• Boolean negation and non-conservativity I: Relevant modal logics 

      Øgaard, Tore Fjetland (Journal article; Peer reviewed, 2020)
      Many 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 ...
    • Boolean negation and non-conservativity II: The variable-sharing property 

      Øgaard, Tore Fjetland (Journal article; Peer reviewed, 2020)
      Many 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 ...
    • Boolean negation and non-conservativity III: the Ackermann constant 

      Øgaard, Tore Fjetland (Journal article; Peer reviewed, 2020)
      It is known that many relevant logics can be conservatively extended by the truth constant known as the Ackermann constant. It is also known that many relevant logics can be conservatively extended by Boolean negation. ...
    • Farewell to Suppression-Freedom 

      Øgaard, Tore Fjetland (Journal article; Peer reviewed, 2020)
      Val Plumwood and Richard Sylvan argued from their joint paper The Semantics of First Degree Entailment (Routley and Routley in Noûs 6(4):335–359, 1972, https://doi.org/10.2307/2214309) and onward that the variable sharing ...
    • Non-Boolean classical relevant logics I 

      Øgaard, Tore Fjetland (Peer reviewed; Journal article, 2019)
      Relevant logics have traditionally been viewed as paraconsistent. This paper shows that this view of relevant logics is wrong. It does so by showing forth a logic which extends classical logic, yet satisfies the Entailment ...
    • Non-Boolean classical relevant logics II: Classicality through truth-constants 

      Øgaard, Tore Fjetland (Journal article; Peer reviewed, 2021)
      This paper gives an account of Anderson and Belnap's selection criteria for an adequate theory of entailment. The criteria are grouped into three categories: criteria pertaining to modality, those pertaining to relevance, ...
    • Substitution in Relevant Logics 

      Øgaard, Tore Fjetland (Peer reviewed; Journal article, 2019)
      This essay discusses rules and semantic clauses relating to Substitution—Leibniz’s law in the conjunctive-implicational form s = t ^ A(s) -> A(t)—as these are put forward in Priest’s books "In Contradiction" and "An ...