Learning relational dynamics of stochastic domains for planning

Probabilistic planners are very flexible tools that can provide good solutions for difficult tasks. However, they rely on a model of the domain, which may be costly to either hand code or automatically learn for complex tasks. We propose a new learning approach that (a) requires only a set of state transitions to learn the model; (b) can cope with uncertainty in the effects; (c) uses a relational representation to generalize over different objects; and (d) in addition to action effects, it can also learn exogenous effects that are not related to any action, e.g., moving objects, endogenous growth and natural development. The proposed learning approach combines a multi-valued variant of inductive logic programming for the generation of candidate models, with an optimization method to select the best set of planning operators to model a problem. Finally, experimental validation is provided that shows improvements over previous work.Peer ReviewedPostprint (author's final draft

Relational Entropic Dynamics of Particles

The general framework of entropic dynamics is used to formulate a relational quantum dynamics. The main new idea is to use tools of information geometry to develop an entropic measure of the mismatch between successive configurations of a system. This leads to an entropic version of the classical best matching technique developed by J. Barbour and collaborators. The procedure is illustrated in the simple case of a system of N particles with global translational symmetry. The generalization to other symmetries whether global (rotational invariance) or local (gauge invariance) is straightforward. The entropic best matching allows a quantum implementation Mach's principles of spatial and temporal relationalism and provides the foundation for a method of handling gauge theories in an informational framework.Comment: Presented at MaxEnt 2015, the 35th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (July 19--24, 2015, Potsdam NY, USA

Learning relational dynamics of stochastic domains for planning

Probabilistic planners are very flexible tools that can provide good solutions for difficult tasks. However, they rely on a model of the domain, which may be costly to either hand code or automatically learn for complex tasks. We propose a new learning approach that (a) requires only a set of state transitions to learn the model; (b) can cope with uncertainty in the effects; (c) uses a relational representation to generalize over different objects; and (d) in addition to action effects, it can also learn exogenous effects that are not related to any action, e.g., moving objects, endogenous growth and natural development. The proposed learning approach combines a multi-valued variant of inductive logic programming for the generation of candidate models, with an optimization method to select the best set of planning operators to model a problem. Finally, experimental validation is provided that shows improvements over previous work.Peer ReviewedPostprint (author's final draft

Relational Spacetime Ontology

In the aftermath of the rediscovery of Einstein’s hole argument by Earman and Norton (1987), we hear that the ontological relational/substantival debate over the status of spacetime seems to have reached stable grounds. Despite Einstein’s early intention to cast GR’s spacetime as a relational entity à la Leibniz-Mach, most philosophers of science feel comfortable with the now standard sophisticated substantivalist (SS) account of spacetime. Furthermore, most philosophers share the impression that although relational accounts of certain highly restricted models of GR are viable, at a deep down level, they require substantival spacetime structures. SS claims that although manifold spacetime points do not enjoy the sort of robust existence provided by primitive identity, it is still natural to be realistic about the existence of spacetime as an independent entity in its own right. It is argued that since the bare manifold lacks the basic spacetime structures –such as geometry and inertia- one should count as an independent spacetime the couple manifold +metric (M, g). The metric tensor field of GR encodes inertial and metrical structure so, in a way, it plays the explanatory role that Newtonian absolute space played in classical dynamics. In a nutshell, according to the SS account of spacetime, one should view the metric field of GR as the modern version of a realistically constructed spacetime since it has the properties –or contains the structures- that Newtonian space had. I will try to dismantle the widespread impression that a relational account of full GR is implausible. To do so, I will start by highlighting that when turning back to the original Leibniz-Newton dispute one sees that substantivalism turns out prima facie triumphant since Newton was able to successfully formulate dynamics. However, to give relationalism a fair chance, one can also put forward the following hypothetical questions: What if Leibniz –or some leibnizian- had had a good relational theory? What role would geometry play in this type of theory? Would it be natural to view geometry and inertia as intrinsic properties of substantival space –if not spacetime? Would it still seem natural to interpret the metric field of GR along substantival lines regardless of the fact that it also encodes important material properties such as energy-momentum? After bringing these questions out into the light I will cast some important doubts on the substantival (SS) interpretation of the metric field. Perhaps the metric turns out to be viewed as a relational matter field. Finally, to strengthen the relational account of spacetime I expect to remove the possible remaining interpretative tension by briefly discussing the relevance of two important facts: i) Dynamical variables are usually linked to material objects in physical theories. The metric field of GR is a dynamical object so, I claim, it should be viewed as a matter field. ii) Barbour and Bertotti (BB2, 1982) have provided and alternative formulation of classical dynamics. They provide a “genuinely relational interpretation of dynamics” (Pooley & Brown 2001). Geometry and inertia become –contra SS- relational structures in BB2

Foundations of Relational Particle Dynamics

Relational particle dynamics include the dynamics of pure shape and cases in which absolute scale or absolute rotation are additionally meaningful. These are interesting as regards the absolute versus relative motion debate as well as discussion of conceptual issues connected with the problem of time in quantum gravity. In spatial dimension 1 and 2 the relative configuration spaces of shapes are n-spheres and complex projective spaces, from which knowledge I construct natural mechanics on these spaces. I also show that these coincide with Barbour's indirectly-constructed relational dynamics by performing a full reduction on the latter. Then the identification of the configuration spaces as n-spheres and complex projective spaces, for which spaces much mathematics is available, significantly advances the understanding of Barbour's relational theory in spatial dimensions 1 and 2. I also provide the parallel study of a new theory for which positon and scale are purely relative but orientation is absolute. The configuration space for this is an n-sphere regardless of the spatial dimension, which renders this theory a more tractable arena for investigation of implications of scale invariance than Barbour's theory itself.Comment: Minor typos corrected; references update

