Digitization and reduction of old astronomical plates of na-tural satellites

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Term-guided method for defining concept

From the ISO point of view on terminology, a concept is defined as a unique combination of essential characteristics (ISO 1087-1, 2019). Nevertheless, not any combination of essential characteristics defines a meaningful concept from the expert point of view. Indeed, for the experts, concepts of interest are those that are named in a natural language. It means that a concept is a set of essential characteristics that is stable enough to be named in a given language. We can notice that some concepts, without any designation in natural language, can be introduced for organizational purposes. Hence, terms can be considered as guidelines for identifying concepts to be defined. For example, the Chinese term “椅子” ( “chair” in English) denotes the following set of essential characteristics {/seat/, /one person/, /without arms/, /with back/, /with foot/}. This unique combination of essential characteristics defines a concept whose name (identifier) in the conceptual system is built from the names of essential characteristics (the concept name is built in such a way to promote transparency of the idea the concept conveys). Based on this formal definition of concepts, we can propose the following definition of the term “chair” written in natural language in compliance with the Aristotelian definition in genus and specific differences: “Seat for one person with back, foot, and without arms”.

Ontoterminology: the example of seats

1). Identifying terms. Terms are the starting point of the ontology building process. We need to identify terms and objects denoted by terms. Terms could be either extracted from books, databases, and the internet or of course, given by experts. For our example, let us consider the terms “chair” (“chaise”), “armchair” (“fauteuil”), “stool” (“tabouret”), “couch” (“canapé”), and “bench” (“banc”) in English and French respectively.
2). Identifying essential characteristics. This step has to be achieved before defining concepts. Domain experts and epistemological principles play an essential role in this step. For example, there are many different seats in the domain of seats, such as chair, armchair, stool, couch, and bench. When we face a seating object, we need to understand it. Then select a proper language to represent it. Identifying essential characteristics also insists on epistemological principles and experts’ knowledge. From a functional point of view, when we face seat objects, it could include essential characteristics: /one person/ and /several persons/. From a structural point of view, we may partition the seat into three components: arm, back, and leg. The differences between arms are with arm, and without arm, so essential characteristics are /with arm/ and /without arm/. Essential characteristics are /with back/ and /without back/ for the back component. The essential characteristics are /with leg/ and /without leg/ for leg component. Let us note that essential characteristics of the same axis of analysis are disjoined. They could not appear in a concept at the same time because it is not logical. For example, a seat could not satisfy the two characteristics of /with arms/ and /without arms/ at the same time. Table 1 shows all the essential characteristics of the seats. Descriptive characteristics include color and weight, which could not change the chair’s nature (concept).
3). Term guided to construct concepts based on essential characteristics. Let us recall the concept definition that is a “unit of knowledge created by a unique combination of characteristics” (ISO 1087-1, 2019). Therefore, to define a concept, we need to combine essential characteristics. Table 1 shows that there are eight essential characteristics organized into four axes of analysis. If we combine all of them, the complete developed Porphyry tree owns 24 (16) terminal concepts, i.e., concepts which can be instantiated. But not all these terminal concepts are relevant in our seat example, e.g., there is no seat with arms and without back since there is no name for denoting such objects. Of course, it does not mean that it is impossible to build such seats, but in our example, we are interested only in seats designating by one of the previously identified terms. Following terms is therefore a very useful means for building concepts. For example, in the seat domain, there are five terms: “chair”, “armchair”, “stool”, “couch”, and “bench”. We only need to construct five concepts. For example, the term “chair” designates the concept <Seat for one person without arms with back with foot> defined by the unique combination of essential characteristics /for one person/, /without arms/, /with back/ and /with foot/.
4). Building ontology by tools. Step 3 focuses on constructing concepts based on essential characteristics. The main work of this step is to build ontology based on concepts by tools. For the ontoterminology approach, there is an assist tool called Tedi to build an ontology. Chapter 3.4 will present the tool to build an ontology.


