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Full Idea
In S4 there are fourteen modalities: no-operator; necessarily; possibly; necessarily-possibly; possibly-necessarily; necessarily-possibly-necessarily; and possibly-necessarily-possibly (each with its negation).
Clarification
S4 is one of the five main systems of modal logic
Gist of Idea
There are seven modalities in S4, each with its negation
Source
Rod Girle (Modal Logics and Philosophy [2000], 3.5)
Book Ref
Girle,Rod: 'Modal Logics and Philosophy' [Acumen 2000], p.46
A Reaction
This is said to be 'more complex' than S5, but also 'weaker'.
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] |