1. Truth-functional logical connectives:
2. ∼ denotes a negation: '∼p' denotes 'not-p'
3. ∧ denotes a conjunction: 'p ∧ q' denotes 'p and q'
4. ∨ denotes an inclusive disjunction: 'p ∨ q' denotes 'p or q'
5. → denotes a material conditional: 'p → q' denotes 'if p then q'
6. ⟷ denotes a material biconditional: 'p ⟷ q' denotes 'p iff q' (or 'if p then q and if q then p')
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9. NOTE: An inclusive disjunction (denoted by '∨') is distinct from an exclusive disjunction (denoted by '⊻')
10. In an inclusive disjunction p ∨ q, at least one of the two disjuncts (p or q) would have to be true
11. In an exclusive disjunction p ⊻ q, at least and at most one of the two disjuncts (p or q) would have to be true
12. Suppose both p and q are true
13. ∴ p ∨ q (for 'p or q' in an inclusive sense) would be true
14. ∴ p ⊻ q (for 'p or q' in an exclusive sense) would be false

1. Quantifiers in first-order predicate or quantificational logic:
2. '∀x' denotes 'for all x'
3. '∃x' denotes 'for some x' or 'there exists at least one x'

1. Modal operators in alethic modal logic:
2. '□p' denotes that 'p is necessarily true'
3. '◇p' denotes that 'p is possibly true'

1. Deontic operators in deontic logic:
2. 'Op' denotes that 'The action whose performance is described in p is obligatory'
3. 'Pp' denotes that 'The action whose performance is described in p is permissible'

1. Epistemic operators in epistemic logic:
2. 'B_ap' denotes that 'Agent a believes that p'
3. 'K_ap' denotes that 'Agent a knows that p'
4. 'C_Gp' denotes that 'A group of agents G has common knowledge that p'

1. Temporal operators in temporal logic:
2. 'Fφ' denotes that 'Finally, at some state on the path, the property φ will hold'
3. 'Gφ' denotes that 'Globally, along the entire path, the property φ will hold'
4. 'Xφ' denotes that 'At the next state of the path, the property φ will hold'
5. 'φUψ' denotes that 'For 2 properties φ and ψ, the 1^st property φ holds at every state along the path until at some state the 2^nd property ψ holds'

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