ANTIMONOTONE LOGICS. ON SOME J. PERZANOWSKI'S RESEARCH IN MODAL LOGICS (Logiki anty-monotoniczne. O pewnych badaniach J. Perzanowskiego nad logikami modalnymi)
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In his logical-philosophical investigations into modal logics, Jerzy Perzanowski put special attention to the place occupied by given modal logic in the lattice of modal logics: logics in close to a given logic were important to him. He appreciated research into the lattice of modal logics and chose it as a subject of a great deal of his scholarly writings. In this field, he encountered the so-called antimonotone logics; he begun research into them but not finished it (cf. Perzanowski (1989, 1989), Makinson (1971)). He presented basic syntax of these logics, but had not described the semantics of these logics, neither relational one, nor algebraic. These logics are interesting to some extent as their descriptions complete the image of the whole of lattice of modal logics. In the paper, his considerations are complemented: the relational as well as algebraic semantics of such logics are presented and the structure of the whole of lattice of modal logics is described.
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