Computation and uncertainty in regulated synergetic machines

Uncertainty is often dealt with by simulating probability, possibility, or belief theories with string-symbolic languages implemented on digital computers; heuristic algorithms of interference are based on different kinds of binary or multivalued logic. In this paper the author suggests that computation and uncertainty may be managed naturally by synergetic, self-organizing dynamical physic systems, which are trained and are regulated to function as 'computing machines'.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In recent years there has been a major trend in uncertainty (more specifically, partial belief) modelling emphasizing the idea that the degree of confidence in an event is not totally determined by the confidence in the opposite event, as assumed in probability theory. Possibility theory belongs to this trend that describes partial belief in terms of certainty and plausibility, viewed as distinct concepts. The distinctive features of possibility theory are its computational simplicity, and its position as a bridge between numerical and symbolic theories of partial belief for practical reasoning. The name ‘possibility theory’ was coined by L. A. Zadeh in the late seventies [Zadeh, 1978a] as an approach to uncertainty induced by pieces of vague linguistic information, described by means of fuzzy sets [Zadeh, 1965]. Possibility theory offers a simple, non-additive modelling of partial belief, which contrasts with probability theory. As we shall see, it provides a potentially more qualitative treatment of partial belief since the operations ‘max’ and ‘min’ play a role somewhat analogous to the sum and the product in probability calculus.

There has been a long-lasting misunderstanding in the literature of artificial intelligence and uncertainty modeling, regarding the role of fuzzy set theory and many-valued logics. The recurring question is that of the mathematical and pragmatic meaningfulness of a compositional calculus and the validity of the excluded middle law. This confusion pervades the early developments of probabilistic logic, despite early warnings of some philosophers of probability. This paper tries to clarify this situation. It emphasizes three main points. First, it suggests that the root of the controversies lies in the unfortunate confusion between degrees of belief and what logicians call “degrees of truth”. The latter are usually compositional, while the former cannot be so. This claim is first illustrated by laying bare the non-compositional belief representation embedded in the standard propositional calculus. It turns out to be an all-or-nothing version of possibility theory. This framework is then extended to discuss the case of fuzzy logic versus graded possibility theory. Next, it is demonstrated that any belief representation where compositionality is taken for granted is bound to at worst collapse to a Boolean truth assignment and at best to a poorly expressive tool. Lastly, some claims pertaining to an alleged compositionality of possibility theory are refuted, thus clarifying a pervasive confusion between possibility theory axioms and fuzzy set basic connectives.

Artificial Intelligence has emerged and been considerably developed in the last fifty years together with the advent of the computer age, as a new scientific area aiming at processing information in agreement with the way humans do. Inevitably, such a range of efforts, both theoretical and application-oriented, and motivated by new concerns, has led to modify and enlarge the way basic notions such as uncertainty, belief, knowledge, or evidence could be thought, represented and handled in practice. In particular, there has been a major trend in uncertainty (more specifically, partial belief) modelling, emphasizing the idea that the degree of confidence in an event is not totally determined by the confidence in the opposite event, as assumed in probability theory. Possibility theory (Dubois and Prade, 1988) belongs to this trend that describes partial belief in terms of certainty and plausibility, viewed as distinct concepts. Belief and plausibility functions (Shafer, 1976), or lower and upper probabilities (Walley, 1991) are other important representatives of this trend. The distinctive features of possibility theory are its computational simplicity, and its position as a bridge between numerical and symbolic theories of partial belief for practical reasoning. Possibility theory, based on a non-additive setting that contrasts with probability theory, provides a potentially more qualitative treatment of partial belief, since the operations “max” and “min” play a role somewhat analogous to the sum and the product in probability calculus. There are two different kinds of possibility theory: one is qualitative and the other is quantitative. They share the same kind of set-functions, but they differ when it comes to conditioning and combination

The goal of a new area of Computing with Words (CWW) is solving computationally tasks formulated in a natural language (NL). The extreme uncertainty of NL is the major challenge to meet this ambitious goal requiring computational approaches to handle NL uncertainties. Attempts to solve various CWW tasks lead to the methodological questions about rigorous and heuristic formulations and solutions of the CWW tasks. These attempts immediately reincarnated the long-time discussion about different methodologies to model uncertainty, namely: Probability Theory, Multi-valued logic, Fuzzy Sets, Fuzzy Logic, and the Possibility theory. The main forum of the recent discussion was an on-line Berkeley Initiative on Soft Computing group in 2014. Zadeh claims that some computing with words tasks are in the province of the fuzzy logic and possibility theory, and probabilistic solutions are not appropriate for these tasks. In this work we propose a useful constructive probabilistic approach for CWW based on sets of specialized K-Measure (Kolmogorov’s measure) probability spaces that differs from the random sets. This work clarifies the relationships between probability and possibility theories in the context of CWW.

