LS

Completeness of Ls (p. 150)

Ls is complete if and only if for every set of sentences, Γ, and any sentence, Φ, if Γ |= Φ, then Γ |- Φ

≡

biconditional; if p then q and if q then p

⊃

conditional; if p then q

∧

conjunction; p and q

|-

deductively yields;

∨

disjunction; p or q or both

|=

logically implies

¬

negation; not p

|

Scheffer-stroke; not both p and q

Interpretation (p. 81)

a function from sentences to truth values, so the value of I(p) is the truth value an interpretation I assigns to a sentence p

Truth-functional language (p. 15)

a language in which the truth value of every sentence is a function of--is completely fixed by--the truth value of its constituent sentences

Logical implication (p. 87)

a set of sentences Γ logically implies a sentence Φ (Γ |= Φ) if and only if Φ cannot be false if Γ (i.e. every sentence in Γ) is true

Model (p. 80)

an interpretation I is a model of a sentence p if and only if I(p) is true; if Γ is a set of sentences, then I is a model of Γ if and only if every sentence of Γ is true under I

Sentence of Ls (p. 76-77)

1. Every member of Cs is a sentence of Ls; 2. If p is a sentence of Ls, then ¬p is a sentence of Ls; 3. If p and q are sentences of Ls, then (p∧q) is a sentence of Ls; 4. If p and q are sentences of Ls, then (p∨q) is a sentence of Ls; 5. If p and q are sentences of Ls, then (p⊃q) is a sentence of Ls; 6. If p and q are sentences of Ls, then (p≡q) is a sentence of Ls; 7. Nothing is a sentence of Ls that is not constructed in accord with rules 1-6

Validity (valid sequence in Ls)

A derivation <Γ, Φ>, is valid if and only if Γ logically implies Φ (Γ |= Φ)

Soundness of Ls (p. 150)

Ls is sound if and only if for every set of sentences, Γ, and any sentence, Φ, if Γ deductively yields Φ (Γ |- Φ), then Γ logically implies Φ (Γ |= Φ)

Contradictory sentence (p. 72)

sentences that are false in all possible worlds

Logical truth (p. 71)

sentences that are true in all possible worlds

Contingent sentence (p. 72)

sentences whose truth values vary with assignments of truth values to its atomic constituents

Logical consequence (p. 87)

the conclusion is a logical consequence of the premises if the argument is a good one and the premises logically imply the conclusion

Object language (p. 83)

the language being talked about

Metalanguage (p. 83)

the language being used to talk about another language