Super-Strict Implications
| dc.contributor.author | Gherardi, Guido | |
| dc.contributor.author | Orlandelli, Eugenio | |
| dc.date.accessioned | 2021-05-05T13:58:33Z | |
| dc.date.available | 2021-05-05T13:58:33Z | |
| dc.date.issued | 2021-01-20 | |
| dc.identifier.issn | 0138-0680 | |
| dc.identifier.uri | http://hdl.handle.net/11089/35350 | |
| dc.description.abstract | This paper introduces the logics of super-strict implications, where a super-strict implication is a strengthening of C.I. Lewis' strict implication that avoids not only the paradoxes of material implication but also those of strict implication. The semantics of super-strict implications is obtained by strengthening the (normal) relational semantics for strict implication. We consider all logics of super-strict implications that are based on relational frames for modal logics in the modal cube. it is shown that all logics of super-strict implications are connexive logics in that they validate Aristotle's Theses and (weak) Boethius's Theses. A proof-theoretic characterisation of logics of super-strict implications is given by means of G3-style labelled calculi, and it is proved that the structural rules of inference are admissible in these calculi. It is also shown that validity in the S5-based logic of super-strict implications is equivalent to validity in G. Priest's negation-as-cancellation-based logic. Hence, we also give a cut-free calculus for Priest's logic. | en |
| dc.language.iso | en | |
| dc.publisher | Wydawnictwo Uniwersytetu Łódzkiego | pl |
| dc.relation.ispartofseries | Bulletin of the Section of Logic;1 | en |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0 | |
| dc.subject | Strict implication | en |
| dc.subject | paradoxes of implication | en |
| dc.subject | connexive implication | en |
| dc.subject | sequent calculi | en |
| dc.subject | structural rules | en |
| dc.title | Super-Strict Implications | en |
| dc.type | Other | |
| dc.page.number | 1-34 | |
| dc.contributor.authorAffiliation | Gherardi, Guido - University of Bologna, Department of Philosophy and Communication Studies I-40126, Via Zamboni 38, Bologna, Italy | en |
| dc.contributor.authorAffiliation | Orlandelli, Eugenio - University of Bologna, Department of Philosophy and Communication Studies I-40126, Via Zamboni 38, Bologna, Italy | en |
| dc.identifier.eissn | 2449-836X | |
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| dc.contributor.authorEmail | Gherardi, Guido - guido.gherardi@unibo.it | |
| dc.contributor.authorEmail | Orlandelli, Eugenio - eugenio.orlandelli@unibo.it | |
| dc.identifier.doi | 10.18778/0138-0680.2021.02 | |
| dc.relation.volume | 50 |
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