¬ one-place logical connective read as “not” or as “is not the case”
~ alternative notation for “not”
& two-place logical connective read as “and” ˄ and
. and, both, yet, still
∨ two-place logical connective read as “or”
⊃ two-place logical connective read as the material conditional “if … then …”
→ alternative notation for if … then
≡ two-place logical connective read as material equivalence “…if and only …”
↔ … if and only if, both or neither …
∀ the universal quantifier read as “for all”
∃ the existential quantifier read as “there is some”
☐ one-place modal operator read as “necessarily”
◇ one-place modal operator read as “possibly”
∈ set-theoretic relationship read as “…is a member of …”
⊤ logical constant for a tautology
⊥ logical constant for a contradiction
⊢ meta-logical constant for syntactic entailment (there is a proof that …)
⊨ meta-logical constant for semantic entailment (there is a model such that …)
∴ therefore
