Boolean negation and non-conservativity I: Relevant modal logics

Under embargo until: 2021-07-15Many relevant logics are conservatively extended by Boolean negation. Not all, however. This paper shows an acute form of non-conservativeness, namely that the Boolean-free fragment of the Boolean extension of a relevant logic need not always satisfy the variable-sharing property. In fact, it is shown that such an extension can in fact yield classical logic. For a vast range of relevant logic, however, it is shown that the variable-sharing property, restricted to the Boolean-free fragment, still holds for the Boolean extended logic.acceptedVersio

Relevance logics, paradoxes of consistency and the K rule II. A non-constructive negation

The logic B+ is Routley and Meyer’s basic positive logic. We define the logics BK+ and BK'+ by adding to B+ the K rule and to BK+ the characteristic S4 axiom, respectively. These logics are endowed with a relatively strong non-constructive negation. We prove that all the logics defined lack the K axiom and the standard paradoxes of consistency

Boolean Conservative Extension Results for some Modal Relevant Logics

This paper shows that a collection of modal relevant logics are conservatively extended by the addition of Boolean negation

Boolean Conservative Extension Results for some Modal Relevant Logics

This paper shows that a collection of modal relevant logics are conservatively extended by the addition of Boolean negation