Ideas of Rod Girle, by Theme

[New Zealand, fl. 2003, Professor at the University of Auckland]

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4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic

7798	There are three axiom schemas for propositional logic

7786	Propositional logic handles negation, disjunction, conjunction; predicate logic adds quantifiers, predicates, relations

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / a. Symbols of PL

7799	Proposition logic has definitions for its three operators: or, and, and identical

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL

7797	Axiom systems of logic contain axioms, inference rules, and definitions of proof and theorems

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4

7794	There are seven modalities in S4, each with its negation

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5

7793	◊p → □◊p is the hallmark of S5

7795	S5 has just six modalities, and all strings can be reduced to those

4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic

7787	Possible worlds logics use true-in-a-world rather than true

7796	Modal logics were studied in terms of axioms, but now possible worlds semantics is added

7788	Modal logic has four basic modal negation equivalences

5. Theory of Logic / B. Logical Consequence / 7. Strict Implication

7789	Necessary implication is called 'strict implication'; if successful, it is called 'entailment'

5. Theory of Logic / H. Proof Systems / 5. Tableau Proof

7790	If an argument is invalid, a truth tree will indicate a counter-example

10. Modality / A. Necessity / 3. Types of Necessity

7800	Analytic truths are divided into logically and conceptually necessary

10. Modality / B. Possibility / 1. Possibility

7801	Possibilities can be logical, theoretical, physical, economic or human

10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds

7792	A world has 'access' to a world it generates, which is important in possible worlds semantics