We introduce a novel framework for decomposing interventional causal effects into synergistic, redundant, and unique components, building on the intuition of Partial Information Decomposition (PID) and the principle of M\"obius inversion. While recent work has explored a similar decomposition of an observational measure, we argue that a proper causal decomposition must be interventional in nature. We develop a mathematical approach that systematically quantifies how causal power is distributed among variables in a system, using a recently derived closed-form expression for the M\"obius function of the redundancy lattice. The formalism is then illustrated by decomposing the causal power in logic gates, cellular automata, and chemical reaction networks. Our results reveal how the distribution of causal power can be context- and parameter-dependent. This decomposition provides new insights into complex systems by revealing how causal influences are shared and combined among multiple variables, with potential applications ranging from attribution of responsibility in legal or AI systems, to the analysis of biological networks or climate models.

Ensoul is a framework proposed for the purpose of creating technologies that create more technologies through the combined use of networks, and nests, of energy homeostatic (enerstatic) loops and open-ended evolutionary techniques. Generative technologies developed by such an approach serve as both simple, yet insightful models of thermodynamically driven complex systems and as powerful sources of novel technologies. "Self Organizing intelligent Ultra Low power Systems" (SOULS) is a term that well describes the technologies produced by such a generative technology, as well as the generative technology itself. The term is meant to capture the abstract nature of such technologies as being independent of the substrate in which they are embedded. In other words, SOULS can be biological, artificial or hybrid in form.

AI Researcher, Cognitive Technologist Inventor - AI Thinking, Think Chain Innovator - AIOT, XAI, Autonomous Cars, IIOT Founder Fisheyebox Spatial Computing Savant, Transformative Leader, Industry X.0 Practitioner How to Create Causality of Machine Intelligence and Learning? Causation, and its powers and forces, processes and mechanisms, physical and mental, social and technological, is the engine of the world (as the positive and negative gravity, or dark energy, for the oscillating universe). Causal reasoning is the driving force of human mind/intelligence/intellect; for real causal mechanisms defines all the world's knowledge. The two opposing types of theories of causation, The Humean idealist theory (causation as regularities & invariants & patterns) the causal realist theory (causation as causal mechanism, causal processes, causal interactions, and causal laws, providing the mechanisms by which the world changes and machine works and human acts; to understand why something ever changes or events happen, we need to see how they are produced by these mechanisms). The Hume's theory holds that causation is entirely constituted by facts about empirical regularities among observable variables; there is no underlying causal nature, causal power, or causal necessity.

AI Researcher, Cognitive Technologist Inventor - AI Thinking, Think Chain Innovator - AIOT, XAI, Autonomous Cars, IIOT Founder Fisheyebox Spatial Computing Savant, Transformative Leader, Industry X.0 Practitioner What is needed to give #AI Consciousness and Emotions? The Real Super Intelligence (RSI) general-purpose technology platform is generalizing most valuable narrow approaches, in the fundamental ways that the global processing of mental/neural causal variables is what real consciousness about. The RSI with its future conscious machines is capable of control, monitoring, self-diagnosing, or introspecting of all internal processes. The RSI's Consciousness or Self-awareness or Self-knowledge does not require a biological origin, like the Neuronal Correlates of Consciousness (NCC), and modeling complex relationships between subjective mental states and brain states, between the conscious mind and the electro-chemical interactions in the brain and the whole body (mind–brain-body problem). This requires reflective and reflexive causal information mechanisms; for computers and machines must be aware of their environments to be categorized as self-aware, self-conscious, or self-knowing AI systems.

Using the mathematical language of information theory, Hoel and his collaborators claim to show that new causes--things that produce effects--can emerge at macroscopic scales. They say coarse-grained macroscopic states of a physical system (such as the psychological state of a brain) can have more causal power over the system's future than a more detailed, fine-grained description of the system possibly could. Just as codes reduce noise (and thus uncertainty) in transmitted data--Claude Shannon's 1948 insight that formed the bedrock of information theory--Hoel claims that macro states also reduce noise and uncertainty in a system's causal structure, strengthening causal relationships and making the system's behavior more deterministic. With Albantakis and Tononi, Hoel formalized a measure of causal power called "effective information," which indicates how effectively a particular state influences the future state of a system.

Imagine that at some time in the not-too-distant future, you've bought a smartphone that comes bundled with a personal digital assistant (PDA) living in the cloud. You assign a sexy female voice to the PDA and give it access to all of your emails, social media accounts, calendar, photo album, contacts, and other bits and flotsam of your digital life. She--for that's how you quickly think of her--knows you better than your mother, your soon-to-be ex-wife, your friends, or your therapist. Her command of English is flawless; you have endless conversations about daily events; she gets your jokes. She is the last voice you hear before you drift off to sleep and the first upon awakening.

On most days, we do not wake up anticipating that we may be suddenly thrust into the sky while popcorn shrimp rains down like confetti, as some guy roars from above: "Hey, there, I'm Jack. And you are in a computer simulation." Instead, we wake up thinking that an atom is an atom, that our physics is inherent to this universe and not prone to arbitrary change by coders, and that our reality is, well, real. Yet there may be another possibility. Game developers have opened up massive, explorable universes and populated them with computer-generated characters based on advanced A.I.

This paper (1)shows that the best supported current psychological theory (Cheng, 1997) of how human subjects judge the causal power or influence of variations in presence or absence of one feature on another, given data on their covariation, tacitly uses a Bayes network which is either a noisy or gate (for causes that promote the effect) or a noisy and gate (for causes that inhibit the effect); (2)generalizes Chengs theory to arbitrary acyclic networks of noisy or and noisy and gates; (3)gives various sufficient conditions for the estimation of the parameters in such networks when there are independent, unobserved causes; (4)distinguishes direct causal influence of one feature on another (influence along a path with one edge) from total influence (influence along all paths from one variable to another) and gives sufficient conditions for estimating each when there are unobserved causes of the outcome variable; (5)describes the relation between Cheng models and a simplified version of the Rubin framework for representing causal relations.

Given a set of experiments in which varying subsets of observed variables are subject to intervention, we consider the problem of identifiability of causal models exhibiting latent confounding. While identifiability is trivial when each experiment intervenes on a large number of variables, the situation is more complicated when only one or a few variables are subject to intervention per experiment. For linear causal models with latent variables Hyttinen et al. (2010) gave precise conditions for when such data are sufficient to identify the full model. While their result cannot be extended to discrete-valued variables with arbitrary cause-effect relationships, we show that a similar result can be obtained for the class of causal models whose conditional probability distributions are restricted to a `noisy-OR' parameterization. We further show that identification is preserved under an extension of the model that allows for negative influences, and present learning algorithms that we test for accuracy, scalability and robustness.

This paper focuses on people's short-run behavior by examining dynamical versions of these three theories, and comparing their predictions to a real-world dataset.