Defining Measures in a Mereological Space (an exploratory paper)

Giuseppina Barbieri, Giangiacomo Gerla



We explore the notion of a measure in a mereological structure and we deal with the difficulties arising. We show that measure theory on connection spaces is closely related to measure theory on the class of ortholattices and we present an approach akin to Dempster’s and Shafer’s. Finally, the paper contains some suggestions for further research.


connection structures; measures; mereological space; mereology; region-based theories of space

Full Text:



Arntzenius, F., “Gunk, topology, and measure”, pages 225–247 in D. Zimmerman (ed.), Oxford Studies in Metaphysics, vol. 4, Oxford: Oxford University Press, 2008. Also: “Gunk, topology and measure”, pages 327–343, Chapter 16, in D. DeVidi, M. Hallett and P. Clark (eds.), Logic, Mathematics, Philosophy: Vintage Enthusiasms. Essays in Honour of John L. Bell, vol. 75 of series “The Western Ontario Series in Philosophy of Science”, Springer, 2011. DOI:

Arntzenius, F., Space, Time, and Stuff, Oxford: Oxford University Press, 2012. DOI:

Barbieri, G., and G. Gerla, “Measures in Euclidean point-free space” (in progress).

Biacino, L., and G. Gerla, “Connection structures”, Notre Dame Journal of Formal Logic 32, 2 (1991): 242–247. DOI:

Clarke, B., “A calculus of individuals based on connnection”, Notre Dame Journal of Formal Logic 22, 3 (1981): 204–218.

Clarke, B., “Individuals and points”, Notre Dame Journal of Formal Logic 26, 1 (1985): 61–75. DOI:

Dempster, A.P., “Upper and lower probabilities induced by a multivalued mapping”, Ann. Math. Stat. 38 (1967): 325–339.

Dempster, A.P., “A generalization of Bayesian inference”, Journal of the Royal Statistical Society, Series B 30 (1968): 205–247.

Gerla, G., and R. Gruszczyński, “Point-free geometry, ovals, and half-planes”, Rev. Symb. Log. 10, 2 (2017): 237–258. DOI:

Gruszczyński, R., and A. Pietruszczak, “The relations of supremum and mereological sum in partially ordered sets”, pages 105–122 in C. Calosi and P. Graziani (eds.), Mereology and the Science, Parts and Wholes in the Contemporary Scientific Context, vol. 371 of Synthese Library, Springer, 2014. DOI:

Gruszczyński, R., and A. Varzi, “Mereology then and now”, Logic and Logical Philosophy 24 (2015): 409–427. DOI:

Horn, A., and A. Tarski, “Measures in Boolean algebras”, Transactions of the American Mathematical Society 64, 3 (1948): 467–497. DOI:

Lando, T., and D. Scott, “A calculus of regions respecting both measure and topology”, Journal of Philosophical Logic 14 (2019): 825–850. DOI:

Leśniewski, S., “On the foundations of mathematics”, Translated from the Polish and with an introduction by Vito F. Sinisi, Topoi 2, 1 (1983): 3–52.

Pietruszczak, A., Metamereology, Toruń: The Nicolaus Copernicus University Scientific Publishing House, 2018. DOI:

Pietruszczak, A., Foundations of the Theory of Parthood. A Study of Mereology, vol. 54 of series “Trends in Logic”, Springer International Publishing, 2020. DOI:

Roeper, P., “Region-based topology”, Journal of Philosophical Logic 26 (1997): 251–309. DOI:

Russell, J., “The structure of gunk: Adventures in the ontology of space”, pages 248–274 in Oxford Studies in Metaphysics, vol. 4, Oxford: Oxford University Press, 2008.

Shafer, G., A Mathematical Theory of Evidence, Princeton University Press, 1976. DOI:

Tarski, A., “Les fondaments de la géométrie des corps”, pages 29–33 in Księga Pamiątkowa Pierwszego Polskiego Zjazdu Matematycznego, suplement to Annales de la Société Polonaise de Mathématique, Kraków, 1929.

Whitehead, A.N., An Enquiry Concerning the Principles of Natural Knowledge, Cambridge University Press, 1919.

Whitehead, A.N., The Concept of Nature, Cambridge University Press, 1920. DOI:

Whitehead, A.N., Process and Reality, New York: The Macmillan Co., 1929.

ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

Partnerzy platformy czasopism