Ideas from 'Modal Logics and Philosophy' by Rod Girle [2000], by Theme Structure

[found in 'Modal Logics and Philosophy' by Girle,Rod [Acumen 2000,1-902683-15-3]].

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4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
There are three axiom schemas for propositional logic
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
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
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
There are seven modalities in S4, each with its negation
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
The simplest of the logics based on possible worlds is Lewis's S5
◊p → □◊p is the hallmark of S5
S5 has just six modalities, and all strings can be reduced to those
4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
Modal logics were studied in terms of axioms, but now possible worlds semantics is added
Possible worlds logics use true-in-a-world rather than true
Modal logic has four basic modal negation equivalences
5. Theory of Logic / B. Logical Consequence / 7. Strict Implication
Necessary implication is called 'strict implication'; if successful, it is called 'entailment'
5. Theory of Logic / H. Proof Systems / 5. Tableau Proof
If an argument is invalid, a truth tree will indicate a counter-example
10. Modality / A. Necessity / 3. Types of Necessity
Analytic truths are divided into logically and conceptually necessary
10. Modality / B. Possibility / 1. Possibility
Possibilities can be logical, theoretical, physical, economic or human
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
A world has 'access' to a world it generates, which is important in possible worlds semantics