This page does not represent the most current semester of this course; it is present merely as an archive.

See also our list of symbols

- Antecedent
- The left-hand operand of a conditional; the X is X \rightarrow Y.
- Axiom
- Something we accept as true without requiring a proof.
- Associative
- Of an operator, meaning the order of operations when several of that operator are applied in a row does not matter. To say some operator \cdot is associative means that (P \cdot Q) \cdot R \equiv P \cdot (Q \cdot R) for all propositions P, Q, and R.
- Biconditional
- See
*Iff*. - Bi-implication
- See
*Iff*. - Commutative
- Of an operator, meaning the order of its operands does not matter. To say some operator \cdot is commutative means that P \cdot Q \equiv Q \cdot P for all propositions P and Q.
- Conjunction
- Logical AND (\land).
- Consequent
- The right-hand operand of a conditional; the Y is X \rightarrow Y.
- Contradiction
- A logical expression that is equivalent to FALSE (\bot).
- De Morgan’s laws
Two specific, related logical equivalences; see our list of equivalences for their form.

Because of their related structure, it is not uncommon to refer to both together in the singular (i.e.

De Morgan’s law

).- Disjunction
- Logical OR (\lor).
- Domain
- The possible values a variable could take under a quantifier; for example, if the domain is
all animals

then \forall x \;.\; F(x) meansF is true for all animals

. - Equivalent
- Two logical expressions P and Q are equivalent if and only if the expression P \leftrightarrow Q is a tautology.
- Formula
- see
*Logical Expression*. - Iff
- A contraction of
if and only if

, a name for the operator \leftrightarrow. - Logical Expression
- One or more propositions or predicates, combined with operators so that the whole is a predicate or proposition.
- Necessary
Cannot happen without. If A is a necessary condition for B, then we know both

- Without A, no B is possible. \lnot A \rightarrow \lnot B
- If you see B, A must also be. B \rightarrow A

Often used to suggest partial causation or a requirement. Compare

*Sufficient*.- Predicate
A single word for two related concepts:

- In logic, an incomplete proposition, where one or more component has been replaced by a
*Variable*. - In programming, a subroutine that (a) has no side-effects and (b) always returns a Boolean value.

- In logic, an incomplete proposition, where one or more component has been replaced by a
- Proposition
- A statement that, by construction, must either be true or false.
- Quantifier
- One of \forall or \exists; some people also include \nexists while others think of that as being shorthand for \lnot \exists.
- Satisfiable
- A satisfiable expression is not a contradiction.
- Sentence
- see
*Logical Expression*. - Sufficient
Always happens if. If A is a sufficient condition for B, then we know both

- If you see A, B must also be. A \rightarrow B
- If you don’t see B, A can’t be. \lnot B \rightarrow \lnot A

Often used to suggest causation. Compare

*Necessary*.- Tautology
- A logical expression that is equivalent to TRUE (\top).
- Universe of Discourse
- see
*Domain*. - Variable
A single word for (at least) three concepts with similar but non-identical meaning:

- In algebra, a place-holder for a single numeric value.
- In logic, a place-holder for a single element from the
*Domain*, generally used with*Quantifiers*and*Predicates*. - In programming, a named region of memory that may take different values at different times.