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First-order logic: Quiz


Question 1: While ________ deals with simple declarative propositions, first-order logic additionally covers predicates and quantification.
Truth tableFallacyAmbiguityPropositional calculus

Question 2: The syntax determines which collections of symbols are legal expressions in first-order logic, while the ________ determine the meanings behind these expressions.
LinguisticsPragmaticsSemanticsFormal semantics

Question 3: One motivation for the use of first-order logic, rather than higher-order logic, is that first-order logic has many ________ properties that stronger logics do not have.
Syntax (logic)Formal proofFormal semanticsMetalogic

Question 4: First-order logic also satisfies several ________ theorems that make it amenable to analysis in proof theory, such as the Löwenheim–Skolem theorem and the compactness theorem.
MetalogicSyntax (logic)Formal semanticsFormal proof

Question 5: Metamath: an ongoing online project to reconstruct mathematics as a huge first-order theory, using first-order logic and the ________ ZFC.
Model theoryMathematical logicSet theoryGeorg Cantor

Question 6: Moreover, if a class of algebraic structures includes an empty structure (for example, there is an empty ________), that class can only be an elementary class in first-order logic if empty domains are permitted or the empty structure is removed from the class.
Partially ordered setBinary relationOrder theoryTotal order

Question 7: First-order logic without equality is often employed in the context of ________ and other higher-order theories of arithmetic, where the equality relation between sets of natural numbers is usually omitted.
Mathematical logicQuantificationSecond-order arithmeticSet theory

Question 8: Their proofs demonstrate a connection between the unsolvability of the decision problem for first-order logic and the unsolvability of the ________.
Turing machineComputability theoryHalting problemAlan Turing

Question 9: ________, mainly due to Willard Quine.
Alfred TarskiPredicate functor logicQuantificationFirst-order logic

Question 10: An alternate approach to the semantics of first-order logic proceeds via ________.
Vector spaceNumber theoryAbstract algebraGroup (mathematics)


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