Dynamics of Pure Shape, Relativity and the Problem of Time

A new approach to the dynamics of the universe based on work by O Murchadha, Foster, Anderson and the author is presented. The only kinematics presupposed is the spatial geometry needed to define configuration spaces in purely relational terms. A new formulation of the relativity principle based on Poincare's analysis of the problem of absolute and relative motion (Mach's principle) is given. The enire dynamics is based on shape and nothing else. It leads to much stronger predictions than standard Newtonian theory. For the dynamics of Riemannian 3-geometries on which matter fields also evolve, implementation of the new relativity principle establishes unexpected links between special relativity, general relativity and the gauge principle. They all emerge together as a self-consistent complex from a unified and completely relational approach to dynamics. A connection between time and scale invariance is established. In particular, the representation of general relativity as evolution of the shape of space leads to unique definition of simultaneity. This opens up the prospect of a solution of the problem of time in quantum gravity on the basis of a fundamental dynamical principle.Comment: 17 pages. To appear in Decoherence and Entropy in Complex Systems (Proceedings of the Conference DICE, Piombino 2002, ed. H. -T. Elze, Spring Lecture Notes in Physics 2003

Organismic Supercategories: III. Qualitative Dynamics of Systems

The representation of biological systems by means of organismic supercategories, developed in previous papers, is further discussed. The different approaches to relational biology, developed by Rashevsky, Rosen and by Baianu and Marinescu, are compared with Qualitative Dynamics of Systems which was initiated by Henri Poincaré (1881). On the basis of this comparison some concrete results concerning dynamics of genetic system, development, fertilization, regeneration, analogies, and oncogenesis are derived

The shape dynamics description of gravity

Classical gravity can be described as a relational dynamical system without ever appealing to spacetime or its geometry. This description is the so-called shape dynamics description of gravity. The existence of relational first principles from which the shape dynamics description of gravity can be derived is a motivation to consider shape dynamics (rather than GR) as the fundamental description of gravity. Adopting this point of view leads to the question: What is the role of spacetime in the shape dynamics description of gravity? This question contains many aspects: Compatibility of shape dynamics with the description of gravity in terms of spacetime geometry, the role of local Minkowski space, universality of spacetime geometry and the nature of quantum particles, which can no longer be assumed to be irreducible representations of the Poincare group. In this contribution I derive effective spacetime structures by considering how matter fluctuations evolve along with shape dynamics. This evolution reveals an "experienced spacetime geometry." This leads (in an idealized approximation) to local Minkowski space and causal relations. The small scale structure of the emergent geometric picture depends on the specific probes used to experience spacetime, which limits the applicability of effective spacetime to describe shape dynamics. I conclude with discussing the nature of quantum fluctuations (particles) in shape dynamics and how local Minkowski spacetime emerges from the evolution of quantum particles.Comment: 16 pages Latex, no figures, arXiv version of a submission to the proceedings of Theory Canada

Quantum Genetics, Quantum Automata and Quantum Computation

The concepts of quantum automata and quantum computation are studied in the context of quantum genetics and genetic networks with nonlinear dynamics. In a previous publication (Baianu,1971a) the formal concept of quantum automaton was introduced and its possible implications for genetic and metabolic activities in living cells and organisms were considered. This was followed by a report on quantum and abstract, symbolic computation based on the theory of categories, functors and natural transformations (Baianu,1971b). The notions of topological semigroup, quantum automaton,or quantum computer, were then suggested with a view to their potential applications to the analogous simulation of biological systems, and especially genetic activities and nonlinear dynamics in genetic networks. Further, detailed studies of nonlinear dynamics in genetic networks were carried out in categories of n-valued, Lukasiewicz Logic Algebras that showed significant dissimilarities (Baianu, 1977) from Bolean models of human neural networks (McCullough and Pitts,1945). Molecular models in terms of categories, functors and natural transformations were then formulated for uni-molecular chemical transformations, multi-molecular chemical and biochemical transformations (Baianu, 1983,2004a). Previous applications of computer modeling, classical automata theory, and relational biology to molecular biology, oncogenesis and medicine were extensively reviewed and several important conclusions were reached regarding both the potential and limitations of the computation-assisted modeling of biological systems, and especially complex organisms such as Homo sapiens sapiens(Baianu,1987). Novel approaches to solving the realization problems of Relational Biology models in Complex System Biology are introduced in terms of natural transformations between functors of such molecular categories. Several applications of such natural transformations of functors were then presented to protein biosynthesis, embryogenesis and nuclear transplant experiments. Other possible realizations in Molecular Biology and Relational Biology of Organisms are here suggested in terms of quantum automata models of Quantum Genetics and Interactomics. Future developments of this novel approach are likely to also include: Fuzzy Relations in Biology and Epigenomics, Relational Biology modeling of Complex Immunological and Hormonal regulatory systems, n-categories and Topoi of Lukasiewicz Logic Algebras and Intuitionistic Logic (Heyting) Algebras for modeling nonlinear dynamics and cognitive processes in complex neural networks that are present in the human brain, as well as stochastic modeling of genetic networks in Lukasiewicz Logic Algebras