# LOGIC – 21082

Logic can refer to either of two things in electronics, computer science, and artificial intelligence (AI).

Boolean algebra is the representation of statements as symbols, along with operations, generating equations. This form of logic is important in the design of digital circuits, including computers. Boolean algebra is a form of deductive logic, because the conclusions are derived, or deduced, in a finite number of steps.

In mathematical induction, a statement is proven true for a sequence of cases. First, the statement is proved deductively for one case. Then it is proved that if the statement is true for some arbitrary case, it is true for the next case in the sequence. This implies truth for the whole sequence, even if the sequence is infinite.Mathematicians consider this perfectly rigorous and acceptable. For a thorough discussion of deductive logic and mathematical induction, a text on symbolic logic is recommended.

Trinary logic allows for a neutral condition, neither true nor false, in addition to the usual true/false (high/low) states. These three values are represented by logic 1 (false), 0 (neutral), and +1 (true). Trinary logic can be easily represented in electronic circuits by positive, zero, and negative currents or voltages.

In fuzzy logic, values cover a continuous range from “totally false,” through neutral, to “totally true.” Fuzzy logic is well suited for the control of certain processes. Its use will become more widespread as AI technology advances. Fuzzy logic can be represented digitally in discrete steps; the number of steps is usually some power of 2.