On strong equivalence theorem for answer set semantics with strong negation
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 108-121.

Voir la notice de l'article provenant de la source Math-Net.Ru

We discuss the problem of finding a minimal deductive base for paraconsistent and ordinary answer set semantics satisfying the strong equivalence theorem.
Keywords: answer set, paraconsistency, strong negation, strong equivalence of logic programs, Nelson logic.
@article{SEMR_2015_12_a2,
     author = {Z. V. Makridin and S. P. Odintsov},
     title = {On strong equivalence theorem for answer set semantics with strong negation},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {108--121},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a2/}
}
TY  - JOUR
AU  - Z. V. Makridin
AU  - S. P. Odintsov
TI  - On strong equivalence theorem for answer set semantics with strong negation
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2015
SP  - 108
EP  - 121
VL  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2015_12_a2/
LA  - en
ID  - SEMR_2015_12_a2
ER  - 
%0 Journal Article
%A Z. V. Makridin
%A S. P. Odintsov
%T On strong equivalence theorem for answer set semantics with strong negation
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2015
%P 108-121
%V 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2015_12_a2/
%G en
%F SEMR_2015_12_a2
Z. V. Makridin; S. P. Odintsov. On strong equivalence theorem for answer set semantics with strong negation. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 108-121. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a2/

[1] J. Alcântara, C. Damásio, L. M. Pereira, “A declarative characterisation of disjunctive paraconsistent answer sets”, Proc. of ECAI 2004, eds. R. López de Mántaras, L. Saitta, IOS Press, 2004, 951–952

[2] N. D. Belnap, “How a computer should think”, Contemporary Aspects of Philosophy, ed. G. Ryle, Oriel Press, Stocksfield, 1976, 30–56

[3] N. D. Belnap, “A Useful Four-Valued Logic”, Modern Uses of Multiple-Valued Logics, eds. J. M. Dunn, G. Epstein, D. Reidel Publishing Company, Dordrecht, 1977, 8–37 | MR

[4] D. De Jong, L. Hendriks, “Characterization of strongly equivalent logic programs in intermediate logics”, Theory and Practice of Logic Programing, 3 (2003), 259—270 | DOI | MR | Zbl

[5] J. Dietrich, Deductive bases of nonmonotonic inference operations, NTZ Report, Universität Leipzig, 1994

[6] J. M. Dunn, “Intuitive semantics for first degree entailments and coupled trees”, Phil. Stud., 29 (1976), 149–168 | DOI | MR

[7] M. Gelfond, V. Lifschitz, “Classical negation in logic programs and disjunctive databases”, New Generation Computing, 9 (1991), 365–385 | DOI | Zbl

[8] V. Lifschitz, D. Pearce, A. Valverde, “Strongly equivalent logic programs”, ACM Trans. on Comput. Log., 2:4 (2001), 526–541 | DOI | MR

[9] D. Nelson, “Constructible falsity”, J. Symb. Log., 14:2 (1949), 16–26 | DOI | MR | Zbl

[10] S. P. Odintsov, N. V. Mayatskiy, “On deductive base for paraconsistent answer set semantics”, J. Appl. Non-Class. Logic, 23:1–2 (2013), 131–146 | MR

[11] S. Odintsov, D. Pearce, “Routley semantics for answer sets”, Proc. 8th International Conference on Logic Programming and Nonmonotonic Reasoning, LNCS, 3662, 2005, 343–355 | MR | Zbl

[12] D. Pearce, “Answer sets and constructive logic. Part II: Extended logic programs and related nonmonotonic formalisms”, Logic Programming and Non-monotonic Reasoning, eds. L. M. Periera, A. Nerode, MIT Press, 1993, 457–475 | MR

[13] D. Pearce, “A new logical characterization of stable models and answer sets”, Proc. of NMELP 96, LNCS, 1216, Springer, 1997, 57–70 | MR

[14] D. Pearce, G. Wagner, “Logic programming with strong negation”, Extensions of Logic Programming, LNCS, 475, Springer, 1991, 311–326 | MR

[15] H. Rasiowa, “$N$-lattices and constructive logic with strong negation”, Fund. Math., 46 (1958), 61–80 | MR | Zbl

[16] H. Rasiowa, An algebraic approach to non-classical logic, PWN, Warsaw; North-Holland, Amsterdam, 1974 | MR

[17] C. Sakama, K. Inoue, “Paraconsistent stable semantics for extended disjunctive programs”, J. Log. Comput., 5 (1995), 265–285 | DOI | MR | Zbl

[18] N. N. Vorob'ev, “A constructive calculus of propositions with strong negation”, Doklady Akademii Nauk SSSR, 85 (1952), 465–468 (in Russian) | MR

[19] N. N. Vorob'ev, “The problem of deducibility in constructive propositional calculus with strong negation”, Doklady Akademii Nauk SSSR, 85 (1952), 689–692 (in Russian) | MR