Three connectives
And (∧)
connects two expressions of the same grammatical category
nouns, verbs, adverbs, adjectives, and, most importantly, sentences.
it’s a binary propositional connector. It can only connect two inputs.
A ∧ B is the conjunction of A and B
There are some issues with coming from natural language, for example:
- Eve married Adam and she became pregnant
- Eve became pregnant and she married Adam.
Has a temporal succession aspect to it, which the formal ∧ does not (and should not!) convey.
- Jean-Paul is reading the newspaper and smoking a cigarette.
Implies simultaneity
- The vase fell on the ground and it broke into pieces.
Implies causality.
Or (∨)
A or B is the disjunction of A and B.
or is a binary connective
or is a propositional connective
Not ¬
Not is unary.
negates the truth value of