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Bilateralism in Proof-Theoretic Semantics

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Abstract

The paper suggests a revision of the notion of harmony, a major necessary condition in proof-theoretic semantics for a natural-deduction proof-system to qualify as meaning conferring, when moving to a bilateral proof-system. The latter considers both forces of assertion and denial as primitive, and is applied here to positive logics, lacking negation altogether. It is suggested that in addition to the balance between (positive) introduction and elimination rules traditionally imposed by harmony, a balance should be imposed also on: (i) negative introduction and elimination rules, and (ii) positive and negative introduction rules. The paper suggests a proof-theoretical definition of duality (not referring to truthtables), using which double harmony is defined. The paper proves that in a doubly-harmonious system, the coordination rule, typical to bilateral systems, is admissible.

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References

  1. Davies, R., & Pfenning, F. (2001). A modal analysis of staged computation. Journal of the ACM, 48(3), 555–604.

    Article  Google Scholar 

  2. Dummett, M. (1991). The logical basis of metaphysics. Cambridge, MA: Harvard University Press.

    Google Scholar 

  3. Francez, N., & Ben-Avi, G. (2011). Proof-theoretic semantic values for logical operators. Review of Symbolic Logic, 4(3), 337–485.

    Article  Google Scholar 

  4. Francez, N., & Dyckhoff, R. (2010). Proof-theoretic semantics for a natural language fragment. Linguistics and Philosophy, 33(6), 447–477.

    Article  Google Scholar 

  5. Francez, N., & Dyckhoff, R. (2012). A note on harmony. Journal of Philosophical Logic, 41(3), 613–628.

    Article  Google Scholar 

  6. Hjortland, O.T. (2009). The structure of logical consequence: proof-theoretic conceptions. PhD thesis, University of St Andrews.

  7. Humberstone, L. (2000). The revival of rejective negation. Journal of Philosophical Logic, 29(4), 331–381.

    Article  Google Scholar 

  8. Incurvati, L., & Smith, P. (2010). Rejection and valuations. Analysis, 70(1), 3–10.

    Article  Google Scholar 

  9. Incurvati, L., & Smith, P. (2012). Is ‘no’ a force-indicator? Sometimes, possibly. Analysis, 72(2), 225–231.

    Article  Google Scholar 

  10. Moortgat, M. (1997). Categorial type logics. In J. van Benthem, & A. ter Meulen (Eds.), Handbook of logic and language (pp. 93–178). North Holland.

  11. Negri, S. (2002). A normalizing system of natural deduction for intuitionistic linear logic. Archive for Mathematical Logic, 41, 789–810.

    Article  Google Scholar 

  12. Pfenning, F., & Davies, R. (2001). A judgmental reconstruction of modal logic. Mathematical Structures in Computer Science, 11, 511–540.

    Article  Google Scholar 

  13. Prawitz, D. (1965). Natural deduction: A proof-theoretical study. Stockholm: Almqvist and Wicksell. Soft cover edition by Dover, 2006.

    Google Scholar 

  14. Prior, A.N. (1960). The runabout inference-ticket. Analysis, 21, 38–39.

    Article  Google Scholar 

  15. Restall, G. (2005). Multiple conclusions. In In 12th international congress on logic, methodology and philosophy of science (pp. 189–205).

  16. Restall, G. (2008). Assertion, denial and non-classical theories. In In proceedings of the fourth world congress of paraconsistency, Melbourne.

  17. Rumfitt, I. (2000). ‘yes’ and ‘no’. Mind, 169(436), 781–823.

    Article  Google Scholar 

  18. Rumfitt, I. (2008). Co-ordination principles: a reply. Mind, 117(468), 1059–1063.

    Article  Google Scholar 

  19. Schroeder-Heister, P. (1984). A natural extension of natural deduction. Journal of Symbolic Logic, 49, 1284–1300.

    Article  Google Scholar 

  20. Tranchini, L. (2010). Refutations: a proof-theoretic account In C. Marletti (Ed.), First Pisa colloquium on logic, language and epistemology (pp. 133–150). Pisa: ETS.

    Google Scholar 

  21. von Plato, J. (2001). Natural deduction with general elimination rules. Archive for Mathematical Logic, 40, 541–567.

    Article  Google Scholar 

  22. Wieckowski, B. (2011). Rules for subatomic derivation. Review of Symbolic Logic, 4(2), 219–236.

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Computer Science Dept., The Technion-IIT, Haifa, Israel

    Nissim Francez

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  1. Nissim Francez
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Correspondence to Nissim Francez.

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Francez, N. Bilateralism in Proof-Theoretic Semantics. J Philos Logic 43, 239–259 (2014). https://doi.org/10.1007/s10992-012-9261-3

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  • DOI: https://doi.org/10.1007/s10992-012-9261-3

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