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Rule-Based Systems
Published in Adrian A. Hopgood, Intelligent Systems for Engineers and Scientists, 2021
Figure 2.9 shows a generalized flowchart for backward chaining from a goal G1. In order to simplify the chart, it has been assumed that each rule has only one condition, so that the satisfaction of a condition can be represented as a single goal. In general, rules have more than one condition. The flowchart in Figure 2.9 is an attempt to represent backward chaining as an iterative process. This is difficult to achieve, as the length of the chain of rules cannot be predetermined. The flowchart has, of necessity, been left incomplete. It contains repeating sections that are identical except for the local variable names, an indication that while it is difficult to represent the process iteratively, it can be elegantly represented recursively. A recursive definition of a function is one that includes the function itself. Recursion is an important aspect of the AI languages Python, Lisp, and Prolog, discussed in Chapter 11, as well as many other computer languages. Box 2.1 shows a recursive definition of backward chaining, where it has again been assumed that rules have only one condition. It is not always necessary to write such a function for yourself as backward chaining forms an integral part of the Prolog language and many expert system shells and AI toolkits (see Chapter 11).
Write Your Math Well
Published in Edward J. Rothwell, Michael J. Cloud, Engineering Writing by Design, 2020
Edward J. Rothwell, Michael J. Cloud
Functions defined on the natural numbers are sometimes defined recursively. A recursive definition has two components: (1) a base case, and (2) an inductive rule. For a function f(n), the base case may be specification of f(0) and the inductive rule a specification of f(n + 1) in terms of f(n). The elementary factorial function n!, for instance, can be defined by the two conditions 0! = 1 and (n + 1)! = (n + 1) · n!. More generally, we need a way to get the recursion started, and a way to get each function value from its predecessor(s). Use the pair of conditions g(n) = g(n – 1) + g(n – 2) and g(1) = g(2) = 1 to compute the first few Fibonacci numbers g(n).
Allocating resources via price management systems: a dynamic programming-based approach
Published in International Journal of Control, 2021
Ali Forootani, Davide Liuzza, Massimo Tipaldi, Luigi Glielmo
In this section, we present the price management algorithms for reservations with bounded time intervals. To this aim, it is worth highlighting some aspects which can be exploited for the actual algorithm implementation. First of all, thanks to the recursive definition of , it is possible to calculate (with ) by taking advantage of the definition of . Indeed, the backwards recursive procedure given by (14)–(16) can be shortened. In particular, being the state transition probabilities between time instants j and j + 1 and considering that the reservation agenda is updated up to the time , we have for any In other words, we can state that: . Similarly, we can show that .
TACO, an automated toolchain for model predictive control of building systems: implementation and verification
Published in Journal of Building Performance Simulation, 2019
F. Jorissen, W. Boydens, L. Helsen
Recursive definition (17) is reformulated by eliminating from the equation such that where is the initial state, , , are matrices and are vectors. A definition for these matrices is presented in Section 3.2. Since terms , and are functions of time intervals i and j only, the discrete time dynamics can be reformulated by introducing variable as where are inputs of the optimization problem, which are pre-computed. This reduces the number of equations that need to be evaluated as part of the optimization problem.
Relational similarity-based model of data part 2: dependencies in data
Published in International Journal of General Systems, 2018
Radim Belohlavek, Vilem Vychodil
Proof Let be a complete residuated lattice with globalization. Then, Definition 6.13(ii) can be restated as follows: and for any such that , we have . If in addition is finite, Definition 6.13 becomes a recursive definition of which is then uniquely given. The situation is similar to the uniqueness of a system of pseudo-intents which determined a Guigues–Duquenne base in the ordinary case (see Ganter and Wille 1997; Guigues and Duquenne 1986).