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
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7786
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Propositional logic handles negation, disjunction, conjunction; predicate logic adds quantifiers, predicates, relations
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7798
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There are three axiom schemas for propositional logic
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4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / a. Symbols of PL
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7799
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Proposition logic has definitions for its three operators: or, and, and identical
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4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
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7797
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Axiom systems of logic contain axioms, inference rules, and definitions of proof and theorems
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
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7794
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There are seven modalities in S4, each with its negation
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
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7793
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◊p → □◊p is the hallmark of S5
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7795
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S5 has just six modalities, and all strings can be reduced to those
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4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
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7787
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Possible worlds logics use true-in-a-world rather than true
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7796
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Modal logics were studied in terms of axioms, but now possible worlds semantics is added
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7788
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Modal logic has four basic modal negation equivalences
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5. Theory of Logic / B. Logical Consequence / 7. Strict Implication
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7789
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Necessary implication is called 'strict implication'; if successful, it is called 'entailment'
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5. Theory of Logic / H. Proof Systems / 5. Tableau Proof
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7790
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If an argument is invalid, a truth tree will indicate a counter-example
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10. Modality / A. Necessity / 3. Types of Necessity
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7800
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Analytic truths are divided into logically and conceptually necessary
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10. Modality / B. Possibility / 1. Possibility
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7801
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Possibilities can be logical, theoretical, physical, economic or human
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10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
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7792
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A world has 'access' to a world it generates, which is important in possible worlds semantics
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