Some paraconsistent sentential calculi

In 8] Jakowski defined by means of an appropriate interpretation a paraconsistent calculusD ₂ . In 9] J. Kotas showed thatD ₂ is equivalent to the calculusM(S5) whose theses are exactly all formulasa such thatMa is a thesis ofS5. The papers 11], 7], 3], and 4] showed that interesting paraconsistent calculi could be obtained using modal systems other thanS5 and modalities other thanM. This paper generalises the above work. LetA be an arbitrary modality (i.e. string ofM's,L's and negation signs). Then theA-extension of a set of formulasX is {¦A X}}. Various properties ofA-extensions of normal modal systems are examined, including a problem of their axiomatizability