Tedi, for ontoTerminology EDItor, has been developed by the Condillac research group of University Savoie Mont-Blanc (Christophe Roche). A software environment dedicated to building multilingual ontoterminology (an ontoterminology is a terminology whose conceptual system is a formal ontology)47. Tedi allows users to define formal ontologies and set of terms in different languages independently of each other. The different sets of terms are linked through the shared ontology48 , allowing to calculate equivalents automatically. Tedi enables users to export ontologies in different exchange formats (RDF/OWL, HTML, CSV). The ontoterminology includes two dimensions: the linguistic dimension and the conceptual dimension. Tedi provides a set of editors dedicated to the conceptual dimension (concept editor, object editor, characteristic editor, relation editor) and editors dedicated to the linguistic dimension (term editor, proper name editor, and feature editor.
Concept editor. Epistemological and logical principles play an essential role in ontoterminology. Under epistemological and logical principles guiding, concept editor is dedicated to ontology building and provides a set of features of the definition of essential characteristics (axes of analysis), descriptive characteristics (attributes), concepts (Figure 2.36), and relations (Figure 2.37)49.
Term editor50. The term editor is dedicated to term definition into different languages sharing the same ontology (Figure 2.38). For every language, the Term editor provides a set of features for the definition of the term itself, including the definition in natural language, contexts, and notes, term status, and PoS. It allows users to specify concept(s) denoted by terms, i.e., The meaning of the term from a terminological point of view. Meanwhile, as different terms share the same ontology, equivalent terms of different languages could be automatically identified.
Exchange format. Tedi could export different formats, such as CSV, HTML, RDF/OWL, JSON, and OTE (a complete definition of the ontoterminology in an XML format). For example, it is exported in HTML formal in French (Figure 2.39).
(Desprès et al. 2019) compared Protégé and Tedi. The example used in this study also comes from the Digital Humanities. Its purpose is to build the ontology and terminology of vases of Ancient Greece. Protégé and Tedi differ on many points that could be summarized by saying that the former is as universal as the latter is specific. Indeed, Protégé is a free, open-source software, the most widely used ontology editor, supported by a large community of users (Musen, 2015). It relies on the Description Logic for the theory of concept and on the W3C recommendations for representation languages. Protégé has a universal aim in the sense that it is not limited to the construction of ontologies for terminological purposes. On the opposite side, Tedi has not a universal purpose. It is a recent software, not in open source. Its first version dates from 2018 when Protégé dates from 1980. It is intended for experts to build ontoterminologies in accordance with the ISO principles on Terminology. Tedi relies on a theory of concept close to the understanding of domain experts. It also implements a methodology that guides experts in building ontoterminologies. Desprès et al. 2019 conclude by stating that the choice between Protégé and Tedi is made mainly based on the objectives of the project and the theory of concept.

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Table of contents :

1 Introduction and aims 
1.1 Context and aims
1.2 Notations
1.3 The manuscript
2 Ephemeris 
2.1 The different kinds of ephemerides
2.1.1 Numerical integrations
2.1.2 Analytical theories
2.1.3 Synthetic representations
2.2 Numerical ephemerides
2.2.1 Generalities (Lainey et al. 2014)
2.2.2 Ephemeris from JPL and NOE
2.3 The ephemeris TASS
2.3.1 The theory
2.3.2 Representation of TASS
2.4 Use of theses ephemerides
3 Frequencies and synthetic representation of motion 
3.1 Integrable system, quasi-periodics series and proper frequencies
3.2 The D’Alembert rule
3.3 FA: the frequency analysis
4 Context and difficulties of the realization 
4.1 Comparison in positions and elements between TASS and JPL ephemerides
4.1.1 Comparison in positions
4.1.2 Comparison in elements
4.2 The main slope in mean longitude : N and λ0
4.3 Comparison in r between TASS and JPL
4.3.1 The periodic part r = λ − Nt − λ0
4.3.2 The comparison
4.4 Correlation of λ0 with the time span
4.4.1 λ0 of TASS
4.4.2 λ0 of JPL
4.5 Conclusion
5 Extension of the frequency analysis by the least squares met-hod 
5.1 The least squares method, term by term
5.2 Reference plane and transformation error
5.3 The least squares method for several terms
6 Test of the method with TASS over 1,000 years 
6.1 Proper frequencies
6.2 Determination of the short period and semi-long period terms
6.3 Determination of the long period terms
6.4 Conclusion
7 Results for the mean longitude of Titan 
7.1 Proper frequencies in the JPL ephemeris
7.2 Determination of the short period and semi-long period terms
7.3 Determination of the long period terms
7.4 Conclusion
8 Digitization and reduction of old astronomical plates of na-tural satellites
8.1 Background
8.2 Plates
8.3 Digitization
8.3.1 Scanner
8.4 Reduction
8.5 New observed satellite astrometric positions
8.6 Comparison with theory
8.7 Conclution
9 Conclusion 
10 Appendix 
10.1 Appendix 1


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