic Programming, ed. by Dov Gabbay, C.J. Hogger, and J.A. Robinson, Vol. 3. Oxford, 1994, pp. 189–215.
Przymusinski and Turner, 1997 – Przymusinski, T.C., and Turner, H. “Update by means of inference rules”, The Journal of Logic Programming, 1997, Vol. 20, pp. 125–143.
Reiter, 1978 – Reiter, R. “On closed world data bases”, in: Logic and Data Bases, ed. by H. Gallaire and J. Minker. Plenum, 1978, pp. 55–76.
Reiter, 1980 – Reiter, R. “A Logic for Default-Reasoning”, Artificial Intelligence, 1980, Vol. 13, pp. 81–132.
Sakama and Inoue, 1999 – Sakama, C., and Inoue, K. “Updating Extended Logic Programs through Abduction”, Proceedings of the 5th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR-99), Volume 1730 of LNAI, ed. by M. Gelfond, N. Leone, and G. Pfeifer. Berlin: Springer, 1999, pp. 147–161.
Shen and Eiter, 2019 – Shen, Y.-D., and Eiter, T. “Determining inference semantics for disjunctive logic programs”, Artificial Intelligence, 2019, Vol. 277, pp. 103–165.
Shepherdson, 1998 – Shepherdson, J.C. “Negation as Failure, Completion and Stratification”, in: Handbook of Logic in Artificial Intelligence and Logic Programming, ed. by D.M. Gabbay, C.J. Hogger, and J.A. Robinson, Vol. 5: Logic Programming. Oxford, 1998, pp. 355–419.
Slota et al., 2014 – Slota, M., Bal´aˇz, M., and Leite, J. “Supporting Strong and Default Negation in Answer-Set Program Updates”, Advances in Artificial Intelligence IBERAMIA 2014, Volume 8864 of Lecture Notes in Computer Science, ed. by A. Bazzan and K. Pichara. Springer, 2014, pp. 41–53.
Slota and Leite, 2010 – Slota, M., and Leite, J. “On Semantic Update Operators for Answer-Set Programs”, in: Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence. IOS Press, 2010, pp. 957–962.
Slota and Leite, 2014 – Slota, M., and Leite, J. “The Rise and Fall of Semantic Rule Updates Based on SE-Models”, Theory and Practice of Logic Programming, 2014, Vol. 14, pp. 869–907.
Turner, 2003 – Turner, H. “Strong equivalence made easy: nested expressions and weight constraints”, Theory and Practice of Logic Programming, 2003, Vol. 3, pp. 609–622.
Zhang and Foo, 1998 – Zhang, Y., and Foo, N.Y. “Updating Logic Programs”, in: Proceedings of the 13th European Conference on Artificial Intelligence (ECAI-98), ed. by Henri Prade. Chichester: John Wiley & Sons, 1998, pp. 403–407.
Banti et al., 2004 – Banti, F., Alferes, J.J. and Brogi, A. “Well Founded Semantics for Logic Program Updates”, in: Advances in Artificial Intelligence – IBERAMIA 2004, Volume 3315 of Lecture Notes in Computer Science, ed. by Chr. Lema1tre, C.A. Reyes, and J.A. Gonz´alez. Springer, 2004, pp. 397–407.
Bidoit and Froidevaux, 1991 – Bidoit, N., and Froidevaux, C. “General logic databases and programs: Default logic semantics and stratification”, Information and Computation, 1991, Vol. 91, No. 1, pp. 15–54.
Buccafurri et al., 1999 – Buccafurri, F., Faber, W. and Leone, N. “Disjunctive Logic Programs with Inheritance”, in: Proceedings of the 1999 International Conference on Logic Programming (ICLP-99), ed. by D. De Schreye. Cambridge: MIT Press, 1999, pp. 79–93.
Clark, 1978 – Clark, K.L. “Negation as failure”, in: Logic and Data Bases, ed. by H. Gallaire and J. Minker. Plenum, 1978, pp. 293–322.
Dam´asio and Pereira, 1996 – Dam´asio, C.V., and Pereira, L.M. “Default Negation in the heads: Why not?”, in: Extensions of Logic Programming, ELP’96, ed. by R. Dyckhoff, H. Herre, and P. Schroeder-Heister, Volume 1050 of Lecture Notes in Artificial Intelligence. Springer, 1996, pp. 103–117.
