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Super-strict Implications

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Warianty tytułu
Języki publikacji
EN
Abstrakty
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
Strony
1-34
Opis fizyczny
Daty
wydano
2021-03-30
Twórcy
  • University of Bologna, Department of Philosophy and Communication Studies I-40126, Via Zamboni 38, Bologna, Italy
  • University of Bologna, Department of Philosophy and Communication Studies I-40126, Via Zamboni 38, Bologna, Italy
Bibliografia
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  • [6] C. I. Lewis, Survey of Symbolic Logic, University of California Press (1918).
  • [7] D. Lewis, Counterfactuals, Harvard University Press (1975).
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  • [12] S. Negri, J. von Plato, Proof Analysis, Cambridge University Press (2011).
  • [13] E. Nelson, Intensional relations, Mind, vol. 39 (1930), pp. 440–453.
  • [14] H. Omori, H. Wansing, Connexive logics. An overview and current trends, Logic and Logical Philosophy, vol. 28(3) (2019), pp. 371–387, DOI: https://doi.org/10.12775/LLP.2019.026
  • [15] 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
  • 16] G. Priest, Negation as cancellation and connexive logic, Topoi, vol. 18 (1999), pp. 141–148, DOI: https://doi.org/10.1023/A:1006294205280
  • [17] 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
  • [18] H. Rasiowa, An Algebraic Approach to Non-classical Logics, Elsevier (1974).
  • [19] R. Routley, V. Routley, Negation and contradiction, Revista Colombiana de Matemáticas, vol. 19 (1985), pp. 201–230.
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  • [23] H. Wansing, D. Skurt, Negation as Cancellation, Connexive Logic, and qLPm, The Australasian Journal of Logic, vol. 15 (2018), pp. 476–488, DOI: https://doi.org/10.26686/ajl.v15i2.4869
Typ dokumentu
Bibliografia
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