Truth Trees in SL

Question 1

Decidability in SL

Answer 1

Procedures to determine consistency and entailment are guaranteed to terminate

Question 2

Inconsistency (Truth Trees)

Answer 2

All branches are closed

Question 3

Consistence (Truth Trees)

Answer 3

At least one branch is open

Question 4

Truth functional truthity

Answer 4

P is TF true iff {~P} is inconsistent

Question 5

Truth functional falsity

Answer 5

P is TF false iff {P} is inconsistent

Question 6

Truth functional indeterminacy

Answer 6

P if TF indeterminate iff it is neither TF true nor false

Question 7

TF Entailment in TTs

Answer 7

(\gamma |= P) iff (\gamma \union {~P}) is TF inconsistent

Question 8

TF equivalence

Answer 8

P === Q in SL iff {~(P === Q)} is inconsistent

Question 9

TF Validity

Answer 9

An argument in SL is TF valid iff the premises with the negation of the conclusion is inconsistent