Some Concerns Regarding Ternary-relation Semantics and Truth-theoretic Semantics in General

This paper deals with a collection of concerns that, over a period of time, led the author away from the Routley–Meyer semantics, and towards proof- theoretic approaches to relevant logics, and indeed to the weak relevant logic MC of meaning containment

Starting the Dismantling of Classical Mathematics

This paper uses the relevant logic, MCQ, of meaning containment to explore mathematics without various classical theses, in particular, without the law of excluded middle

Starting the Dismantling of Classical Mathematics

This paper uses the relevant logic, MCQ, of meaning containment to explore mathematics without various classical theses, in particular, without the law of excluded middle

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