Lexicon of Arguments

 

Hughes I 65
System/Part/Hughes/Cresswell(s):parts of formulas are not themselves parts of the system already to which the formulas belong to. - ((s) "p" can never be an axiom, otherwise all sentences would be true.)
Hughes I 237
Non-regular systems/Modal Logic/Hughes/Cresswell: can include formulas of the form
p. ~ p
where the eradication of the modal operator simply results in p,
E.g. systems with e.g.
C 13 MMp - "no statement is necessarily necessary"
>Modal operators, >Deletion.
MMp simply results in
p - p. ~ p.
Hughes I 243
>"Non-normal worlds"/Kripke: (here also assessed with 0).
I 258
Def regular: is a system in which the modal status is maintained.
>Modalities
Hughes I 238
Non-regular systems/modal logics/Hughes/Cresswell: Problem: in S1 - S3, neither a nor b are themselves a thesis - they also have no common variable either. - Problem in the case of (a v b): could be valid while neither a nor b would be valid.
Solution/Halldén: "normal interpretation": here either a or b is valid, but neither I-a nor I-b is valid. So there are valid formulas that are not theorems.
>Theorems, >Logic, >Formulas.