Analýza událostí a jejich temporálních aspektů s využitím Transparentní intensionální logiky

Abstract

Logic, in its basic forms, such as the systems of propositional or predicate logic, makes it possible to formalize a static view of a static universe. Predicates usually express the attribution of a property or a relationship to individuals in a particular world and time. However, it is desirable that logic should also make it possible to formalize dynamic changes of these attributions throughout a time-span.

This thesis applies the system of Transparent Intensional Logic (TIL) to capture those temporal aspects of events. TIL is a logical system that has undergone considerable development, especially in the area of natural language processing and analysis. It is a hyperintensional, typed λ-calculus that operates on partial functions. TIL is equipped with two independent modal parameters, namely possible worlds (type ω) and times (type τ), and methods for formalizing and reasoning with tenses of verbs and episodic events have been developed within TIL.

The thesis adheres to these foundations, and its goal is to further develop the theory of dynamic reasoning in two basic aspects. The first is a formal representation of time objects, based on the expressions that are commonly used in natural language, and relationships between these objects. This concerns in particular time points, time intervals, time periods, calendar dates, related calendar objects, and the associated phenomena such as daylight-saving time or time zones. The second aspect is formal representation of processes in TIL with focus on capturing the sequences in which process activities occur in time. This corresponds to the methods as applied in common graphical tools for process modelling. The result is an interphase between the TIL process model and the TIL ontologies, including constraints.

For a suitable formalization of time objects, this work is inspired by the methods applied in temporal modal logics. However, it makes in particular use of the representation of time objects in programming languages and in the formal system Process Specification Language (PSL), which, like TIL, formalizes time aspects of events in the form of a time argument (in contrast to modal logics that formalize time using a modal operator).

The main advantage of the proposed approach is a clear link between different types of objects (due to applying higher order functions). The primitive language term "year" corresponding to time duration is used to analyse more complex language expressions such as "2017 years", "year 2017", "the first moment of the year 2017" and "January 1st, 2017". The expressive power and flexibility of TIL is exploited in modelling time intervals and relationships between them in a fine-grained way.

The proposed process notation is then based on the analysis of several well-known visual notations and the PSL notation. Based on the common features of these notations, the thesis proposes a process notation designed for TIL. To illustrate the applicability of this proposed notation, a method of translation of processes recorded in the form of a UML activity diagram to the process notation proposed in this work is described. The resulting system of TIL constructions is then merged with an ontology formalized in TIL (either directly in TIL or by translation from another form of representation), and the way of deducing new pieces of analytic information from this combined logical theory is demonstrated.