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Full Idea
To say that an axiom system is 'weakly complete' is to say that every valid wff of the system is derivable as a thesis. ..The system is 'strongly complete' if it cannot have any more theses than it has without falling into inconsistency.
Gist of Idea
A system is 'weakly' complete if all wffs are derivable, and 'strongly' if theses are maximised
Source
GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1)
Book Ref
Hughes,G./Cresswell,M.: 'An Introduction to Modal Logic' [Methuen 1972], p.19
A Reaction
[They go on to say that Propositional Logic is strongly complete, but Modal Logic is not]
| 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] |
| 9541 | The Law of Transposition says (P→Q) → (¬Q→¬P) [Hughes/Cresswell] |
| 9543 | The rules preserve validity from the axioms, so no thesis negates any other thesis [Hughes/Cresswell] |
| 9544 | A system is 'weakly' complete if all wffs are derivable, and 'strongly' if theses are maximised [Hughes/Cresswell] |