Who Cares about Axiomatization? Representation, Invariance, and Formal Ontologies

The philosophy of science of Patrick Suppes is centered on two important notions that are part of the title of his recent book (Suppes 2002): Representation and Invariance. Representation is important because when we embrace a theory we implicitly choose a way to represent the phenomenon we are studying. Invariance is important because, since invariants are the only things that are constant in a theory, in a way they give the “objective” meaning of that theory. Every scientific theory gives a representation of a class of structures and studies the invariant properties holding in that class of structures. In Suppes’ view, the best way to define this class of structures is via axiomatization. This is because a class of structures is given by a definition, and this same definition establishes which are the properties that a single structure must possess in order to belong to the class. These properties correspond to the axioms of a logical theory. In Suppes’ view, the best way to characterize a scientific structure is by giving a representation theorem for its models and singling out the invariants in the structure. Thus, we can say that the philosophy of science of Patrick Suppes consists in the application of the axiomatic method to scientific disciplines. What I want to argue in this paper is that this application of the axiomatic method is also at the basis of a new approach that is being increasingly applied to the study of computer science and information systems, namely the approach of formal ontologies. The main task of an ontology is that of making explicit the conceptual structure underlying a certain domain. By “making explicit the conceptual structure” we mean singling out the most basic entities populating the domain and writing axioms expressing the main properties of these primitives and the relations holding among them. So, in both cases, the axiomatization is the main tool used to characterize the object of inquiry, being this object scientific theories (in Suppes’ approach), or information systems (for formal ontologies). In the following section I will present the view of Patrick Suppes on the philosophy of science and the axiomatic method, in section 3 I will survey the theoretical issues underlying the work that is being done in formal ontologies and in section 4 I will draw a comparison of these two approaches and explore similarities and differences between them

The NEXT double beta decay experiment

NEXT (Neutrino Experiment with a Xenon TPC) aims to observe the neutrinoless double beta decay of \ensuremath{{}^{136}\rm Xe} in a high-pressure gas xenon Time Projection Chamber using electroluminescence to amplify the signal from ionization. The two main advantages of this technology are a high energy resolution and the possibility of reconstructing electron tracks. NEXT-100 is an electroluminescent, asymmetric TPC which will host 100 kg of the \ensuremath{{}^{136}\rm Xe} isotope at 15 bar of pressure. On one side, a sparse array of photomultipliers records both the primary scintillation signal, which gives the starting time of the event, and electroluminescence, which gives a precise measurement of the total deposited energy. On the other side, a dense grid of silicon photomultipliers provides the reconstruction of the electron tracks. Being able to reconstruct the position of a track is doubly useful: on the one hand, it allows the correction of the energy of the event, which varies according to position, and on the other hand it provides an extra handle for background rejection, since a two-electron track shows higher energy density at both ends, while a single-electron track only at one end. After a prototyping period (2009-2014) NEXT has completed the construction and started the operation of its first phase (NEW) in the Laboratorio Subterr\'aneo de Canfranc, in the Spanish Pyrenees, with the objectives of measuring the NEXT background model and the two-neutrino mode of the double beta decay.Comment: Proceedings of EPS-HEP 2017, Venice (Italy), July 201

Transitive decomposition of symmetry groups for the nn-body problem

Periodic and quasi-periodic orbits of the $n$-body problem are critical points of the action functional constrained to the Sobolev space of symmetric loops. Variational methods yield collisionless orbits provided the group of symmetries fulfills certain conditions (such as the \emph{rotating circle property}). Here we generalize such conditions to more general group types and show how to constructively classify all groups satisfying such hypothesis, by a decomposition into irreducible transitive components. As examples we show approximate trajectories of some of the resulting symmetric minimizers