### Ideas of GE Hughes/M Cresswell, by Theme

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

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###### 4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
 9540 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'.
###### 4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
 9541 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.
###### 4. Formal Logic / B. Propositional Logic PL / 4. Soundness of PL
 9543 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]
###### 5. Theory of Logic / K. Features of Logics / 4. Completeness
 9544 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]