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Ideas of GE Hughes/M Cresswell, by Text

[New Zealand, fl. 1968, Professor at Wellington University, NZ.]

1968 An Introduction to Modal Logic
Ch.1 p.10 A 'value-assignment' (V) is when to each variable in the set V assigns either the value 1 or the value 0
     Full Idea: A 'value-assignment' (V) is when to each variable in the set V assigns either the value 1 or the value 0.
     From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1)
     A reaction: In the interpreted version of the logic, 1 and 0 would become T (true) and F (false). The procedure seems to be called nowadays a 'valuation'.
Ch.1 p.15 The Law of Transposition says (P→Q) → (¬Q→¬P)
     Full Idea: The Law of Transposition says that (P→Q) → (¬Q→¬P).
     From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1)
     A reaction: That is, if the consequent (Q) of a conditional is false, then the antecedent (P) must have been false.
Ch.1 p.19 The rules preserve validity from the axioms, so no thesis negates any other thesis
     Full Idea: An axiomatic system is most naturally consistent iff no thesis is the negation of another thesis. It can be shown that every axiom is valid, that the transformation rules are validity-preserving, and if a wff α is valid, then ¬α is not valid.
     From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1)
     A reaction: [The labels 'soundness' and 'consistency' seem interchangeable here, with the former nowadays preferred]
Ch.1 p.19 A system is 'weakly' complete if all wffs are derivable, and 'strongly' if theses are maximised
     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.
     From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1)
     A reaction: [They go on to say that Propositional Logic is strongly complete, but Modal Logic is not]