Descriptive Complexity, Computational Tractability, and the Logical and Cognitive Foundations of Mathematics

In computational complexity theory, decision problems are divided into complexity classes based on the amount of computational resources it takes for algorithms to solve them. In theoretical computer science, it is commonly accepted that only functions for solving problems in the complexity class P, solvable by a deterministic Turing machine in polynomial time, are considered to be tractable. In cognitive science and philosophy, this tractability result has been used to argue that only functions in P can feasibly work as computational models of human cognitive capacities. One interesting area of computational complexity theory is descriptive complexity, which connects the expressive strength of systems of logic with the computational complexity classes. In descriptive complexity theory, it is established that only first-order (classical) systems are connected to P, or one of its subclasses. Consequently, second-order systems of logic are considered to be computationally intractable, and may therefore seem to be unfit to model human cognitive capacities. This would be problematic when we think of the role of logic as the foundations of mathematics. In order to express many important mathematical concepts and systematically prove theorems involving them, we need to have a system of logic stronger than classical first-order logic. But if such a system is considered to be intractable, it means that the logical foundation of mathematics can be prohibitively complex for human cognition. In this paper I will argue, however, that this problem is the result of an unjustified direct use of computational complexity classes in cognitive modelling. Placing my account in the recent literature on the topic, I argue that the problem can be solved by considering computational complexity for humanly relevant problem solving algorithms and input sizes.Peer reviewe

Listen to me! Public announcements to agents that pay attention - or not

International audienceIn public announcement logic it is assumed that all agents pay attention (listen to/observe) to the announcement. Weaker observational conditions can be modelled in event (action) model logic. In this work, we propose a version of public announcement logic wherein it is encoded in the states of the epistemic model which agents pay attention to the announcement. This logic is called attention-based announcement logic, abbreviated ABAL. We give an axiomatization and prove that complexity of satisfiability is the same as that of public announcement logic, and therefore lower than that of action model logic [2]. We exploit our logic to formalize the concept of joint attention that has been widely discussed in the philosophical and cognitive science literature. Finally, we extend our logic by integrating attention change

31th International Conference on Information Modelling and Knowledge Bases

Information modelling is becoming more and more important topic for researchers, designers, and users of information systems.The amount and complexity of information itself, the number of abstractionlevels of information, and the size of databases and knowledge bases arecontinuously growing. Conceptual modelling is one of the sub-areas ofinformation modelling. The aim of this conference is to bring together experts from different areas of computer science and other disciplines, who have a common interest in understanding and solving problems on information modelling and knowledge bases, as well as applying the results of research to practice. We also aim to recognize and study new areas on modelling and knowledge bases to which more attention should be paid. Therefore philosophy and logic, cognitive science, knowledge management, linguistics and management science are relevant areas, too. In the conference, there will be three categories of presentations, i.e. full papers, short papers and position papers

30th International Conference on Information Modelling and Knowledge Bases

Information modelling is becoming more and more important topic for researchers, designers, and users of information systems. The amount and complexity of information itself, the number of abstraction levels of information, and the size of databases and knowledge bases are continuously growing. Conceptual modelling is one of the sub-areas of information modelling. The aim of this conference is to bring together experts from different areas of computer science and other disciplines, who have a common interest in understanding and solving problems on information modelling and knowledge bases, as well as applying the results of research to practice. We also aim to recognize and study new areas on modelling and knowledge bases to which more attention should be paid. Therefore philosophy and logic, cognitive science, knowledge management, linguistics and management science are relevant areas, too. In the conference, there will be three categories of presentations, i.e. full papers, short papers and position papers

Organizational settlements: theorizing how organizations respond to institutional complexity

Research on hybrid organizations and institutional complexity commonly depicts the presence of multiple logics within organizations as an exceptional situation. In this essay, we argue that all organizations routinely adhere to multiple institutional logics. Institutional complexity only arises episodically, when organizations embrace a newly salient logic. We propose two concepts to develop this insight. First, we suggest the notion of organizational settlement to refer to the way in which organizations durably incorporate multiple logics. Second, we define organizational hybridization as a change process whereby organizations abandon their existing organizational settlement and transition to a new one, incorporating a newly salient logic. Overall, we propose a shift in attention from the exceptionality of hybrid configurations of multiple logics towards exploring the dynamics of transitions from one state of complexity to another

Fundamental Principles of Neural Organization of Cognition

The manuscript advances a hypothesis that there are few fundamental principles of neural organization of cognition, which explain several wide areas of the cognitive functioning. We summarize the fundamental principles, experimental, theoretical, and modeling evidence for these principles, relate them to hypothetical neural mechanisms, and made a number of predictions. We consider cognitive functioning including concepts, emotions, drives-instincts, learning, “higher” cognitive functions of language, interaction of language and cognition, role of emotions in this interaction, the beautiful, sublime, and music. Among mechanisms of behavior we concentrate on internal actions in the brain, learning and decision making. A number of predictions are made, some of which have been previously formulated and experimentally confirmed, and a number of new predictions are made that can be experimentally tested. Is it possible to explain a significant part of workings of the mind from a few basic principles, similar to how Newton explained motions of planets? This manuscript summarizes a part of contemporary knowledge toward this goal

Nature as a Network of Morphological Infocomputational Processes for Cognitive Agents

This paper presents a view of nature as a network of infocomputational agents organized in a dynamical hierarchy of levels. It provides a framework for unification of currently disparate understandings of natural, formal, technical, behavioral and social phenomena based on information as a structure, differences in one system that cause the differences in another system, and computation as its dynamics, i.e. physical process of morphological change in the informational structure. We address some of the frequent misunderstandings regarding the natural/morphological computational models and their relationships to physical systems, especially cognitive systems such as living beings. Natural morphological infocomputation as a conceptual framework necessitates generalization of models of computation beyond the traditional Turing machine model presenting symbol manipulation, and requires agent-based concurrent resource-sensitive models of computation in order to be able to cover the whole range of phenomena from physics to cognition. The central role of agency, particularly material vs. cognitive agency is highlighted