(a). Discuss with appropriate intuition the relevance of unit clause heuristics ,
disjunction form of literals , and CNF representation of the KB with respect to
inference algorithms in propositional logic (while explaining, show the cases that could
happen in case these are not true)..
(b). For propositional logic, “ backward chaining is more effective compared to the
forward chaining algorithm ”. Discuss with examples and proper justification in favor or
against this claim.
Answers
Answer:
statement can be defined as a declarative sentence, or part of a sentence, that is capable of having a truth-value, such as being true or false. So, for example, the following are statements:
George W. Bush is the 43rd President of the United States.
Paris is the capital of France.
Everyone born on Monday has purple hair.
Sometimes, a statement can contain one or more other statements as parts. Consider for example, the following statement:
Either Ganymede is a moon of Jupiter or Ganymede is a moon of Saturn.
While the above compound sentence is itself a statement, because it is true, the two parts, “Ganymede is a moon of Jupiter” and “Ganymede is a moon of Saturn”, are themselves statements, because the first is true and the second is false.
The term proposition is sometimes used synonymously with statement. However, it is sometimes used to name something abstract that two different statements with the same meaning are both said to “express”. In this usage, the English sentence, “It is raining”, and the French sentence “Il pleut”, would be considered to express the same proposition; similarly, the two English sentences, “Callisto orbits Jupiter” and “Jupiter is orbited by Callisto” would also be considered to express the same proposition. However, the nature or existence of propositions as abstract meanings is still a matter of philosophical controversy, and for the purposes of this article, the phrases “statement” and “proposition” are used interchangeably.
Propositional logic, also known as sentential logic, is that branch of logic that studies ways of combining or altering statements or propositions to form more complicated statements or propositions. Joining two simpler propositions with the word “and” is one common way of combining statements. When two statements are joined together with “and”, the complex statement formed by them is true if and only if both the component statements are true. Because of this, an argument of the following form is logically valid:
Paris is the capital of France and Paris has a population of over two million.
Therefore, Paris has a population of over two million.
Propositional logic largely involves studying logical connectives such as the words “and” and “or” and the rules determining the truth-values of the propositions they are used to join, as well as what these rules mean for the validity of arguments, and such logical relationships between statements as being consistent or inconsistent with one another, as well as logical properties of propositions, such as being tautologically true, being contingent, and being self-contradictory. (These notions are defined below.)
Propositional logic also studies way of modifying statements, such as the addition of the word “not” that is used to change an affirmative statement into a negative statement. Here, the fundamental logical principle involved is that if a given affirmative statement is true, the negation of that statement is false, and if a given affirmative statement is false, the negation of that statement is true.
What is distinctive about propositional logic as opposed to other (typically more complicated) branches of logic is that propositional logic does not deal with logical relationships and properties that involve the parts of a statement smaller than the simple statements making it up. Therefore, propositional logic does not study those logical characteristics of the propositions below in virtue of which they constitute a valid argument:
George W. Bush is a president of the United States.
George W. Bush is a son of a president of the United States.
Therefore, there is someone who is both a president of the United States and a son of a president of the United States.
Explanation:
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