Ideas from 'Modal Logics and Philosophy' by Rod Girle [2000], by Theme Structure
[found in 'Modal Logics and Philosophy' by Girle,Rod [Acumen 2000,1902683153]].
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4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
7798

There are three axiom schemas for propositional logic

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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
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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
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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
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There are seven modalities in S4, each with its negation

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
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◊p → □◊p is the hallmark of S5

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

4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
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Possible worlds logics use trueinaworld rather than true

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

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Modal logic has four basic modal negation equivalences

5. Theory of Logic / B. Logical Consequence / 7. Strict Implication
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Necessary implication is called 'strict implication'; if successful, it is called 'entailment'

5. Theory of Logic / H. Proof Systems / 5. Tableau Proof
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If an argument is invalid, a truth tree will indicate a counterexample

10. Modality / A. Necessity / 3. Types of Necessity
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Analytic truths are divided into logically and conceptually necessary

10. Modality / B. Possibility / 1. Possibility
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Possibilities can be logical, theoretical, physical, economic or human

10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
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A world has 'access' to a world it generates, which is important in possible worlds semantics
