Consistency In logic, ‘consistency’ has two meanings.

Consistency In logic, ‘consistency’ has two meanings. Consistency of a system of rules.

Consistency In logic, ‘consistency’ has two meanings. Consistency of a system of rules. If an argument is provable in the system, then that argument is valid.

Consistency In logic, ‘consistency’ has two meanings. Consistency of a group of statements.

Consistency In logic, ‘consistency’ has two meanings. Consistency of a group of statements. This is closer to the ordinary use of the word. John may be wrong. but at least he is consistent.

Consistency A group of statements is consistent iff It is (logically) possible that they be T together.

Consistency A group of statements is consistent iff It is (logically) possible that they be T together. iff There is a row of their truth table where their outputs are all T together.

Consistency A group of statements is consistent iff It is (logically) possible that they be T together. iff There is a row of their truth table where their outputs are all T together. Sample: -Q, P>Q is consistent.

Consistency A group of statements is consistent iff It is (logically) possible that they be T together. iff There is a row of their truth table where their outputs are all T together. Sample: -Q, P>Q is consistent. P Q -Q P>Q T T F T F T T F F F T T * *

Consistency A group of statements is consistent iff It is (logically) possible that they be T together. iff There is a row of their truth table where their outputs are all T together. Sample: -Q, P>Q is consistent. P Q -Q P>Q T T F T F T T F F F T T * * They can be T together.

Testing for Consistency To show A and B are consistent... with a table: There is a single row where A and B are both T.

Testing for Consistency To show A and B are consistent... with a table: There is a single row where A and B are both T. with a proof: No proof test is possible.

Testing for Consistency To show A and B are consistent... with a table: There is a single row where A and B are both T. with a proof: No proof test is possible. with a tree:The tree for A, B is open.

Testing for Consistency To show A and B are consistent... with a table: There is a single row where A and B are both T. with a proof: No proof test is possible. with a tree:The tree for A, B is open. A tree is essentially a consistency check.

Testing for Consistency To show A and B are consistent... with a table: There is a single row where A and B are both T. with a proof: No proof test is possible. with a tree:The tree for A, B is open. Sample. This tree shows that the group -Q, P>Q is consistent.

Testing for Consistency To show A and B are consistent... with a table: There is a single row where A and B are both T. with a proof: No proof test is possible. with a tree:The tree for A, B is open. Sample. This tree shows that the group -Q, P>Q is consistent. -Q P>Q -P Q *

Validity and Consistency There is an important relationship between validity and consistency that is the basis for the tree validity test.

Validity and Consistency There is an important relationship between validity and consistency that is the basis for the tree validity test. A, B | C is valid iff it is impossible that A=T, B=T and C=F.

Validity and Consistency There is an important relationship between validity and consistency that is the basis for the tree validity test. A, B | C is valid iff it is impossible that A=T, B=T and C=F. iff it is impossible that A=T, B=T and -C=T.

Validity and Consistency There is an important relationship between validity and consistency that is the basis for the tree validity test. A, B | C is valid iff it is impossible that A=T, B=T and C=F. iff it is impossible that A=T, B=T and -C=T. iff the group A, B, -C is inconsistent.

Validity and Consistency There is an important relationship between validity and consistency that is the basis for the tree validity test. A, B | C is valid iff it is impossible that A=T, B=T and C=F. iff it is impossible that A=T, B=T and -C=T. iff the group A, B, -C is inconsistent. iff the tree for A, B, -C is closed.

Validity and Consistency There is an important relationship between validity and consistency that is the basis for the tree validity test. A, B | C is valid iff the tree for A, B, -C is closed.

Summary of the Tests To show A and B are consistent... with a table: There is a single row where A and B are both T. with a proof: No proof test is possible. with a tree:The tree for A, B is open. For more click here