Electronegativity and Chemical Bond Types (Covalent Polar, Covalent Non-Polar, Ionic Bonds)
Electronegativity and Chemical Bond Types (Covalent Polar, Covalent Non-Polar, Ionic Bonds)

Distribution Tableaux, Distribution Models

Abstract

:

1. Introduction

2. Preliminaries

2.1. Syllogistic

2.2. Distribution

  • is distributed in p if and only if p entails a proposition of the form “every is …”
  • is not distributed in p if and only if is distributed in the contradictory of p.

2.3. Term Functor Logic

2.4. TFL Tableaux

3. Distribution Models

4. Conclusions

Funding

Acknowledgments

Conflicts of Interest

References

  1. Geach, P.T. Reference and Generality: An Examination of Some Medieval and Modern Theories; Contemporary Philosophy/Cornell University, Cornell University Press: Ithaca, NY, USA, 1962. [Google Scholar]
  2. Williamson, C. Traditional Logic as a Logic Distribution-values. Log. Et Anal. 1971, 14, 729–746. [Google Scholar]
  3. Sommers, F. Distribution Matters. Mind 1975, LXXXIV, 27–46. [Google Scholar] [CrossRef]
  4. Sommers, F. The Logic of Natural Language; Clarendon Library of Logic and Philosophy, Clarendon Press: New York, NY, USA; Oxford University Press: Oxford, UK, 1982. [Google Scholar]
  5. Wilson, F. The distribution of terms: A defense of the traditional doctrine. Notre Dame J. Form. Log. 1987, 28, 439–454. [Google Scholar] [CrossRef]
  6. Englebretsen, G. Something to Reckon with: The Logic of Terms; Canadian Electronic Library, Books Collection; University of Ottawa Press: Ottawa, ON, Canada, 1996. [Google Scholar]
  7. Sommers, F.; Englebretsen, G. An Invitation to Formal Reasoning: The Logic of Terms; Ashgate: Farnham, UK, 2000. [Google Scholar]
  8. Englebretsen, G. Bare Facts and Naked Truths: A New Correspondence Theory of Truth; Ashgate Pub. Limited: Farnham, UK, 2006. [Google Scholar]
  9. Castro-Manzano, J.M.; Reyes-Cárdenas, P.O. Term Functor Logic Tableaux. South Am. J. Log. 2018, 4, 1–22. [Google Scholar]
  10. de Rijk, L. Peter of Spain (Petrus Hispanus Portugalensis): Tractatus: Called Afterwards Summule Logicales. First Critical ed. from the Manuscripts; van Gorcum & Co.: Assen, The Netherlands, 1972. [Google Scholar]
  11. Arnauld, A.; Nicole, P.; Buroker, J. Antoine Arnauld and Pierre Nicole: Logic Or the Art of Thinking; Cambridge Texts in the History of Philosophy; Cambridge University Press: Cambridge, UK, 1996. [Google Scholar]
  12. Keynes, J. Studies and Exercises in Formal Logic: Including a Generalisation of Logical Processes in Their Application to Complex Inferences; Macmillan: London, UK, 1887. [Google Scholar]
  13. Sommers, F. On a Fregean Dogma. In Problems in the Philosophy of Mathematics; Lakatos, I., Ed.; Studies in Logic and the Foundations of Mathematics; Elsevier: Amsterdam, The Netherlands, 1967; Volume 47, pp. 47–81. [Google Scholar] [CrossRef]
  14. Englebretsen, G. The New Syllogistic; Peter Lang: Bern, Switzerland, 1987. [Google Scholar]
  15. Englebretsen, G.; Sayward, C. Philosophical Logic: An Introduction to Advanced Topics; Bloomsbury Academic: London, UK, 2011. [Google Scholar]
  16. Quine, W.V.O. Predicate Functor Logic. In Proceedings of the Second Scandinavian Logic Symposium; Fenstad, J.E., Ed.; North-Holland: Amsterdam, The Netherlands, 1971. [Google Scholar]
  17. Noah, A. Predicate-functors and the limits of decidability in logic. Notre Dame J. Form. Log. 1980, 21, 701–707. [Google Scholar] [CrossRef]
  18. Kuhn, S.T. An axiomatization of predicate functor logic. Notre Dame J. Form. Log. 1983, 24, 233–241. [Google Scholar] [CrossRef]
  19. Sommers, F. Intelectual Autobiography. In The Old New Logic: Essays on the Philosophy of Fred Sommers; Oderberg, D.S., Ed.; Bradford Book: Cambridge, MA, USA, 2005; pp. 1–24. [Google Scholar]
  20. Bastit, M. Jan Łukasiewicz contre le dictum de omni et de nullo. Philos. Sci. 2011, 15, 55–68. [Google Scholar] [CrossRef]
  21. D’Agostino, M.; Gabbay, D.M.; Hähnle, R.; Posegga, J. Handbook of Tableau Methods; Springer: Berlin/Heidelberg, Germany, 1999. [Google Scholar]
  22. Priest, G. An Introduction to Non-Classical Logic: From If to Is; Cambridge Introductions to Philosophy; Cambridge University Press: Cambridge, UK, 2008. [Google Scholar]
  23. Hähnle, R. Tableaux and Related Methods. In Handbook of Automated Reasoning (in 2 volumes); Robinson, J.A., Voronkov, A., Eds.; Elsevier: Amsterdam, The Netherlands; MIT Press: Cambridge, MA, USA, 2001; pp. 100–178. [Google Scholar] [CrossRef]
  24. Carnap, R. Die alte und die neue Logik. Erkenntnis 1930, 1, 12–26. [Google Scholar] [CrossRef]
  25. Geach, P.T. Logic Matters; University of California Press: Berkeley, CA, USA, 1980. [Google Scholar]
First Second Third Fourth
Figure Figure Figure Figure
Proposition
1. All mammals are animals.
2. All dogs are mammals.
All dogs are animals.
Proposition TFL
1. All mammals are animals.
2. All dogs are mammals.
All dogs are animals.
Proposition Arithmetic Sum
1.
2.
Proposition Arithmetic Sum
1.
2.

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Castro-Manzano, J.-M. Distribution Tableaux, Distribution Models. Axioms 2020, 9, 41. https://doi.org/10.3390/axioms9020041

Castro-Manzano J-M. Distribution Tableaux, Distribution Models. Axioms. 2020; 9(2):41. https://doi.org/10.3390/axioms9020041

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Castro-Manzano, J.-Martín. 2020. “Distribution Tableaux, Distribution Models” Axioms 9, no. 2: 41. https://doi.org/10.3390/axioms9020041

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