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Logical Consequence
a sentence S is a logical consequence of a set of premises if it is impossible for the premises all to be true while S is false TERM 2
Logical Equivalence
DEFINITION 2 2 sentences are logically equivalent if they have the same truth values in all possible circumstances (ignores spurious cases) TERM 3
Logical Possibility
DEFINITION 3 A sentence that there is no reason it can't be true or it there is any possible situation in which it is true TERM 4
Logical Truth
DEFINITION 4 A sentence that is a logical consequence of any set of premises, meaning it is impossible to be false (ignores spurious cases) TERM 5
Logical Validity
DEFINITION 5 If the conclusion is a logical consequence of the premises
Tautological Consequence
S is a tautological consequence of the premises if and only if every row of their joint truth table that assigns true to each premise also assigns true to S. TERM 7
Tautological Equivalence
DEFINITION 7 2 sentences Q & S are tautologically equivalent if and only if every row of their truth table assigns the same value to the main connectives of Q & S. TERM 8
Tautology
DEFINITION 8 When every row of the truth table for S assigns true to its main connective. TERM 9
Syntactical Elements of FOL
DEFINITION 9 Vocabulary: the stock of symbols, categorized into defined, functional types Grammar: rules for constructing expressions (sentences) out of symbols Transformation Rules: inference rules TERM 10
Soundness
DEFINITION 10 An argument is sound when it is valid, and both its conclusion and all of its premises are true
