Characteristics of an Axiomatic systems are ................. . (1) Consistency (2) Completeness (3) Independence (4) Contingent
Consistency, completeness and independence
An axiomatic system starts from a set of axioms and derives theorems through rules of inference. Logicians evaluate such a system by certain meta-logical properties.
(1) Consistency: no formula and its negation can both be derived; this is the most essential requirement. It is a characteristic.
(2) Completeness: every truth (every valid formula) of the domain is derivable as a theorem. It is a characteristic.
(3) Independence: no axiom can be derived from the remaining axioms, so the axiom set has no redundancy. It is a characteristic.
(4) Contingent: contingency is a property of individual statements whose truth depends on the facts; it is not a property of an axiomatic system. It is not a characteristic.
Hence, the answer is Consistency, completeness and independence.
Similar Questions
Match List I and List II and select the correct answer from the codes given below :
List I List II (a) ~ (p ∨ ~ p) (1) Identity (b) ~ (p • ~ p) (2) Contingency (c) ~ (p ⊃ q) (3) Tautology (d) p ⊃ p (4) Contradiction Codes :
(a) (b) (c) (d)
Which of the following is not the characteristics of an effective decision procedure ?
Correct formulation of the Rule U.I. (Universal Instantiation) is ........... .
Law of contradiction states that :
Correct symbolization of the following proposition is — “All successful politicians and orators are hard-working”.
“Sudhir had not locked the gates yesterday. Either the watchman or Sudhir locks the gates. Therefore, the watchman must have locked the gates yesterday”. This argument is ..................... .
If the statement ‘p’ is true and the statement ‘q’ is false, the truth value of the statements ‘p ≡ ~ q’ and ‘~ q ⊃ ~ p’ are :
In the ranking of a competitive examination Vishal was above Vijay but below Shyam. Mohan was above Shyam but below Rohan. Vijay was between Vishal and Ashok. Who is third from the top ?
Ragini facing East walks 10 meter, then she turns to her left and walks 12 meter. Then she turns to her right in $45^o$ and walks 15 meter. Then, how much distance she has walked from the starting point and which direction is she facing now ?
In the Wason selection task for propositional reasoning, ‘participants develop a general idea of the rule, then construct examples that follow the rule’ is referred to as :
Important Questions from Deductive - Teaching
Match List I and List II and select the correct answer from the codes given below :
List I List II (a) ~ (p ∨ ~ p) (1) Identity (b) ~ (p • ~ p) (2) Contingency (c) ~ (p ⊃ q) (3) Tautology (d) p ⊃ p (4) Contradiction Codes :
(a) (b) (c) (d)
Which of the following is not the characteristics of an effective decision procedure ?
Correct formulation of the Rule U.I. (Universal Instantiation) is ........... .
Law of contradiction states that :
Correct symbolization of the following proposition is — “All successful politicians and orators are hard-working”.
