{'fraction_non_alphanumeric': 0.028586839266450916, 'fraction_numerical': 0.0010787486515641855, 'mean_word_length': 4.741486068111455, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Toward a formal ontology of time and aspect

We present a work in the scope of formal ontologies, notion taken from the knowledge representation community. What we study is the concept of time and aspect described and conceptualized from linguistics. Our aim is thus to propose a formal ontology of time and aspect considering temporal concepts introduced in a formal way. Introduction Our aim is to precise some concepts and properties of time for building ontologies where temporal notions are essential when we take into account the evolution of objects trough time. This approach is in the scope of formal ontologies researches as developed for instance by N. Guarino’s or B. Smith. Different articles introduced temporal concepts in ontologies (i.e. GFO reusing the notions endurant and perdurant objects...), however our approach is founded on a theory of aspectuality and temporality in natural language. The basic concept of state, event and process and related concepts like sequence of events, enunciative process, continuity between resultative state and event, temporal reference systems... are useful to propose a formal ontology of time. This paper is a part of a program aimed at relating linguistic descriptions from a theoretical point of view and ontologies. The methodology The general methodology adopted in the frame of this work starts from a linguistic problem to go to a systematic analysis. The linguistic notions that we investigate are that of time and aspect. Those notions are first mathematically conceptualized (for instance topological intervals). It enables thus to visually represent them and secondly to build by abstraction a formal language ( for us, an applicative system of aspectual operators and temporal relations) which expresses aspectual and temporal operations identified in language. To summarize this general framework, we give the following diagram: Formal framework We first introduce the formal notions we use to work out the problem of time and aspectuality analysis aiming at the conceptualization and formalization of an ontology of time captured by categories of tenses and aspect in natural languages. Historically the applicative formalisms have been studied through combinatory logic, developed by Curry who introduced a logic of abstract operators and composition of them using a fundamental operation called application. The notion of functional types introduced by Church is incorporated in the applicative formalism giving the combinatory logic with types. The basic structure is thus an operator applying to an operand to build a result. However the expressivity of such formalism can be restrict by using types. Hence, the application of an operator is allowed only if takes as argument an operand with a specific type. This notion of type is introduced to characterize different classes of objects (absolute operands) and operators. We give then the explicit construction rule of functional types: [T] (1) Primitive types are Types (2) If α and β are Types, then Fαβ is a Type F is the functional type constructor. Now we introduce a typed applicative system. In such system, operators, operands and results are typed. The meaning of the type Fαβ is the following: it is a type of an operator which can be applied to an operand with the type α and the result of this application is with the type β. The application rule is given as follow: [APPt] [X: Fαβ] [Y: α] -[XY : β] We give an illustration of the formal language established to describe the time and aspect theory as presented in [Des94]. From this theoretical point of view, we assume that an utterance is the result of temporal, aspectual and Is_represented_by