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

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
7791

The simplest of the logics based on possible worlds is Lewis's 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
7796

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

7787

Possible worlds logics use trueinaworld rather than true

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 counterexample

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
