Viability theory is an area of mathematics that studies the evolution of dynamical systems under constraints on the system state.[1][2] It was developed to formalize problems arising in the study of various natural and social phenomena, and has close ties to the theories of optimal control and set-valued analysis.
Theory of Constraints - The Decision Lab
The theory of constraints is a systems-based methodology that identifies and addresses the weakest link in a process or system.
Requisite Variety - gordonbrander.com
If a system is to be stable, the number of states of its control mechanism must be greater than or equal to the number of states in the system being controlled.
Institutions: abstract model theory for specification and programming | Journal of the ACM
There is a population explosion among the logical systems used in computing science. Examples include first-order logic, equational logic, Horn-clause logic, higher-order logic, infinitary logic, dynamic logic, intuitionistic logic, order-sorted logic, ...
At least it's an ethos?
The limits of optimal control, from the maximalist and minimalist perspectives
ver.ooo
Curious about systems — how they behave, how they fail, and what they get up to when nobody is steering.
An attempt to explain category theory to biologists in 15 minutes | David Spivak
The Abstraction Fallacy: Why AI Can Simulate But Not Instantiate Consciousness
Computational functionalism dominates current debates on AI consciousness. This is the hypothesis that subjective experience emerges entirely from abstract causal topology, regardless of the underlying physical substrate. We argue this view fundamentally mischaracterizes how physics relates to information. We call this mistake the Abstraction Fallacy. Tracing the causal origins of abstraction reveals that symbolic computation is not an intrinsic physical process. Instead, it is a mapmaker-dependent description. It requires an active, experiencing cognitive agent to alphabetize continuous physics into a finite set of meaningful states. Consequently, we do not need a complete, finalized theory of consciousness to assess AI sentience—a demand that simply pushes the question beyond near-term resolution and deepens the AI welfare trap. What we actually need is a rigorous ontology of computation. The framework proposed here explicitly separates simulation (behavioral mimicry driven by vehicle causality) from instantiation (intrinsic physical constitution driven by content causality). Establishing this ontological boundary shows why algorithmic symbol manipulation is structurally incapable of instantiating experience. Crucially, this argument does not rely on biological exclusivity. If an artificial system were ever conscious, it would be because of its specific physical constitution, never its syntactic architecture. Ultimately, this framework offers a physically grounded refutation of computational functionalism to resolve the current uncertainty surrounding AI consciousness.
Requisite variety and its implications for the control of complex systems
Recent work on the fundamental processes of regulation in biology (Ashby, 1956) has shown the importance of a certain quantitative relation called the law of requisite variety. After this relation had been found, we appreciated that it was related to a theorem in a world far removed from the biological—that of Shannon on the quantity of noise or error that could be removed through a correction-channel (Shannon and Weaver, 1949; theorem 10). In this paper I propose to show the relationship between the two theorems, and to indicate something of their implications for regulation, in the cybernetic sense, when the system to be regulated is extremely complex. Since the law of requisite variety uses concepts more primitive than those used by entropy, I will start by giving an account of that law.
How Complex Systems Fail
All of the interesting systems (e.g. transportation, healthcare, power generation) are inherently and unavoidably hazardous by the own nature. The frequency of hazard exposure can sometimes be changed but the processes involved in the system are themselves intrinsically and irreducibly hazardous. It is the presence of these hazards that drives the creation of defenses against hazard that characterize these systems.
Data-Driven Control Based on the Behavioral Approach: From Theory to Applications in Power Systems
Physics aims to describe, classify, and predict natural phenomena, while engineering aims to design new or modify existing ones. A phenomenon is characterized by some observed variables.
Axioms and Computation
We have seen that the version of the Calculus of Constructions that has been implemented in Lean includes dependent function types, inductive types, and a hierarchy of universes that starts with an impredicative, proof-irrelevant Prop at the bottom. In this chapter, we consider ways of extending the CIC with additional axioms and rules. Extending a foundational system in such a way is often convenient; it can make it possible to prove more theorems, as well as make it easier to prove theorems that could have been proved otherwise. But there can be negative consequences of adding additional axioms, consequences which may go beyond concerns about their correctness. In particular, the use of axioms bears on the computational content of definitions and theorems, in ways we will explore here.
Dynamical Systems Group | Complex Systems, Engineered
Systems engineering firm that operationalizes emerging technology for high-reliability organizations. Scientific Computing, MBSE, Systems Integration.
Polynomial Functors: A Mathematical Theory of Interaction
This monograph is a study of the category of polynomial endofunctors on the category of sets and its applications to modeling interaction protocols and dynamical systems. We assume basic categorical background and build the categorical theory from the ground up, highlighting pictorical techniques and concrete examples to build intuition and provide applications.
Finite-Choice Logic Programming | Proceedings of the ACM on Programming Languages
Logic programming, as exemplified by datalog, defines the meaning of a program as its unique smallest model: the deductive closure of its inference rules. However, many problems call for an enumeration of models that vary along some set of choices while ...
Foundations of Algebraic Specification and Formal Software Development
This book provides foundations for software specification and formal software development from the perspective of work on algebraic specification, concentrating on developing basic concepts and studying their fundamental properties. These foundations are built on a solid mathematical basis, using elements of universal algebra, category theory and logic, and this mathematical toolbox provides a convenient language for precisely formulating the concepts involved in software specification and development. Once formally defined, these notions become subject to mathematical investigation, and this interplay between mathematics and software engineering yields results that are mathematically interesting, conceptually revealing, and practically useful. The theory presented by the authors has its origins in work on algebraic specifications that started in the early 1970s, and their treatment is comprehensive. This book contains five kinds of material: the requisite mathematicalfoundations; traditional algebraic specifications; elements of the theory of institutions; formal specification and development; and proof methods. While the book is self-contained, mathematical maturity and familiarity with the problems of software engineering is required; and in the examples that directly relate to programming, the authors assume acquaintance with the concepts of functional programming. The book will be of value to researchers and advanced graduate students in the areas of programming and theoretical computer science.