Introduction

This labs describes about the qualifiers.We describe various definations and give examples for Universal quantifiers, Existential quantifiers, Complex sentences.We also differenciated between Propositional logic and First order logic .It was a good learning experience about how FUZZY works.

Objects is something perceptible by senses, especially by vision or touch; a material thing. It is the smallest component and instance of the program.

Relations (Relatings) It is a property which assigns truth values to combination of k individuals and is a connection between two objects or classes.

Functions (include domain) It is a one to one relationship among to quantaties.A function expresses dependence between two quantaties one of which is arguments of the function and the other is the value of the function.

Reify (Reification) It is used to represent facts that must be evaluated in some ways.Hierarchy of Evidence (especially as it plays out in computing) .

Universal quantifier

For all x, x being a person, if x is a father then he must be a son of someone too. V x Father(x) => son(x).

Existential quantifiers:

∃x necklace(x) /\ OnNeck? ? (x,Mona)

“There exists a necklace which is on Mona’s neck.”

Complex sentences:

¬equal(cube(two), sixteen) “two cube does not equal to sixteen”

Propositional logic considers world as 'facts', which can be either true or false.It is less expensive.Proposition Logic is used for expressing rules and rationality within a system. The rules are expressed using logical formulae which can be seen in two ways, semantics : refers to the meaning behind a string of symbols and syntax : refers to the structure of a string of symbols and the rules which govern the creation of strings of symbols . It has limited expressive power. First order logic considers world as 'objects' or 'Relations' or functions. It is more expensive.This is the procedural approach which can be contrasted with the declarative nature of propositional logicIt is more expressive language. In this we have to identify the task and then assemble the relevant knowledge.The third step is to decide on a vocabulary of predicates, functions and constants. We have to Encode general knowledge about the domain and a description of the specific problem instance.Pose queries to the interface procedure and then get answers.The final step is to Debug the knowledge base.

The main advantage of FUZZY LOGIC is it can be implemented in hardware, software, or a combination of both.It is a problem-solving control system methodology that lends itself to implementation in systems ranging from simple, small, embedded micro-controllers to large, networked, multi-channel PC or workstation-based data acquisition and control systems.

FUZZY LOGIC works on some numerical parameters in order to operate such as what is considered significant error and significant rate-of-change-of-error, but exact values of these numbers are usually not critical unless very responsive performance is required in which case empirical tuning would determine them. For example, a simple temperature control system could use a single temperature feedback sensor whose data is subtracted from the command signal to compute "error" and then time-differentiated to yield the error slope or rate-of-change-of-error, hereafter called "error-dot". Error might have units of degs F and a small error considered to be 2F while a large error is 5F. The "error-dot" might then have units of degs/min with a small error-dot being 5F/min and a large one being 15F/min. These values don't have to be symmetrical and can be "tweaked" once the system is operating in order to optimize performance. Generally, FL is so forgiving that the system will probably work the first time without any tweaking.

CONCLUSION

First Order Logic provides better or increased expressive power than Propositional Logic (PL) to define various worlds. whereas Propositional logic is not adequate for formalizing valid arguments that rely on the internal structure of the propositions involved. Fuzzy Logic was a better method for sorting and handling data but has proven to be a excellent choice for many control system applications since