Model Inference System

The foundations of ILP are laid out by [Muggleton 95], and surveys [Sammut 93] [Muggleton and De Raedt 94] and a compilation [Muggleton 92] are available. Moreover, special ILP workshops exist. This present survey is organized as follows. First, in Section 3.4.1, we present Shapiro s Model Inference System, the pioneering learner of ILP. Then, in Section 3.4.2, we briefly discuss other relevant model-based systems. 

Shapiro pointed out that the oracle of his Model Inference System (MIS, see Section 3.4.1) could be partly mechanized by the incorporation of constraints and partial specifications [Shapiro 82, page 79]. The idea is investigated by [Lichtenstein and Shapiro 88], whose system asks non-ground queries to an oracle. 

This Model Inference System (MIS, see Section 3.4.1) has spawned a lot of renewed interest in generalization models. For instance, [Tinkham 90] extends Shapiro s results to a second-order search space. Simultaneously, but independently, [Gegg-Harrison 89] also suggests generalization operators within a second-order logic, though for an entirely different application. 

On the other hand, studies with three-dimensional isotropic lamellar matrices have shown that Azone is a weakly polar molecule, which can occupy the interfacial region as well as the hydrocarbon interior of bilayers [86,87]. The contrasting observations of Azone promoting the assembly of reversed-type liquid-crystal phases (e.g., reversed hexagonal and reversed micellar) in simple model lipid systems [88-90], while also favoring the formation of lamellar structures in one of these mixtures [91], adds further confusion to the discussion [92]. This notwithstanding, the studies by Schiickler and co-workers [91] emphasize the differences in the calorimetric profiles of intact human stratum comeum (HSC) and model SC lipid mixtures Although these systems are clearly useful and versatile, extrapolation of inferences from model lipids to the intact membrane must be performed with caution. 

In this paper we describe the application of an adaptive network based fuzzy inference system (ANFIS) predictor to the estimation of the product compositions in a binary methanol-water continuous distillation column from available on-line temperature measurements. This soft sensor is then applied to train an ANFIS model so that a GA performs the searching for the optimal dual control law applied to the distillation column. The performance of the developed ANFIS estimator is further tested by observing the performance of the ANFIS based control system for both set point tracking and disturbance rejection cases. 

For signaling pathways, recent years have seen an increasing number of studies of specific pathways where mathematical modeling is applied to infer systems properties from the models. These applications include the mitogen-activated protein (MAP)-kinase pathways [14-16], apoptotic pathways [17-19], the Wnt/j6-Catenin [20], and the Janus kinase-signal transduction and activator of transcription (JAK-STAT) pathway [21], A regulatory network that has been studied intensively is the cell cycle [7, 22, 23]. 

Fuzzy inference systems are also known as fuzzy associative memories, fuzzy models, fuzzy-rule-based systems, or fuzzy controllers. 

Streams (and other nonfinite or nonterminating objects) are very natural for modeling systems. All of the inference systems had problems representing streams. To some extent, DDD has this problem too stream networks are a syntax extension and, therefore, a shallow embedding in the Scheme theory. ... 

Ascher, A. and H. Feingold (1984). Repairable Systems Reliability Modeling, Inference, Misconceptions and Their Causes. Matcel-Dekfen... 

Complete consistency is seen in the systematic changes of microstructural variables (inferred through the model) with system material changes. For example, for THF/MEK-cast samples, takes values 66%, 10%, 4% as polymer composition ranges over 0.48 PS, 0.29 PS, 0.27 PS... 

Neuro-Fuzzy Inference System models first described in [59] and used in [60, 61]. This approach has proven to be a powerful means of using detailed experimental characterization knowledge online for system control. The methodology has been tested on a Serenergy H3-350 methanol reformer HTPEM fuel cell system, and includes characterizing the steam reformer ex... 

Justesen KK, Andreasen SJ, Shaker HR et al (2013) Gas composition modeling in a reformed methanol fuel cell system using adaptive neuro-fuzzy inference systems. Int J Hydrog Energy 38 10577-10584... 

One realistic way to analyse a system with unavailable data is to employ subjective assessment using the combination of fuzzy logic and Evidential Reasoning (ER). Compared to the traditional fuzzy inference mechanism (i.e. max-min fuzzy operations), an ER approach has the advantage of avoiding the loss of useful information in its inference processes hence, it can be suitable for modelling complex systems. 

Ascher, H. Feingold, H. 1984. Repairable Systems Modelling, Inferences, Misconceptions and their causes. New York, Marcel Decker. 

Neuro fuzzy modeling is a useful technique that combines the advantages of neural networks and fuzzy inference systems. In this approach, the fuzzy model is architecturally the same as a neural network. In this case one could use, for example error back-propagation to train the network to find the parameters of the fuzzy model. The most well-known method is the so-called ANFIS method the Adaptive-Network based Fuzzy Inference System. The method will be explained in this chapter and several examples will be developed as an illustration. 

The fuzzy logic inference system for identification of the Sugeno type model can be implemented as a five layer network (Ojala, 1994 Sfetsos, 2000) and is shown in Fig. 29.1. 

Throughout this chapter, the state space approach is chosen to model dynamic systems, together with a discreet-time formulation of the problem. In multi-robot localization, the state vector represents the poses of the robots comprising the team. In order to inspect inferences about a dynamie system, at least two models are required first, a model deseribing the time evolution of the state, i.e. the system dynamie model or state transition model, and seeond, a model deseribing the relation between die noisy measmements and the state, i.e. the measurement or observation model. 

An inference system commonly used to develop fuzzy models is the Mamdani fuzzy inference system. The Mamdani approach was developed in the 1970s and was the first inference method applied to control systems [15]. The Mamdani inference procedure describes the output variables as fuzzy sets. The approach uses max-min composition in which the minimum of the two antecedents is taken for a particular rule and the maximum combination of the rules is determined for aggregating the effects of aU the rules. The effect of the max combiner on the output membership functions is to generate an "envelope" of the fired output membership functions. In order to defuzzify this output set, the centroid (weighted average) of the envelope is found by integrating over the 2-dimensional shape. The defuzzification process of the Mamdani approach is computationally intensive. 

Another inference system commonly used is the Standard Additive Model (SAM). The SAM inference approach is based on correlation-product inference. This overcomes the loss of information associated with the conelation-min inference in the Mamdani inference method. Also, the additive-combiner in the SAM makes defuzzification simpler than the max-combiner of Mamdani inference. The additive-combiner also accounts for the information in the overlap of the fired output sets that the max-combiner ignores. 

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