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Single Idea 7799

[filed under theme 4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / a. Symbols of PL ]

Full Idea

The operators of propositional logic are defined as follows: 'or' (v) is not-A implies B; 'and' (ampersand) is not A-implies-not-B; and 'identity' (three line equals) is A-implies-B and B-implies-A.

Gist of Idea

Proposition logic has definitions for its three operators: or, and, and identical

Source

Rod Girle (Modal Logics and Philosophy [2000], 6.5)

Book Ref

Girle,Rod: 'Modal Logics and Philosophy' [Acumen 2000], p.94

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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]