Classical systems of mereology identify a maximuml set of jointly exhaustive and pairwise disjoint (RCC5) relations. The amount of information that is carried by each member of this set of (crisp) relations is determined by the number of bits of information that are required to distinguish all the members of the set. It is postulated in this paper, that vague mereological relations are limited in the amount of information they can carry. That is, if a crisp mereological relation can carry N bits of information, then a vague mereological relation can carry only bits. The aim of this paper is it to explore these ideas in the context of various systems of vague mereological relations. The resulting formalism is non-classical in the sense of quantum information theory.
Arntzenius, F. (2012). Space, Time, & Stuff. Oxford Univ. Press.
2.
Balashov, Y. (2004). Special relativity, coexistence and temporal parts: A reply to Gilmore. http://philsci-archive.pitt.edu/1872/.
3.
Ballarin, C. (2017). HOL/Algebra/Lattice.thy.
4.
Beltrametti, E.G., Cassinelli, G. & Carruthers, P.A. (1984). The Logic of Quantum Mechanics. Encyclopedia of Mathematics and Its Applications (Vol. 15). Cambridge University Press. doi:10.1017/CBO9781107340725.
5.
Bennett, B., Mallenby, D. & Third, A. (2008). An ontology for grounding vague geographic terms. In C.Eschenbach and M.Gruninger (Eds.), Proceedings of the 5th International Conference on Formal Ontology in Information Systems (FOIS-08). IOS Press.
6.
Bittner, T. (2023). Quantum mereology. Under revision.
7.
Bittner, T. & Stell, J.G. (1998). A boundary-sensitive approach to qualitative location. Annals of Mathematics and Artificial Intelligence, 24, 93–114. doi:10.1023/A:1018945131135.
8.
Borsuk, K. & Szmielew, W. (1960). Foundations of Geometry. Amsterdam: North-Holland Publishing Company.
9.
Brading, K.A. & Castellani, E. (2002). Symmetries in physics: Philosophical reflections. http://philsci-archive.pitt.edu/926/.
10.
Brukner, C., Zukowski, M. & Zeilinger, A. (2001). The essence of entanglement. arXiv:quant-ph/0106119.
11.
Burrough, P. & Frank, A.U. (Eds.) (1995). Geographic Objects with Indeterminate Boundaries. GISDATA Series II. London: Taylor and Francis.
12.
Calosi, C., Fano, V. & Tarozzi, G. (2011). Quantum ontology and extensional mereology. Foundations of Physics, 41(11), 1740. doi:10.1007/s10701-011-9590-z.
13.
Calosi, C. & Tarozzi, G. (2014). Parthood and composition in quantum mechanics. In C.Calosi and P.Graziani (Eds.), Mereology and the Sciences: Parts and Wholes in the Contemporary Scientific Context (pp. 53–84). Cham Springer International Publishing. doi:10.1007/978-3-319-05356-1.
14.
Chen, L. & Chen, Y.-X. (2006). Classification of GHZ-type, W-type, and GHZ-W-type multiqubit entanglement. Phys. Rev. A, 74. doi:10.1103/PhysRevA.74.062310.
15.
Ciardelli, I. (2018). Questions as information types. Synthese, 195(1), 321–365. doi:10.1007/s11229-016-1221-y.
16.
Cohn, A.G., Bennett, B., Goodday, J. & Gotts, N. (1997). Qualitative spatial representation and reasoning with the region connection calculus. Geoinformatica, 1(3), 1–44. doi:10.1023/A:1009712514511.
17.
Cohn, A.G. & Gotts, N.M. (1996). The ‘egg-yolk’ representation of regions with indeterminate boundaries. In P.Burrough and A.U.Frank (Eds.), Geographic Objects with Indeterminate Boundaries. GISDATA Series II (pp. 171–187). London: Taylor and Francis.
18.
Cohn, A.G. & Hazarika, S.M. (2001). Qualitative spatial representation and reasoning: An overview. Fundamenta Informaticae, 46(1–2), 1–29.
19.
Cohn, A.G., Randell, D.A. & Cui, Z. (1995). Taxonomies of logically defined qualitative spatial relations. International Journal of Human Computer Studies, 43, 831–846. doi:10.1006/ijhc.1995.1077.
20.
Cristani, M., Cohn, A.G. & Bennett, B. (2000). Spatial locations via morpho-mereology. In Proceedings of KR ’2000.
21.
Dirac, P. (1930). Principles of Quantum Mechanics. Oxford: Clarendon Press.
22.
Donnelly, M. (2022). Mereological vagueness and existential vagueness. Synthese, 168, 53–79. doi:10.1007/s11229-008-9312-z.
23.
Earman, J. (2002). Laws, symmetry, and symmetry breaking; invariance, conservation principles, and objectivity. http://philsci-archive.pitt.edu/878/.
24.
Einstein, A. (1951). Relativity: The Special and the General Theory. New York: Crown Publishers Inc.