Many dynamic systems in physics, chemistry, biology, engineering and information sciences can be characterized by impulsive dynamics caused by abrupt jumps at certain instants during the process. These complex dynamic behaviour can be modelled by singular and impulsive differential systems. This paper formulates and studies a model of singular and impulsive interval uncertain dynamic systems with time delay. Several fundamental issues such as global exponential robust stability of such systems are established. A numerical example is given for illustration and interpretation of the theoretical results.

In this chapter I provide a brief introduction to the field of Logic-Based Artificial Intelligence (LBAI). I then discuss contributions to LBAI contained in the chapters and some of the highlights that took place at the workshop on LBAI from which the papers are drawn. The areas of LBAI represented in the book are: commonsense reasoning; knowledge representation; nonmonotonic reasoning; abductive and inductive reasoning; logic, probability and decision making; logic for causation and actions; planning and problem solving; logic, planning and high-level robotics; logic for agents and actions; theory of beliefs; logic and language; computational logic; system implementations; and logic applications to mechanical checking and data integration.

Pedestrian dynamics is an interdisciplinary field of research. Psychologists, sociologists, traffic engineers, physicists, mathematicians and computer scientists all strive to understand the dynamics of a moving crowd. In principle, computer simulations offer means to further this understanding. Yet, unlike for many classic dynamical systems in physics, there is no universally accepted locomotion model for crowd dynamics. On the contrary, a multitude of approaches, with very different characteristics, compete. Often only the experts in one special model type are able to assess the consequences these characteristics have on a simulation study. Therefore, scientists from all disciplines who wish to use simulations to analyze pedestrian dynamics need a tool to compare competing approaches. Developers, too, would profit from an easy way to get insight into an alternative modeling ansatz. Vadere meets this interdisciplinary demand by offering an open-source simulation framework that is lightweight in its approach and in its user interface while offering pre-implemented versions of the most widely spread models.

A dynamic physical system often undergoes phase transitions in response to fluctuations induced on system parameters. For example, hurricane activity is the climate system's response initiated by a liquid-vapor phase transition associated with non-linearly coupled fluctuations in the ocean and the atmosphere. Because our quantitative knowledge about highly non-linear dynamic systems is very meager, scientists often resort to linear regression techniques such as Least Absolute Deviation (LAD) to learn the non-linear system's response (e.g., hurricane activity) from observed or simulated system's parameters (e.g., temperature, precipitable water, pressure). While insightful, such models still offer limited predictability, and alternatives intended to capture non-linear behaviors such as Stepwise Regression are often controversial in nature. In this paper, we hypothesize that one of the primary reasons for lack of predictability is the treatment of an inherently multi-phase system as being phase less. To bridge this gap, we propose a hybrid approach that first predicts the phase the system is in, and then estimates the magnitude of the system's response using the regression model optimized for this phase. Our approach is designed for systems that could be characterized by multi-variate spatio-temporal data from observations, simulations, or both.

