Logic - Semantics of propositional logic

structures, truth values/tables,tautologies, contradictions, logical equivalence, validity/invalidity, consistency/inconsistency (all in formal language L1)

structure interpretation

giving truth value to sentence letter

partial structures

shows only truth value of letters that appear in argument

compositionality

meaning of whole is function of meaning of parts

|Ωb| = T

Ω is true in structure b

conjunction

T, F, F, F

disjunction

T, T, T, F

material implication

T, F, T, T

material equivalence

T, F, F, T

tautologies - logically true

iff true in all L1 structures

contradictions - logically false

iff false in all L1 structures

Logically equivalent sentences

iff truth values are the same in every L1 structure

L |= Q

L entails Q is valid

|= Q

Q is a logical truth

validity

iff set of premises with ¬conclusion is inconsistent