Truth tables - artificial intelligence, Computer Engineering

Truth Tables - artificial intelligence:

In propositional logic, where we are limited to expressing sentences where propositions are true or false - we can check whether a specific statement is true or false by working out the truth of ever larger sub statements using the truth of the propositions themselves. To tests the truth of sub statements, in the presence of connectives, we have to know how to deal with truth assignments. For instance, if we know that  isis_male(barack_obama) and  is president(barack_obama)  are true, then we know that the sentence:

is_president(barack_obama)∧ is_male(barack_obama)

is also true, because we know that a sentence of the form P∧Q is true when P and Q both are true.

This table allows us to read the truth of the connectives in the following manner. Imagine we are looking at row 3. This says that, if Q is true and P is false, then

1.   ¬P is true

2.   P∧Q is true

3.   P ∨Q is false

4.   P -> Q is true

5.   P <-> Q is false

Note down that, if P is false, then regardless of whether Q is true or false, the statement P->Q is true. This takes a little getting used to, but may be a very valuable tool in theorem proving: if we know that something is false, it may imply anything we want it to. So, the following sentence is true: "Barack Obama is female" implies that "Barack Obama is an alien", because thesentence that Barack Obama is female was false, so the result that Barack Obama is an alien may be deduced in a sound way.

Each row of a truth table describes the connectives for a specific assignment of true and false to the individual propositions in a sentence. We say each assignment a model: it represents a specific possible state of the world. For 2 propositions P and Q there are 4 models.

In general, for propositional sentences, a model is also only a specific assignment of truth values to its distinct propositions. A sentence which contains propositions will have 2n possible models and so 2n rows in its truth table. A sentence S will be false or true for a given model M - when S is true we say 'M is a model of S'.

Sentences which are always true, regardless of the truth of the distinct propositions, are known as tautologies (or valid sentences). For all models,Tautologies are true. For illustration, if I said that "Tony Blair is prime minister or Tony Blair is not prime minister", this is basically a content-free sentence, because we could  have replaced the predicate of being Tony Blair with any predicate and the sentence would still have been correct.

Tautologies are not always as simple to notice as the one above, and we may use truth tables to be sure that a statement we have written is true, regardless of the truth of the distinct propositions it contains. For doing this, the columns of our truth table will be headed with ever larger sections of the sentence, till the final column contains the complete sentence. As before, the rows of the truth table will represent all the possible models for the sentence, for example each possible assignment of truth values to the individual propositions in the sentence.In the truth table,we will use these initial truth values to assign truth values to the subsentencesand then use these new truth values to assign truth values to bigger subsentences and so on. If the last column (the entire sentence) is always assigned true, then its means, whatever the truth values of the propositions being discussed, the complete sentence will turn out to be true.

Posted Date: 10/2/2012 7:33:01 AM | Location : United States







Related Discussions:- Truth tables - artificial intelligence, Assignment Help, Ask Question on Truth tables - artificial intelligence, Get Answer, Expert's Help, Truth tables - artificial intelligence Discussions

Write discussion on Truth tables - artificial intelligence
Your posts are moderated
Related Questions
What is Priority interrupt. It is a system that establishes a priority over the several resources to determined which condition are to be serviced first when two or more reques

What are the fundamental steps in program development The basic steps in program development are as follows: a. Program coding, design and documentation. b. Preparation o

Defines a macro Defines a macro with the given name, having as its value the given replacement text. After that (for the rest of the current source file), wherever the preproce

What is a Priority Interrupt? Ans: A priority interrupt is a type of interrupt that establishes a priority over the many sources to determine which condition is to be serviced

What is commitment unit? When out-of-order execution is permitted, a special control unit is required to guarantee in-order commitment. This is known as the commitment unit. It

Q. Illustrate benefits of register addressing mode? The key benefits of register addressing are: Register access is faster than memory access and henceforth register add

Q. Which things should microprocessor validate? A microprocessor should validate: Powerful addressing modes More addressing capability More throughput Po

Q. Design a 3-bit counter using sequential logic with following counting sequence using JK- flip-flops which counts the sequence 0, 3, 2, 7, 5 and repeat.

Which interface converts SQL requirements in the SAP development system to those of the database? Database Interface converts SQL in the SAP.

3-variable K-maps have 8 squares which arenormally arranged in 4 columns and 2 rows.Columns are labeled with 2 variables. The columns are arranged so that either A or B cha