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A new approach to classical relevance

(2015) STUDIA LOGICA. 103(5). p.919-954
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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.
Keywords
Relevance logic, Algebraic semantics, Classical negation, Relevant implication, Non-transitive implication

Citation

Please use this url to cite or link to this publication:

MLA
Verdée, Peter, and Inge De Bal. “A New Approach to Classical Relevance.” STUDIA LOGICA 103.5 (2015): 919–954. Print.
APA
Verdée, Peter, & De Bal, I. (2015). A new approach to classical relevance. STUDIA LOGICA, 103(5), 919–954.
Chicago author-date
Verdée, Peter, and Inge De Bal. 2015. “A New Approach to Classical Relevance.” Studia Logica 103 (5): 919–954.
Chicago author-date (all authors)
Verdée, Peter, and Inge De Bal. 2015. “A New Approach to Classical Relevance.” Studia Logica 103 (5): 919–954.
Vancouver
1.
Verdée P, De Bal I. A new approach to classical relevance. STUDIA LOGICA. 2015;103(5):919–54.
IEEE
[1]
P. Verdée and I. De Bal, “A new approach to classical relevance,” STUDIA LOGICA, vol. 103, no. 5, pp. 919–954, 2015.
@article{5816352,
  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.},
  author       = {Verdée, Peter and De Bal, Inge},
  issn         = {0039-3215},
  journal      = {STUDIA LOGICA},
  keywords     = {Relevance logic,Algebraic semantics,Classical negation,Relevant implication,Non-transitive implication},
  language     = {eng},
  number       = {5},
  pages        = {919--954},
  title        = {A new approach to classical relevance},
  url          = {http://dx.doi.org/10.1007/s11225-014-9599-3},
  volume       = {103},
  year         = {2015},
}

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