### 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