Definitions (TFL and FOL) Flashcards
TFL: Tautology / theorem
A sentence is a tautology/theorem iff it is always true
TFL: (provably) equivalent
Two sentences are (provably) equivalent iff they can be proved from each other
TFL: unsatisfiable/inconsistent
A sentence is unsatisfiable/inconsistent if one can derive a contradiction from it
TFL: satisfiable/consistent
Sentences are consistent iff they are not inconsistent
TFL: (proof-theoretically) contingent
A sentence is (proof-theoretically) contingent if it is not a tautology or contradiction
TFL: Valid
An argument is valid if one can derive the conclusion from the premises (the conclusion is never false while the premises are true)
TFL: Invalid
An argument is invalid if it is possible for the premises to be true while the conclusion is false
TFL: Sound
An argument is sound if it is valid and has all true premises
FOL: Valid
An argument is valid iff every interpretation makes the conclusion true or the premises false
FOL: Validity
A sentence is a validity iff it is always true
FOL: Equivalent
Two sentences are equivalent iff they can be proved from each other (+ they always have the same truth value)
FOL: jointly satisfiable
Sentences are jointly satisfiable iff there is an interpretation where they are both true
FOL: First-order validity
Something is a first-order validity if it can be deduced from no premises
FOL: Sound
An argument is sound if it is valid and has all true premises
FOL: Inconsistent
An inconsistent sentence is a sentence whose negation can be derived without any premises
