structure for 'Formal Logic'    |     alphabetical list of themes    |     expand these ideas

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