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### 4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL

#### [definitions of the main concepts in propositional logic]

16 ideas
 9517 The 'scope' of a connective is the connective, the linked formulae, and the brackets [Lemmon]
 9516 A 'well-formed formula' follows the rules for variables, ¬, →, ∧, ∨, and ↔ [Lemmon]
 9518 A 'theorem' is the conclusion of a provable sequent with zero assumptions [Lemmon]
 9519 A 'substitution-instance' is a wff formed by consistent replacing variables with wffs [Lemmon]
 9530 A wff is 'contingent' if produces at least one T and at least one F [Lemmon]
 9528 A wff is a 'tautology' if all assignments to variables result in the value T [Lemmon]
 9529 A wff is 'inconsistent' if all assignments to variables result in the value F [Lemmon]
 9532 'Subcontrary' propositions are never both false, so that A∨B is a tautology [Lemmon]
 9531 'Contrary' propositions are never both true, so that ¬(A∧B) is a tautology [Lemmon]
 9534 Two propositions are 'equivalent' if they mirror one another's truth-value [Lemmon]
 9533 A 'implies' B if B is true whenever A is true (so that A→B is tautologous) [Lemmon]
 9540 A 'value-assignment' (V) is when to each variable in the set V assigns either the value 1 or the value 0 [Hughes/Cresswell]
 13422 'Conjunctive Normal Form' is ensuring that no disjunction has a conjunction within its scope [Bostock]
 13421 'Disjunctive Normal Form' is ensuring that no conjunction has a disjunction within its scope [Bostock]
 13689 'Theorems' are formulas provable from no premises at all [Sider]
 13520 A 'tautology' must include connectives [Wolf,RS]