Generalised geometric logic

Document Type : Research Paper


Madras School of Economics, Chennai, India



This paper introduces a notion of generalised geometric logic. Connections of generalised geometric logic with the L-topological system and L-topological space are established.


Main Subjects

[1] Chakraborty, M.K. and Jana, P., Fuzzy topology via fuzzy geometric logic with graded consequence, Int. J. Approx. Reasoning 80 (2017), 334-347.
[2] Chang, C.L., Fuzzy topological spaces, J. Math. Anal. Appl. 24 (1968), 182-190.
[3] Das, R. and Jana, P., Generalised Geometric Logic: A Logic for expressing a Neural Network Architecture (submitted).
[4] Denniston, J.T., Melton, A., and Rodabough, S.E., Interweaving algebra and topology: Lattice-valued topological systems, Fuzzy Sets and Systems 192 (2012), 58-103.
[5] Hajek, P., “Mathematics of Fuzzy Logic”, Kluwer Academic Publishers, 1998.
[6] Healy, M.J., Continuous functions and neural network semantics, Nonlinear Anal. 30(3) (1997), 1335-1341.
[7] H¨ohle, U., Fuzzy topologies and topological space objects in a topos, Fuzzy Sets and Systems 19 (1986), 299-304.
[8] Hwang, N., Jana, P., and Parikh, R., Ethical agents, The 34th Stony Brook International Conference on Game Theory, July 24-27, 2023.
[9] Jana, P., Topological systems, Topology and Frame: in fuzzy context, Reminiscing Ideas and Interactions, Essays in honour of Mihir Kr. Chakraborty, Calcutta Logic Circle, Kolkata, 2011, p. 142.
[10] Jana, P. and Chakraborty, M.K., Categorical relationships of fuzzy topological systems with fuzzy topological spaces and underlying algebras, Ann. of Fuzzy Math. and Inform. 8(5) (2014), 705-727.
[11] Johnstone, P.T., “Sketches of an Elephant: A Topos Theory Compendium”, Oxford Logic Guides, Oxford University Press, 2(44), 2002.
[12] Johnstone, P.T., “Topos Theory”, Academic Press, 1977.
[13] Mac Lane, S. and Moerdijk, I., “Sheaves in Geometry and Logic”, Springer Verlag, 1992.
[14] Nov´ak, V., Perfilieva, I., and Moˇckoˇr, J., “Mathematical Principles of Fuzzy Logic”, Kluwer, 1999.
[15] Nov´ak, V., First order fuzzy logic, Studia Logica 46 (1987), 87-109.
[16] Pavelka, J., On fuzzy logic, Z. Math. Logik. Grud. Math. 25(1) 45-52.
[17] Solovyov, S., Variable-basis topological systems versus variable-basis topological spaces, Soft Comput. 14(10) (2010), 1059-1068.
[18] Vickers, S.J., Geometric Logic in Computer Science, in: Proceedings of the First Imperial College Department of ComputingWorkshop on Theory and Formal Methods, Springer-Verlag, (1993), 37-54.
[19] Vickers, S.J., Issues of logic, algebra and topology in ontology, in: R. Poli, M. Healy, A. Kameas (Eds.), Theory and Applications of Ontology: Computer Applications, volume 2 of Theory and Applications of Ontology, 2010.
[20] Vickers, S.J., “Topology via Constructive Logic”, in Logic, Language and Computation, 1999.
[21] Vickers, S.J., “Topology Via Logic”, 5, Cambridge Tracts Theoret. Comput. Sci., 1989.
[22] Zadeh, L.A., Fuzzy sets, Information and Control 8 (1965), 338-353.