Chapter ObjeCtives
After studying this chapter, you will be able to:
• Use the formal symbols of propositional logic.
• Find the truth value of an expression in propositional logic.
• Construct formal proofs in propositional logic, and use such proofs to determine the validity of English language arguments.
• Use the formal symbols of predicate logic.
• Find the truth value in some interpretation of an expression in predicate logic.
• Use predicate logic to represent English language sentences.
• Construct formal proofs in predicate logic, and use such proofs to determine
the validity of English language arguments.
• Understand how the programming language Prolog is built on predicate logic.
• Mathematically prove the correctness of programs that use assignment statements and conditional statements.
You have been selected to serve on jury duty for a criminal case. The attorney for the
defense argues as follows:
If my client is guilty, then the knife was in the drawer. Either the knife was not in the
drawer or Jason Pritchard saw the knife. If the knife was not there on October 10,
it follows that Jason Pritchard did not see the knife. Furthermore, if the knife was
there on October 10, then the knife was in the drawer and also the hammer was in
the barn. But we all know that the hammer was not in the barn. Therefore, ladies
and gentlemen of the jury, my client is innocent.
Question: Is the attorney’s argument sound? How should you vote?
It’s much easier to answer this question if the argument is recast in the notation
of formal logic. Formal logic strips away confusing verbiage and allows us to
concentrate on the underlying reasoning being applied. In fact, formal logic—the
subject of this chapter—provides the foundation for the organized, careful method
of thinking that characterizes any reasoned activity—a criminal investigation, a
scientific experiment, a sociological study. In addition, formal logic has direct
applications in computer science. The last two sections of this chapter explore
a programming language based on logic and the use of formal logic to verify
the correctness of computer programs. Also, circuit logic (the logic governing
1 1
Formal Logic
C h a p t e r
After studying this chapter, you will be able to:
• Use the formal symbols of propositional logic.
• Find the truth value of an expression in propositional logic.
• Construct formal proofs in propositional logic, and use such proofs to determine the validity of English language arguments.
• Use the formal symbols of predicate logic.
• Find the truth value in some interpretation of an expression in predicate logic.
• Use predicate logic to represent English language sentences.
• Construct formal proofs in predicate logic, and use such proofs to determine
the validity of English language arguments.
• Understand how the programming language Prolog is built on predicate logic.
• Mathematically prove the correctness of programs that use assignment statements and conditional statements.
You have been selected to serve on jury duty for a criminal case. The attorney for the
defense argues as follows:
If my client is guilty, then the knife was in the drawer. Either the knife was not in the
drawer or Jason Pritchard saw the knife. If the knife was not there on October 10,
it follows that Jason Pritchard did not see the knife. Furthermore, if the knife was
there on October 10, then the knife was in the drawer and also the hammer was in
the barn. But we all know that the hammer was not in the barn. Therefore, ladies
and gentlemen of the jury, my client is innocent.
Question: Is the attorney’s argument sound? How should you vote?
It’s much easier to answer this question if the argument is recast in the notation
of formal logic. Formal logic strips away confusing verbiage and allows us to
concentrate on the underlying reasoning being applied. In fact, formal logic—the
subject of this chapter—provides the foundation for the organized, careful method
of thinking that characterizes any reasoned activity—a criminal investigation, a
scientific experiment, a sociological study. In addition, formal logic has direct
applications in computer science. The last two sections of this chapter explore
a programming language based on logic and the use of formal logic to verify
the correctness of computer programs. Also, circuit logic (the logic governing
1 1
Formal Logic
C h a p t e r