2000 | Modal Logics and Philosophy |
1.1 | p.1 | 7786 | Propositional logic handles negation, disjunction, conjunction; predicate logic adds quantifiers, predicates, relations |
1.1 | p.2 | 7787 | Possible worlds logics use true-in-a-world rather than true |
1.2 | p.3 | 7788 | Modal logic has four basic modal negation equivalences |
1.2 | p.7 | 7789 | Necessary implication is called 'strict implication'; if successful, it is called 'entailment' |
1.4 | p.8 | 7790 | If an argument is invalid, a truth tree will indicate a counter-example |
2.1 | p.13 | 7791 | The simplest of the logics based on possible worlds is Lewis's S5 |
3.2 | p.29 | 7792 | A world has 'access' to a world it generates, which is important in possible worlds semantics |
3.3 | p.34 | 7793 | ◊p → □◊p is the hallmark of S5 |
3.5 | p.46 | 7795 | S5 has just six modalities, and all strings can be reduced to those |
3.5 | p.46 | 7794 | There are seven modalities in S4, each with its negation |
6.5 | p.92 | 7796 | Modal logics were studied in terms of axioms, but now possible worlds semantics is added |
6.5 | p.92 | 7798 | There are three axiom schemas for propositional logic |
6.5 | p.92 | 7797 | Axiom systems of logic contain axioms, inference rules, and definitions of proof and theorems |
6.5 | p.94 | 7799 | Proposition logic has definitions for its three operators: or, and, and identical |
7.3 | p.114 | 7800 | Analytic truths are divided into logically and conceptually necessary |
7.3 | p.114 | 7801 | Possibilities can be logical, theoretical, physical, economic or human |