Eiter et al., 2002 – Eiter, Th., Fink, M., Sabbatini, G. and Tompits, H. “On properties of update sequences based on causal rejection”, Theory and Practice of Logic Programming, 2002, Vol. 2, No. 6, pp. 711–767.
Eshghi and Kowalski, 1989 – Eshghi, K., and Kowalski, R.A. “Abduction compared with negation as failure”, in: Proc. 6th International Conference on Logic Programming, ed. by G. Levi and M. Martelli. MIT Press, 1989, pp. 234–255.
Gelder, et al., 1991 – Gelder, A. Van, Ross, K.A. and Schlipf, J.S. “The well-founded semantics for general logic programs”, Journal of the ACM, 1991, Vol. 38, No. 3, pp. 620–650.
Gelfond and Lifschitz, 1988 – Gelfond, M., and Lifschitz, V. “The Stable Model Semantics for Logic Programming”, in: 5th International Conference on Logic Programming, ed. by R. Kowalski and K. A. Bowen. MIT Press, 1988, pp. 1070–1080.
Gelfond and Lifschitz, 1998 – Gelfond, M., and Lifschitz, V. “Action Languages”, Electronic Transactions on Artificial Intelligence, 1998, Vol. 2, pp. 193–210.
Gelfond and Lifschitz, 1991 – Gelfond, M., and Lifschitz, V. “Classical negation in logic programs and disjunctive databases”, New Generation Computing, 1991, Vol. 9, No. 3–4, pp. 365–385.
Inoue and Sakama, 1998 – Inoue, K., and Sakama, C. “Negation as failure in the head”, Journal of Logic Programming, 1998, Vol. 35, pp. 39–78.
Jonker, 1994 – Jonker, C. “Constraints and Negations in Logic Programming”, Ph.D. diss., Department of Philosophy, Utrecht University, 1994.
Kakas et al., 1998 – Kakas, A.C., Kowalski, R.A. and Toni, F. “The Role of Abduction”, in: Handbook of Logic in Artificial Intelligence and Logic Programming, ed. by D.M. Gabbay, C.J. Hogger, and J.A. Robinson, Volume 5: Logic Programming. Oxford, 1998, pp. 235–324.
Leite, 1997 – Leite, J.A. “Logic Program Updates”, Master’s thesis, Dept. de Inform´atica, Faculdade de Ciˆencias e Tecnologia, Universidade Nova de Lisboa, 1997.
Leite, 2003 – Leite, J.A. Evolving Knowledge Bases. Volume 81 of Frontiers in Artificial Intelligence and Applications. IOS Press, 2003.
Leite, 2004 – Leite, J.A. “On Some Differences Between Semantics of Logic Program Updates”, Advances in Artificial Intelligence – IBERAMIA 2004, Volume 3315 of Lecture Notes in Computer Science, ed. by Chr. Lema1tre, C.A. Reyes, and J.A. Gonz´alez. Springer, 2004, pp. 375–385.
Leite and Pereira, 1998a – Leite, J.A., and Pereira, L.M. “Generalizing updates: from models to programs”, LPKR’97: ILPS’97 workshop on Logic Programming and Knowledge Representation. Springer, 1998. pp. 224–246.
Leite and Pereira, 1998b – Leite, J.A., and Pereira, L.M. “Iterated Logic Program Updates”, in: Proceedings of the 1998 Joint International Conference and Symposium on Logic Programming (JICSLP-98), ed. by J. Jaffar. Cambridge: MIT Press, 1998, pp. 265–278.
Lifschitz, 1996 – Lifschitz, V. “Foundations of logic programming”, in: Principles of Knowledge Representation, ed. by G. Brewka. Stanford, California: CSLI, 1996, pp. 69–128.
Lifschitz et al., 2001 – Lifschitz, V., Pearce, D. and Valverde, A. “Strongly equivalent logic programs”, ACM Transactions on Computational Logic, 2001, Vol. 2, pp. 526–541.
Lifschitz and Woo, 1992 – Lifschitz, V., and Woo, T. “Answer sets in general nonmonotonic reasoning (Preliminary report)”, in: Principles of Knowledge Representation and Reasoning (KR92), ed. by B. Nebel, C. Rich, and W. Swartout. Morgan-Kaufmann, 1992, pp. 603–614.