PACS numbers: 93.30.Ge, 94.20.Cf, 94.20.Dm, 94.20.Fg Purpose: to present temperature variations of electrons and ions obtained at the Institute of Ionosphere (Kharkiv) with an incoherent scatter radar during the 23rd solar cycle minimum, and compare the obtained results with the corresponding data of IRI-2012 model. Design/methodology/approach : Data are obtained by incoherent scattering. Method of solving the inverse radiophysics problem was used for analysis. Two-dimensional ambiguity function was used for specification. Findings: It has been found that in most cases the IRI-2012 model overestimates the values of electron and ion temperatures as against experimental data. The maximum differences are observed at night and can be about 500 K in summer, and 700 K in winter. Also, the effects of sunrise and sunset in magnetoconjugate area are considered. Conclusions: It is confirmed that to adequately describe processes in the ionosphere it is necessary to have a systematic approach which takes into account interaction in ionospheric regions located in magneto-conjugate area. Such regularities must be taken into account for correction of ionospheric model for the Central European region. Key words: method of incoherent scattering, electron temperature, ion temperature, magneto-conjugate area Manuscript submitted: 22.02.2016 Radio phys. radio astron. 2016, 21(2): 132-140 REFERENCES 1. CHERNOGOR, L. F., 2006. Earth–atmosphere–ionosphere–magnetosphere as an open dynamic nonlinear physical system (Part 1). Nelinejnyj mir. vol. 4, no. 12, pp. 655–697 (in Russian). 2. CHERNOGOR, L. F., 2007. Earth–atmosphere–ionosphere–magnetosphere as an open dynamic nonlinear physical system (Part 2). Nelinejnyj mir. vol. 5, no. 4, pp. 198–231 (in Russian). 3. EVANS, J. V., 1969. Theory and Practice of Ionospheric Study by Thomson Scatter Radar. Proc. IEEE. vol. 57, is. 4, pp. 496–530. https://doi.org/10.1109/PROC.1969.7005 4. BILITZA, D. and HOEGY, W. R., 1990. Solar activity variations of ionospheric plasma temperatures. Adv. Space Res. vol. 10, no. 8, pp. 81–90. DOI: https://doi.org/10.1016/0273-1177(90)90190-B 5. TRISKOVA, L., TRUHLIK, V. and SMILAUER, J., 2003. An empirical model of ion composition in the outer ionosphere. Adv. Space Res. vol. 31, no. 3, pp. 653–663. DOI: https://doi.org/10.1016/S0273-1177(03)00040-1 6. OYAMA, K., 1991. Electron temperature measurements carried out by Japanese scientific satellites. Adv. Space Res. vol. 11, no. 10, pp. 149–158. DOI: https://doi.org/10.1016/0273-1177(91)90337-J 7. ARAUJO-PRADERE, E. A., REDMON, R., FEDRIZZI, M., VIERECK, R. and FULLER-ROWELL, T. J., 2011. Some Characteristics of the Ionospheric Behavior During the Solar Cycle 23–24 Minimum. Sol. Phys. vol. 274, is. 1, pp. 439–456. DOI: https://doi.org/10.1007/s11207-011-9728-3 8. SOLOMON, S. C., WOODS, T. N., DIDKOVSKY, L. V., EMMERT, J. T. and QIAN, L., 2010. Anomalously low solar extreme ultraviolet irradiance and thermospheric density during solar minimum. Geophys. Res. Lett. vol. 37, id. L16103. DOI: https://doi.org/10.1029/2010GL044468 9. TARAN, V. I., 2001. Study of the ionosphere in the natural and artificially excited states dy method of incoherent scattering. Geomagnetizm i aeronomija. vol. 41, no. 5, pp. 659–666 (in Russian). 10. DOMNIN, I. F., KOTOV, D. V. and CHERNOGOR, L. F., 2012. Optimization of the ionospheric plasma parameters estimation using the incoherent scatter technique. Nelineinyi mir. vol. 10, no. 6, pp. 380–386 (in Russian). 11. SIUSIUK, M. N., KOTOV, D. V. and BOGOMAZ, A. V., 2011. Modeling two-dimensional uncertainty function in incoherent scatter radar. Vestnik Natsionalnogo tekhnicheskogo universiteta. no. 44, pp. 81–84 (in Russian). 12. TRUHLIK, V., BILITZA, D. and TRISKOVA, L, 2012. A new global empirical model of the electron temperature with the inclusion of the solar activity variations for IRI. Earth Planets Space. vol. 64, pp. 531–543. DOI: https://doi.org/10.5047/eps.2011.10.016 13. APONTE, N., BRUM, CH. G. M., SULZER, M. P. and GONZALEZ, S. A., 2013. Measurements of the O+ to H+ transition height and ion temperatures in the lower topside ionosphere over Arecibo for equinox conditions during the 2008–2009 extreme solar minimum. J. Geophys. Res. Space Phys. vol. 118, pp. 4465–4470. DOI: https://doi.org/10.1002/jgra.50416 14. PICONE, J. M., HEDIN, A. E. and DROB, D. P., 2002. NRLMSISE-00 empirical model of the atmosphere: Statistical comparisons and scientific issues. J. Geophys. Res. Space Phys. vol. 107, no. A12, id. 1468. DOI: 0.1029/2009JA009430 15. CARLSON, H. C., 1966. Ionospheric Heating by Magnetic Conjugate-Point Photoelectron. J. Geophys. Res. Space Phys. vol. 71, no. 1, pp. 195–199. DOI: 10.1029/JZ07li001p00195 16. KAKINAMI, Y., BALAN, N., LIU, J. Y. and OYAMA, K., 2010. Predawn ionospheric heating observed by Hinotori satellite. J. Geophys. Res. vol. 115, id. A01304. DOI: 10.1029/2009JA014334 17. Bryunelli, B. E. and Namgaladze, A. A., 1987. Physics of the ionosphere. Moscow: Nauka Publ. (in Russian).

