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Single Idea 13689
[filed under theme 4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
]
Full Idea
Formulas provable from no premises at all are often called 'theorems'.
Gist of Idea
'Theorems' are formulas provable from no premises at all
Source
Theodore Sider (Logic for Philosophy [2010], 2.6)
Book Ref
Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.47
Related Idea
Idea 9518
A 'theorem' is the conclusion of a provable sequent with zero assumptions [Lemmon]
The
16 ideas
with the same theme
[definitions of the main concepts in propositional logic]:
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9517
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The 'scope' of a connective is the connective, the linked formulae, and the brackets
[Lemmon]
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9516
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A 'well-formed formula' follows the rules for variables, ¬, →, ∧, ∨, and ↔
[Lemmon]
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9518
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A 'theorem' is the conclusion of a provable sequent with zero assumptions
[Lemmon]
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9519
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A 'substitution-instance' is a wff formed by consistent replacing variables with wffs
[Lemmon]
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9529
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A wff is 'inconsistent' if all assignments to variables result in the value F
[Lemmon]
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9531
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'Contrary' propositions are never both true, so that ¬(A∧B) is a tautology
[Lemmon]
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9534
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Two propositions are 'equivalent' if they mirror one another's truth-value
[Lemmon]
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9530
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A wff is 'contingent' if produces at least one T and at least one F
[Lemmon]
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9532
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'Subcontrary' propositions are never both false, so that A∨B is a tautology
[Lemmon]
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9533
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A 'implies' B if B is true whenever A is true (so that A→B is tautologous)
[Lemmon]
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9528
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A wff is a 'tautology' if all assignments to variables result in the value T
[Lemmon]
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9540
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A 'value-assignment' (V) is when to each variable in the set V assigns either the value 1 or the value 0
[Hughes/Cresswell]
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13422
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'Conjunctive Normal Form' is ensuring that no disjunction has a conjunction within its scope
[Bostock]
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13421
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'Disjunctive Normal Form' is ensuring that no conjunction has a disjunction within its scope
[Bostock]
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13689
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'Theorems' are formulas provable from no premises at all
[Sider]
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13520
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A 'tautology' must include connectives
[Wolf,RS]
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