25.
Ellerman, D. (2022). Follow the Math!: The mathematics of quantum mechanics as the mathematics of set partitions linearized to (Hilbert) vector spaces. Foundations of Physics, 52(5). doi:10.1007/s10701-022-00608-3.
26.
Fine, K. (1975). Vagueness, truth and logic. Synthese, 30, 265–300.
27.
Griffiths, D.J. (2004). Introduction to Quantum Mechanics. Addison Wesley.
28.
Grinbaum, A. (2005). Information-theoretic principle entails orthomodularity of a lattice. Foundations of Physics Letters, 18(6), 563–572. doi:10.1007/s10702-005-1129-0.
29.
Groenendijk, J.A.G. (2003). Questions and answers: Semantics and logic. In R.Bernardi and M.Moortgat (Eds.), Proceedings of the 2nd CologNET-ElsET Symposium. Questions and Answers: Theoretical and Applied Perspectives (pp. 16–23).
30.
Hilbert, D. (1924). Die Grundlagen der Physik. Mathematische Annalen, 92(1–2), 1–32. doi:10.1007/BF01448427.
31.
Hilbert, D. (2005). The Foundations of Geometry. Project Gutenberg.
32.
Hintikka, J. (1962). Knowledge and Belief: An Introduction to the Logic of the Two Notions. Contemporary Philosophy. Cornell University Press. https://books.google.com/books?id=N28OAAAAIAAJ.
33.
Klein, F. (1872). Vergleichende Betrachtungen über neuere geometrische Forschungen. Erlangen: A. Deichert.
34.
Kofler, J. & Zeilinger, A. (2013). Quantum information and randomness. arXiv:1301.2515.
35.
Maplesoft, a division of Waterloo Maple Inc. (2020). Maple (2020.2).
36.
Maudlin, T. (1998). Part and whole in quantum mechanics. In E.Castellani (Ed.), Interpreting Bodies: Classical and Quantum Objects in Modern Physics. Princeton University Press.
37.
Paulson, L.C. (1994). Isabelle: A Generic Theorem Prover. Springer.
38.
Redhead, M. (1995). From Physics to Metaphysics. Cambridge University Press.
39.
Romero, G.E. (2012). Philosophical problems of space-time theories. In Gravitation and Cosmology.
40.
Rovelli, C. (1996). Relational quantum mechanics. Int. J. Theor. Phys., 35, 1637–1678. doi:10.1007/BF02302261.
41.
Roy, A.J. & Stell, J.G. (2001). Spatial relations between indeterminate regions. International Journal of Approximate Reasoning, 205–234. doi:10.1016/S0888-613X(01)00033-0.
42.
Santos, P., Bennett, B. & Sakellariou, G. (2005). Supervaluation semantics for an inland water feature ontology. In L.P.Kaelbling and A.Saffiotti (Eds.), Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI-05) (pp. 564–569). Edinburgh: Professional Book Center. http://ijcai.org/papers/1187.pdf.
43.
Shannon, C.E. (1948). A mathematical theory of communication. The Bell System Technical Journal, 27(3), 379–423. doi:10.1002/j.1538-7305.1948.tb01338.x.
44.
Simons, P. (1987). Parts, a Study in Ontology. Oxford: Clarendon Press.
45.
Simons, P. (1991). Part/whole II: Mereology since 1900. In H.Burkhardt and B.Smith (Eds.), Handbook of Metaphysics and Ontology (pp. 673–675). Muenchen: Philosophia.
46.
Smith, B. & Brogaard, B. (2002). Quantum mereotopology. Annals of Mathematics and Artificial Intelligence, 35(1–2).
47.
Teller, P. (1997). An Interpretative Introduction to Quantum Field Theory. Princeton University Press.
48.
Timpson, C.G. (2006). Philosophical aspects of quantum information theory. arXiv e-prints. arXiv:quant-ph/0611187.
49.
Varzi, A. (2000). Mereological commitments. Dialectica, 54(4), 283–305. doi:10.1111/j.1746-8361.2000.tb00286.x.
50.
Varzi, A. (2003). Mereology. E.N.Zalta (Ed.), Stanford Encyclopedia of Philosophy. Stanford: CSLI(internet publication).
51.
Varzi, A.C. (1998). Basic problems of mereotopology. In N.Guarino (Ed.), Formal Ontology in Information Systems (pp. 29–38).
52.
von Neumann, J. (1932). Mathematical Foundations of Quantum Mechanics. Springer.
53.
Wheeler, J.A. (1989). Information, physics, quantum: The search for links. In Proceedings III International Symposium on Foundations of Quantum Mechanics (pp. 354–358). Physics Department, Princeton University.
54.
Williamson, T. (1994). Vagueness. Routledge.
55.
Zeilinger, A. (1999). A foundational principle for quantum mechanics. Foundations of Physics, 29(4), 631–643. doi:10.1023/A:1018820410908.
