Abstract
We present a sequent calculus for extensional mereology. It extends the classical first-order sequent calculus with identity by rules of inference corresponding to well-known mereological axioms. Structural rules, including cut, are admissible.
Similar content being viewed by others
References
Cotnoir A., Bacon B.: Non-wellfounded mereology. The Review of Symbolic Logic 5(2), 187–204 (2012)
Davey, B. A., and H. A. Priestley, Introduction to Lattices and Order, Cambridge University Press, Cambridge, 1990.
Gentzen, G., New version of the consistency proof for elementary number theory, in M. E. Sazbo, (ed.), The Collected Papers of Gerhard Gentzen, chap. 8, North-Holland, Amsterdam, 1969, pp. 252–286.
Hovda P.: What is classical mereology?. Journal of Philosophical Logic 38(1), 55–82 (2009)
Leonard, H., and N. Goodman, The calculus of individuals and its uses, The Journal of Symbolic Logic 5(2):45–55, 1940.
Negri, S., Contraction-free sequent calculi for geometric theories with an application to Barr’s theorem, Archive for Mathematical Logic 42(4):389–401, 2003.
Negri S.: Proof analysis in modal logic. Journal of Philosophical Logic 34(5–6), 507–544 (2005)
Negri, S., Proof analysis beyond geometric theories: From rule systems to systems of rules, Journal of Logic and Computation, first published online, 2014.
Negri, S., and J. von Plato, Cut elimination in the presence of axioms, Bulletin of Symbolic Logic 4(4):418–435, 1998.
Negri, S., and J. von Plato, Structural Proof Theory, Cambridge University Press, Cambridge, 2001.
Negri, S., and J. von Plato, Proof Analysis: A Contribution to Hilbert’s Last Problem, Cambridge University Press, Cambridge, 2011.
Simons P.: Parts. A Study in Ontology. Clarendon Press, Oxford (1987)
Takeuti, G., Proof Theory, North-Holland, Amsterdam, 1975.
Tennant, N., Ultimate normal forms for parallelized natural deductions, Logic Journal of the IGPL 10(3):299–337, 2002.
Tennant, N., Parts, classes and Parts of Classes: An anti-realist reading of Lewesian mereology, Synthese 190(4):709–742, 2013.
Troelstra A. S., Schwichtemberg H.: Basic Proof Theory, 2nd edn. Cambridge University Press, Cambridge (2000)
Varzi, A., Mereology, The Stanford Encyclopedia of Philosophy, 2014.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Maffezioli, P. Analytic Rules for Mereology. Stud Logica 104, 79–114 (2016). https://doi.org/10.1007/s11225-015-9623-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11225-015-9623-2