Formalization of bond graph using higher-order-logic theorem proving

Since L. Zadeh proposed the concept of a fuzzy set in 1965 the relationships between probability theory and possibility theory have been discussed. Both theories seem to be similar in the sense that they both are concerned with some type of uncertainty and both use the [0,1] interval for their measures as the range of their respective functions. (At least as long as one considers normalized fuzzy sets only!) Other uncertainty measures, which were already mentioned in chapter 4, also focus on uncertainty and could therefore be included in such a discussion. The comparison between probability theory and fuzzy set theory is difficult primarily for two reasons: 1. The comparison could be made on very different levels, that is, mathematically, semantically, linguistically, and so on. 2. Fuzzy set theory is not or is no longer a uniquely defined mathematical structure, such as Boolean algebra or dual logic. It is rather a very general family of theories (consider, for instance, all the possible operations which were already defined in chapter 3 or of different types of membership functions). In this respect, fuzzy set theory could rather be compared with the different existing theories of multivalued logic.

47 - The Trainer System: Applying QR Techniques to Intelligent Tutoring Systems

This report summarizes techniques that use possibility theory to estimate the risk of terrorist acts. These techniques were developed under the sponsorship of the Department of Homeland Security (DHS) as part of the National Infrastructure Simulation Analysis Center (NISAC) project. The techniques have been used to estimate the risk of various terrorist scenarios to support NISAC analyses during 2004. The techniques are based on the Logic Evolved Decision (LED) methodology developed over the past few years by Terry Bott and Steve Eisenhawer at LANL. [LED] The LED methodology involves the use of fuzzy sets, possibility theory, and approximate reasoning. LED captures the uncertainty due to vagueness and imprecision that is inherent in the fidelity of the information available for terrorist acts; probability theory cannot capture these uncertainties. This report does not address the philosophy supporting the development of nonprobabilistic approaches, and it does not discuss possibility theory in detail. The references provide a detailed discussion of these subjects. [Shafer] [Klir and Yuan] [Dubois and Prade] Suffice to say that these approaches were developed to address types of uncertainty that cannot be addressed by a probability measure. An earlier report discussed in detail the problems with using a probability measure to evaluate terrorist risk. [Darby Methodology]. Two related techniques are discussed in this report: (1) a numerical technique, and (2) a linguistic technique. The numerical technique uses traditional possibility theory applied to crisp sets, while the linguistic technique applies possibility theory to fuzzy sets. Both of these techniques as applied to terrorist risk for NISAC applications are implemented in software called PossibleRisk. The techniques implemented in PossibleRisk were developed specifically for use in estimating terrorist risk for the NISAC program. The LEDTools code can be used to perform the same linguistic evaluation as performed in PossibleRisk. [LEDTools] LEDTools is a general purpose linguistic evaluation tool and allows user defined universes of discourse and approximate reasoning rules, whereas PossibleRisk uses predefined universes of discourse (risk, attack, success, loss, and consequence) and rules. Also LEDTools has the capability to model a large number of threat scenarios with a graph and to integrate the scenarios (paths from the graph) into the linguistic evaluation. Example uses of PossibleRisk and LEDTools for the possibilistic evaluation of terrorist risk are provided in this report.

Model calibration is challenging for large-scale system models with a great number of variables. Existing approaches to partitioning system models and prioritizing data acquisition rely on heuristics rather than formal treatments. The sensor placement problem in physical dynamic systems points to a promising avenue for formalizing data acquisition priorities, which addresses the following question for system models: With the model at hand and pre-existing data availability on a subset of model variables, what are the (next) k model variables that would bring the largest utility to model calibration, once their data are acquired? In this study, we formalize this problem as a combinatorial optimization and adapt two solutions, the information-entropy approach and the miss-probability approach, from physical dynamic systems to system models in management sciences. Next, based on the idea of the data availability partition, we develop a third solution. The new approach can be understood from the entropy perspective and is embedded in the theoretical framework for the evaluation of side information. Our solution applies to system models of all topologies: analytical results of the optimal placement are derived for binary/multinary trees; for general (directed) tree structures, an algorithm to determine the optimal placement is devised, whose complexity is upper-bounded by [Formula: see text] for an n-variable system; for arbitrary model topologies with the presence of loops, sequential-optimal and simulated-annealing schemes are formulated. Three approaches are compared on a validating example; our solution outperforms the two alternatives. Application on a multicompartment system demonstrates the toolkit’s practical use. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods &amp; Analysis. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0128 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0128 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .