Abstract
In this paper we present a logic that determines when implications in a classical logic context express a relevant connection between antecedent and consequent. In contrast with logics in the relevance logic literature, we leave classical negation intact—in the sense that the law of non-contradiction can be used to obtain relevant implications, as long as there is a connection between antecedent and consequent. On the other hand, we give up the requirement that our theory of relevance should be able to define a new standard of deduction. We present and argue for a list of requirements such a logical theory of classical relevance needs to meet and go on to formulate a system that respects each of these requirements. The presented system is a Tarski (i.e. monotonic, reflexive and transitive) logic that extends the relevance logic R with a new relevant implication which allows for Disjunctive Syllogism and similar rules. This is achieved by interpreting the logical symbols in the antecedents in a stronger way than the logical symbols in consequents. A proof theory and an algebraic semantics are formulated and interesting metatheorems (soundness, completeness and the fact that it satisfies the requirements for classical relevance) are proven. Finally we give a philosophical motivation for our non-standard relevant implication and the asymmetric interpretation of antecedents and consequents.
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Presented by Andrzej Indrzejczak; Received October 19, 2013
During the research for this paper, Peter Verdée was a post-doctoral fellow of the Fund for Scientific Research – Flanders. At the time of the submission of this paper, he is a post-doctoral fellow of FAPESP, São Paulo, Brazilië.
Inge De Bal is a pre-doctoral fellow of the Fund for Scientific Research – Flanders.
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Verdée, P., Bal, I.D. A New Approach to Classical Relevance. Stud Logica 103, 919–954 (2015). https://doi.org/10.1007/s11225-014-9599-3
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DOI: https://doi.org/10.1007/s11225-014-9599-3