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2020 | 49 | 4 | 327-342
Tytuł artykułu

The Phenomenology of Second-Level Inference: Perfumes in The Deductive Garden

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We comment on certain features that second-level inference rules commonly used in mathematical proof sometimes have, sometimes lack: suppositions, indirectness, goal-simplification, goal-preservation and premise-preservation. The emphasis is on the roles of these features, which we call 'perfumes', in mathematical practice rather than on the space of all formal possibilities, deployment in proof-theory, or conventions for display in systems of natural deduction.
Rocznik
Tom
49
Numer
4
Strony
327-342
Opis fizyczny
Daty
wydano
2020-12-30
Twórcy
  • Les Etangs, B2 Domaine de la Ronce 92410 Ville d'Avray France
Bibliografia
  • [1] G. Gentzen, Untersuchungen über das logische Schliessen, Mathematische Zeitschrift, vol. 23 (1934), pp. 176–210, 405–431, DOI: http://dx.doi.org/10.1007/BF01201353 English translation: Investigation into logical deduction, pp. 68–131 of The Collected Papers of Gerhard Gentzen, ed. M. E. Szabo. North-Holland, Amsterdam, 1969.
  • [2] J. Harrison, Without loss of generality, [in:] S. Berghofer, T. Nipkow (eds.), Theorem-Proving in Higher Order Logics, vol. 5674 of Lecture Notes in Computer Science, Springer, Berlin (2009), pp. 43–59, DOI: http://dx.doi.org/10.1007/978-3-642-03359-9_3
  • [3] A. Indrzejczak, Natural Deduction, Hybrid Systems and Modal Logic, Springer, Dordrecht (2010), DOI: http://dx.doi.org/10.1007/978-90481-8785-0
  • [4] A. Indrzejczak, Natural Deduction, Internet Encyclopedia of Philosophy, (2015), URL: https://iep.utm.edu/nat-ded/ consulted 16.07.2020.
  • [5] S. Ja_skowski, On the rules of suppositions in formal logic, Studia Logica, vol. 1 (1934), pp. 1–32.
  • [6] D. Kalish, R. Montague, Logic: Techniques of Formal Reasoning, Harcourt Brace, New York (1964), also second edition with co-author G. Mar, Oxford University Press, 2001.
  • [7] J. Lucas, Introduction to Abstract Mathematics, 2nd ed., Rowman & Little_eld, Maryland, USA (1990).
  • [8] D. Makinson, Sets, Logic and Maths for Computing, 3rd ed., Undergraduate Topics in Computer Science, Springer, London (2020), DOI: http://dx.doi.org/10.1007/978-1-4471-2500-6
  • [9] D. Makinson, Relevance-sensitive truth-trees, [in:] Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs, Outstanding Contributions to Logic, Springer, Berlin (2021), to appear.
  • [10] J. Pelletier, A brief history of natural deduction, History and Philosophy of Logic, vol. 20 (1999), pp. 1–31, DOI: http://dx.doi.org/10.1080/014453499298165
  • [11] J. Pelletier, A. P. Hazen, A history of natural deduction, [in:] D. Gabbay, F. J. Pelletier, E. Woods (eds.), Handbook of the History of Logic, vol. 11, North-Holland, Amsterdam (2012), pp. 341–414, DOI: http://dx.doi.org/10.1016/B978-0-444-52937-4.50007-1
  • [12] E. Schechter, Constructivism is di_cult, American Mathematical Monthly, vol. 108 (2001), pp. 50–54, DOI: http://dx.doi.org/10.1080/00029890.2001.11919720
  • [13] R. Sikorski, Boolean Algebras, 2nd ed., Springer, Berlin (1964), DOI: http://dx.doi.org/10.1007/978-3-662-01507-0
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-doi-10_18778_0138-0680_2020_23
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