Browsing Bergen Open Research Archive by Author "Øgaard, Tore Fjetland"
Now showing items 1-10 of 10
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Boolean negation and non-conservativity I: Relevant modal logics
Øgaard, Tore Fjetland (Journal article; Peer reviewed, 2021)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, 2021)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, 2021)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. ... -
Confused Entailment
Øgaard, Tore Fjetland (Journal article; Peer reviewed, 2022)Priest argued in his paper Fusion and Confusion (Priest, 2015a) for a new concept of logical consequence over the relevant logic B, one where premises my be “confused” together. This paper develops Priest’s idea. Whereas ... -
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, 2021)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, ... -
Relevance through topical unconnectedness: Ackermann and Plumwood’s motivational ideas on entailment
Øgaard, Tore Fjetland (Journal article; Peer reviewed, 2023)Ackermann’s motivational spin on his theory of rigorous implication is analyzed and it is shown to contain en equivalent idea to Plumwood’s notion of suppression freedom. The formal properties these ideas back turn out to ... -
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 ... -
The weak variable sharing property
Øgaard, Tore Fjetland (Journal article, 2023)An algebraic type of structure is shown forth which is such that if it is a characteristic matrix for a logic, then that logic satisfies Meyer's weak variable sharing property. As a corollary, it is shown that RM and all ...