Logical Analysis of Input and Output Sensitivity in the Logic of Information Flows

Abstract

The logic of information flows (LIF) is a recent framework that is used to model complex systems and understand how information propagates in such systems. These complex systems are built by combining atomic modules, which can be thought of as computational units. The computation is thus a dynamic process that takes some input and produces some output. Although the exact inputs and outputs for the atomic modules (basic computation units) are specified by the language, the inputs and outputs of the entire complex system are not defined. This brings us to the main question we want to address in this work: developing intuitive notions that define what inputs and outputs of (complex) dynamic systems are. Moreover, understanding inputs and outputs is a natural desire for logical reasoning of dynamic processes; this work is an attempt to provide solid foundations for this important problem. Furthermore, we will see that the developed input and output notions provide insights into various aspects of LIF expressions. Through inputs and outputs, we can analyze composition, which is one of the central operations for dynamic processes. Moreover, by taking inputs and outputs carefully into account, we will see that LIF provides insight in other formalisms, such as the executable fragment of first-order logic. All in all, a rigorous treatment of the fundamental notions of inputs and outputs for LIF-like dynamic logical formalisms was, to the best of our knowledge, lacking so far in the literature. In this thesis, we propose an approach to fill that gap