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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

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The 15 ideas from Rod Girle

7786	Propositional logic handles negation, disjunction, conjunction; predicate logic adds quantifiers, predicates, relations [Girle]

7787	Possible worlds logics use true-in-a-world rather than true [Girle]

7788	Modal logic has four basic modal negation equivalences [Girle]

7789	Necessary implication is called 'strict implication'; if successful, it is called 'entailment' [Girle]

7790	If an argument is invalid, a truth tree will indicate a counter-example [Girle]

7792	A world has 'access' to a world it generates, which is important in possible worlds semantics [Girle]

7793	◊p → □◊p is the hallmark of S5 [Girle]

7795	S5 has just six modalities, and all strings can be reduced to those [Girle]

7794	There are seven modalities in S4, each with its negation [Girle]

7796	Modal logics were studied in terms of axioms, but now possible worlds semantics is added [Girle]

7798	There are three axiom schemas for propositional logic [Girle]

7799	Proposition logic has definitions for its three operators: or, and, and identical [Girle]

7797	Axiom systems of logic contain axioms, inference rules, and definitions of proof and theorems [Girle]

7800	Analytic truths are divided into logically and conceptually necessary [Girle]

7801	Possibilities can be logical, theoretical, physical, economic or human [Girle]