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Single Idea 7790
[filed under theme 5. Theory of Logic / H. Proof Systems / 5. Tableau Proof
]
Full Idea
The truth trees method for establishing the validity of arguments and formulas is easy to use, and has the advantage that if an argument or formula is not valid, then a counter-example can be retrieved from the tree.
Gist of Idea
If an argument is invalid, a truth tree will indicate a counter-example
Source
Rod Girle (Modal Logics and Philosophy [2000], 1.4)
Book Ref
Girle,Rod: 'Modal Logics and Philosophy' [Acumen 2000], p.8
Related Idea
Idea 13613
A completed open branch gives an interpretation which verifies those formulae [Bostock]
The
15 ideas
from 'Modal Logics and Philosophy'
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7786
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Propositional logic handles negation, disjunction, conjunction; predicate logic adds quantifiers, predicates, relations
[Girle]
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7787
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Possible worlds logics use true-in-a-world rather than true
[Girle]
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7788
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Modal logic has four basic modal negation equivalences
[Girle]
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7789
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Necessary implication is called 'strict implication'; if successful, it is called 'entailment'
[Girle]
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7790
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If an argument is invalid, a truth tree will indicate a counter-example
[Girle]
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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
[Girle]
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7793
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◊p → □◊p is the hallmark of S5
[Girle]
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7795
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S5 has just six modalities, and all strings can be reduced to those
[Girle]
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7794
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There are seven modalities in S4, each with its negation
[Girle]
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7796
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Modal logics were studied in terms of axioms, but now possible worlds semantics is added
[Girle]
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7798
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There are three axiom schemas for propositional logic
[Girle]
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7799
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Proposition logic has definitions for its three operators: or, and, and identical
[Girle]
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7797
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Axiom systems of logic contain axioms, inference rules, and definitions of proof and theorems
[Girle]
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7800
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Analytic truths are divided into logically and conceptually necessary
[Girle]
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7801
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Possibilities can be logical, theoretical, physical, economic or human
[Girle]
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