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Super-Strict Implications

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EN
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.

Rocznik

Tom

50

Numer

1

Opis fizyczny

Daty

wydano
2021

Twórcy

  • University of Bologna, Department of Philosophy and Communication Studies, Italy
  • University of Bologna, Department of Philosophy and Communication Studies, Italy

Bibliografia

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  • J. Heylen, L. Horsten, Strict Conditionals: A Negative Result, The Philosophical Quarterly, vol. 56(225) (2006), pp. 536–549, DOI: https://doi.org/10.1111/j.1467-9213.2006.457.x
  • D. Hitchcock, Does the Traditional Treatment of Enthymemes Rest on a Mistake?, Argumentation, vol. 12 (1998), pp. 15–37, DOI: https://doi.org/10.1007/978-3-319-53562-3_5
  • C. I. Lewis, Survey of Symbolic Logic, University of California Press (1918).
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  • S. Negri, J. von Plato, Proof Analysis, Cambridge University Press (2011).
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  • C. Pizzi, T. Williamson, Strong Boethius' Thesis and Consequential Implication, Journal of Philosophical Logic, vol. 26 (1997), pp. 569–588, DOI: https://doi.org/10.1023/A:1004230028063
  • G. Priest, Negation as cancellation and connexive logic, Topoi, vol. 18 (1999), pp. 141–148, DOI: https://doi.org/10.1023/A:1006294205280
  • E. Raidl, Strengthened Conditionals, [in:] B. Liao, Y. N. Wáng (eds.), Context, Conict and Reasoning, Springer Singapore (2020), pp. 139–155, DOI: https://doi.org/10.1007/978-981-15-7134-3_11
  • H. Rasiowa, An Algebraic Approach to Non-classical Logics, Elsevier (1974).
  • R. Routley, V. Routley, Negation and contradiction, Revista Colombiana de Matemáticas, vol. 19 (1985), pp. 201–230.
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  • A. S. Troelstra, D. van Dalen, Constructivism in Mathematics, North-Holland (1988).
  • M. Vidal, When Conditional Logic met Connexive Logic, [in:] IWCS 2017 - 12th International Conference on Computational Semantics (2017), pp. 1–11, URL: https://www.aclweb.org/anthology/W17-6816
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Bibliografia

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