Geodesic
The Disjunction Property in the Class of Paraconsistent Extensions of Minimal Logic
Algebra i logika, Tome 43 (2004) no. 2, pp. 235-252

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We consider the disjunction property, $\mathbf{DP}$, in the class of extensions of minimal logic $\mathbf{L}_{j}$. Conditions are described under which $\mathbf{DP}$ is translated from the class $\mathbf{PAR}$ of properly paraconsistent extensions of the logics of class $\mathbf{L}_{j}$ into the class $\mathbf{INT}$ of intermediate extensions and the class $\mathbf{NEG}$ of negative extensions, and conditions for its being translated back into $\mathbf{PAR}$. The logic $\mathbf{L}_{F}$ in $\mathbf{PAR}$, which specifies conditions for $\mathbf{DP}$ to be translated from $\mathbf{PAR}$ into $\mathbf{NEG}$, is defined and is characterized in terms of $j$-algebras and Kripke frames. Moreover, we show that ${\mathbf L}_F$ is decidable and possesses the disjunction property.
Keywords: paraconsistent extension of minimal logic, $j$-algebra - Kripke frame, disjunction property. 
@article{AL_2004_43_2_a7,
     author = {M. V. Stukacheva},
     title = {The {Disjunction} {Property} in the {Class} of {Paraconsistent} {Extensions} of {Minimal} {Logic}},
     journal = {Algebra i logika},
     pages = {235--252},
     publisher = {mathdoc},
     volume = {43},
     number = {2},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2004_43_2_a7/}
}
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M. V. Stukacheva. The Disjunction Property in the Class of Paraconsistent Extensions of Minimal Logic. Algebra i logika, Tome 43 (2004) no. 2, pp. 235-252. http://geodesic.mathdoc.fr/item/AL_2004_43_2_a7/