The research proposal Quanto-Metric aims to explore the conceptual foundations and the inner architecture of Quantum Mechanics, by widening our research vision and incorporating methods and techniques used by other disciplines. Our point of departure is relational logic, as it is developed by C. S. Peirce during the years 1870-1880. All essential laws of Quantum Mechanics (the probability rule, the commutation rules) are derived then from the relational logic of Peirce. The double line representation of relations leads to the depiction of the quantum logical process as a 'stringy' geometry. This geometry is reminiscent of the Regge's discrete version of Riemannian geometry, of Penrose's spin networks and of the geometrogenesis models developed by Markopoulou. The project leads to a deeper and more integrated understanding of the quantum realities, and for the first time Logic, Quantum Mechanics, String Theory, Geometry, are brought together. The concrete outputs of the project include i) at least 3 peer reviewed research papers, to be published in scientific journals ii) two review articles, including the logical, philosophical and theological implications of our relational approach iii) dissemination of the research results by presenting them in scientific meetings and in conferences for the broad public. The expected outcome will be the elaboration of a new paradigm, inspired by relational and categorical principles, and qualified as synthetic, holistic, geometric. Within the new paradigm it would be possible to formulate novel ways of inquiry and analysis. The project will favor the search for new logical syntaxes and will have as an enduring impact to view logic as an experimental science and science as a logic argument.