Multivalued logics

The inference engine was designed to use multivalued logic, i.e., it handles inexact reasoning. Confidence factors (CF) are contained in the THEN clauses of each rule. The equation for combining positive confidences is ... 

A Multivalued Logic Predicate Calculus Approach to Synthesis Pla ining... 

Zwicky 1933-1934 Idea of flexibility of scientific truth use of multivalued logics in science... 

Truth Values For applications of multivalued logic, we need further graduation in addition to the binary truth values true ... 

The term fuzzy logic has two different meanings. More specifically, in a narrow sense, fuzzy logic, FLn, is a logical system which may be viewed as an extension and generalization of classical multivalued logics. But in a wider sense, fuzzy logic, FLw, is almost synonymous with the theory of fuzzy sets (Zadeh 1975). 

Basically, fuzzy logic (FL) is a multivalued logic, which allows intermediate values to be defined between conventional evaluations like true/false, yes/no, and high/low. Fuzzy logic is an extension of the traditional logic to intermediate and approximate values. 

Tapia, M.A. Guima,T.A. KatbabA. 1991. Calculus fora multivalued-logic algebraic sy em. Applied Mathematics and Computation, 42(3) 255-285. 

The basic assumption upon which two-valued logic is based, that every proposition is either true or false, has been questioned since Aristotle. For example, propositions about future events are neither actually true, nor actually false, but potentially either. Consequently, their truth-value is undetermined, at least prior to the event. Propositions whose truth-value is problematic are not limited to future events. For example, propositions that imply physical or chemical measurements depend on the limitations of mea-surement. While several types of multivalued logic have been proposed, here we will discuss the infinite-valued logic, whose truth-values are represented by all the real numbers in the interval [0,1]. This is also called standard Lukasiewicz logic L. The primitives of this logic are defined as... 

Tapia, M.A., Guima, T.A., Katbab, A. 1991. Calculus for a multivalued-logic algebraic system. Applied Mathematics and Computation 42 255-285. 

The alternative way to deal with unknown or other such states is to catch the good ones and throw out the bad. This approach should be used wiffi more caution as not all synthesis tools support the required constructs. The advantage of this method is that the VHDL can be constructed so that the simulation will accurately reflect the operation of the synthesized circuit design. Wiih the previous method, tfds would only occur after the initialization signal had been issued. This topic is discussed in more detail in Chapter 8 when multivalued logic systems are introduced. 

As CLK is only read by the process in the clock expression the last approach has been demonstrated. Using multivalued logic types such as td ulogic makes the design process a little more complex and is discussed fully in Chapter 7. 

GREGATE has also made no difference. This is related to how the signal has been used in this circuit Generally, designing with multivalued logic will affect how the code has to be written. This is discussed furdier in Chapter 7. 

There are many multivalued logic systems available in the VHDL environment. BIT is the simplest, but the IEEE library and tool vendor libraries contain others that are in common use and so can be considered portable. The IEEE STD LOGIC l 164 package contains the standard multivalued... 

This multivalued logic is very commonly used and is provided under various guises. The IEEE libraries contain declarations for the type Lo c4 and die subt5Tpe XOIZ. Vendors usually supply arithmetic operators for the XOIZ type as well as providing vectored t es containing XOIZ elements. 

The STD LOGIC l 164 package contains the industry-standard set of multivalued logic systems. The standard logic system comes in two forms ... 

The multivalued logic systems outlined above are subsets and supersets of other systems. However, as the discussion in Chapter 3 on types and subtypes explained, objects of different types caimotbe university interchanged or equated. For example, given the type declarations ... 

It has already been stated that in a multivalued logic system it is not correct to assume that not 0 is I. Consider the statement ... 

To demonstrate the use of multivalued logic systems the industry-standard td Jogic type is used throughout this example. This will have conse-... 

State coverage for multivalued logic using if and Case statements... 

Do remember the key points about multivalued logic design ... 

This chapter has demonstrated how VHDL can be applied to the design of control logic to construct state machines with complex state maps. The main issue that has been highlighted is the use of multivalued logic in a design and how this affects both the simulation and s)mthesis processes. 

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