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Single Idea 7797
[filed under theme 4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
]
Full Idea
An axiom system for a logic contains three elements: a set of axioms; a set of inference rules; and definitions for proofs and theorems. There are also definitions for the derivation of conclusions from sets of premises.
Gist of Idea
Axiom systems of logic contain axioms, inference rules, and definitions of proof and theorems
Source
Rod Girle (Modal Logics and Philosophy [2000], 6.5)
Book Ref
Girle,Rod: 'Modal Logics and Philosophy' [Acumen 2000], p.92
The
15 ideas
from Rod Girle
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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7799
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Proposition logic has definitions for its three operators: or, and, and identical
[Girle]
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7798
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There are three axiom schemas for propositional logic
[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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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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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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