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

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.
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) means F 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• In logic, an incomplete proposition, where one or more component has been replaced by a Variable.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.
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.