Minker, 1994 – Minker, J. “Overview of disjunctive logic progamming”, Annals of Mathematics and Artificial Intelligence, 1994, Vol. 12, pp. 1–24.
Odintsov and Pearce, 2005 – Odintsov, S., and Pearce, D. “Routley Semantics for Answer Sets”, in: Logic Programming and Nonmonotonic Reasoning, ed. by Ch. Baral, G. Greco, N. Leone, and G. Terracina, Volume 3662 of Lecture Notes in Artificial Intelligence. Springer, 2005, pp. 343–355.
Pearce, 1997 – Pearce, D. “A new logical characterization of stable models and answer sets”, in: Non-Monotonic Extensions of Logic Programming, ed. by J. Dix, L.M. Pereira, and T. Przymusinski, Volume 1216 of Lecture Notes in Computer Science. Springer, 1997, pp. 57–70.
Pearce, 1999 – Pearce, D. “From here to there: Stable negation in logic programming”, in: What is Negation?, ed. by D. Gabbay and H. Wansing. Kluwer, 1999, pp. 161–181.
Pearce, 2006 – Pearce, D. “Equilibrium logic”, Annals of Mathematics and Artificial Intelligence, 2006, Vol. 47, pp. 3–41.
Poole, 1994 – Poole, D. “Default Logic”, in: Handbook of Logic in Artificial Intelligence and Logic Programming, ed. by Dov Gabbay, C.J. Hogger, and J.A. Robinson, Vol. 3. Oxford, 1994, pp. 189–215.
Przymusinski and Turner, 1997 – Przymusinski, T.C., and Turner, H. “Update by means of inference rules”, The Journal of Logic Programming, 1997, Vol. 20, pp. 125–143.
Reiter, 1978 – Reiter, R. “On closed world data bases”, in: Logic and Data Bases, ed. by H. Gallaire and J. Minker. Plenum, 1978, pp. 55–76.
Reiter, 1980 – Reiter, R. “A Logic for Default-Reasoning”, Artificial Intelligence, 1980, Vol. 13, pp. 81–132.
Sakama and Inoue, 1999 – Sakama, C., and Inoue, K. “Updating Extended Logic Programs through Abduction”, Proceedings of the 5th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR-99), Volume 1730 of LNAI, ed. by M. Gelfond, N. Leone, and G. Pfeifer. Berlin: Springer, 1999, pp. 147–161.
Shen and Eiter, 2019 – Shen, Y.-D., and Eiter, T. “Determining inference semantics for disjunctive logic programs”, Artificial Intelligence, 2019, Vol. 277, pp. 103–165.
Shepherdson, 1998 – Shepherdson, J.C. “Negation as Failure, Completion and Stratification”, in: Handbook of Logic in Artificial Intelligence and Logic Programming, ed. by D.M. Gabbay, C.J. Hogger, and J.A. Robinson, Vol. 5: Logic Programming. Oxford, 1998, pp. 355–419.
Slota et al., 2014 – Slota, M., Bal´aˇz, M., and Leite, J. “Supporting Strong and Default Negation in Answer-Set Program Updates”, Advances in Artificial Intelligence IBERAMIA 2014, Volume 8864 of Lecture Notes in Computer Science, ed. by A. Bazzan and K. Pichara. Springer, 2014, pp. 41–53.
Slota and Leite, 2010 – Slota, M., and Leite, J. “On Semantic Update Operators for Answer-Set Programs”, in: Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence. IOS Press, 2010, pp. 957–962.
Slota and Leite, 2014 – Slota, M., and Leite, J. “The Rise and Fall of Semantic Rule Updates Based on SE-Models”, Theory and Practice of Logic Programming, 2014, Vol. 14, pp. 869–907.
Turner, 2003 – Turner, H. “Strong equivalence made easy: nested expressions and weight constraints”, Theory and Practice of Logic Programming, 2003, Vol. 3, pp. 609–622.
Zhang and Foo, 1998 – Zhang, Y., and Foo, N.Y. “Updating Logic Programs”, in: Proceedings of the 13th European Conference on Artificial Intelligence (ECAI-98), ed. by Henri Prade. Chichester: John Wiley & Sons, 1998, pp. 403–407.