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
Possible worlds logics use true-in-a-world rather than true
Modal logic has four basic modal negation equivalences
Modal logics were studied in terms of axioms, but now possible worlds semantics is added
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