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The lattice of Belnapian modal logics: Special extensions and counterparts

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Odintsov S. P., Speranski S. O.

Logic and Logical Philosophy

2016

vol. 25

issue 1

3-33

Let K be the least normal modal logic and BK its Belnapian version, which enriches K with ‘strong negation’. We carry out a systematic study of the lattice of logics containing BK based on: • introducing the classes (or rather sublattices) of so-called explosive, complete and classical Belnapian modal logics; • assigning to every normal modal logic three special conservative extensions in these classes; • associating with every Belnapian modal logic its explosive, complete and classical counterparts. We investigate the relationships between special extensions and counterparts, provide certain handy characterisations and suggest a useful decomposition of the lattice of logics containing BK.

Negation in the language of theology – some issues

71%

Olszewski A.

Zagadnienia Filozoficzne w Nauce

2018

issue 65

The paper consists of two parts. In the first one I present some general remarks regarding the history of negation and attempt to answer the philosophical question concerning the essence of negation. In the second part I resume the theological teaching on the degrees of certainty (notae theologice) and point to five forms of negation – known from other areas of research -- as applied in the framework of theological investigations.

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1 Logic and Logical Philosophy

1 Zagadnienia Filozoficzne w Nauce

1 Odintsov S. P.

1 Olszewski A.

1 Speranski S. O.

1 2018

1 2016

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The lattice of Belnapian modal logics: Special extensions and counterparts

Negation in the language of theology – some issues