Geodesic
Combining intuitionistic connectives and Routley negation
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 21-41

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Logic $N^*$ was defined as a logical framework for studying deductive bases of the well founded semantics (WFS) of logics programs with negation. Its semantical definition combines Kripke frames for intuitionistic logic with Routley's $*$-operator, which is used to interpret the negation operation. In this paper we develop algebraic semantics for $N^*$, describe its subdirectly irreducible algebraic models, describe completely the lattice of normal $HT^2$-extensions. The logic $HT^2$ is a finite valued extension of $N^*$, which is a deductive base of WFS. The last result can be used to check the maximality of this deductive base.
Keywords: Routley semantics, negation as modality, negation in logic programming, algebraic semantics
Mots-clés : Heyting–Ockham algebra. 
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     author = {S. P. Odintsov},
     title = {Combining intuitionistic connectives and {Routley} negation},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {21--41},
     publisher = {mathdoc},
     volume = {7},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2010_7_a2/}
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S. P. Odintsov. Combining intuitionistic connectives and Routley negation. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 21-41. http://geodesic.mathdoc.fr/item/SEMR_2010_7_a2/