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First-Order Logic

This quiz covers the fundamental concepts and principles of First-Order Logic, a branch of mathematical logic that deals with the study of formal languages and their use in reasoning and proof.

15 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

In First-Order Logic, a predicate is a function that maps a tuple of terms to a truth value.

  1. True
  2. False
Question 2 Multiple Choice (Single Answer)

Which of the following is a valid quantifier in First-Order Logic?

  1. ∀
  2. ∃
  3. ¬
  4. ∧
Question 3 Multiple Choice (Single Answer)

The domain of discourse in First-Order Logic refers to the set of objects over which the variables in a formula can range.

  1. True
  2. False
Question 4 Multiple Choice (Single Answer)

In First-Order Logic, a term can be a variable, a constant, or a function applied to other terms.

  1. True
  2. False
Question 5 Multiple Choice (Single Answer)

The principle of universal generalization in First-Order Logic states that if a formula is true for all values of a variable in a domain, then it is universally true.

  1. True
  2. False
Question 6 Multiple Choice (Single Answer)

Which of the following is a logical connective in First-Order Logic?

  1. ∧
  2. ∨
  3. ¬
  4. ∀
Question 7 Multiple Choice (Single Answer)

In First-Order Logic, a well-formed formula (WFF) is a formula that is syntactically correct and follows the rules of the language.

  1. True
  2. False
Question 8 Multiple Choice (Single Answer)

The satisfiability of a formula in First-Order Logic refers to the existence of an interpretation that makes the formula true.

  1. True
  2. False
Question 9 Multiple Choice (Single Answer)

In First-Order Logic, a model of a formula is an interpretation that makes the formula true.

  1. True
  2. False
Question 10 Multiple Choice (Single Answer)

The deductive closure of a set of formulas in First-Order Logic is the set of all formulas that can be derived from the given set using the rules of inference.

  1. True
  2. False
Question 11 Multiple Choice (Single Answer)

Which of the following is a rule of inference in First-Order Logic?

  1. Modus Ponens
  2. Universal Instantiation
  3. Existential Generalization
  4. Resolution
Question 12 Multiple Choice (Single Answer)

In First-Order Logic, a theory is a set of formulas that is closed under the rules of inference.

  1. True
  2. False
Question 13 Multiple Choice (Single Answer)

The completeness theorem for First-Order Logic states that every consistent theory has a model.

  1. True
  2. False
Question 14 Multiple Choice (Single Answer)

Which of the following is a decidable fragment of First-Order Logic?

  1. Propositional Logic
  2. Monadic Predicate Logic
  3. Full First-Order Logic
  4. Second-Order Logic
Question 15 Multiple Choice (Single Answer)

In First-Order Logic, the Herbrand universe of a set of formulas is the set of all ground terms that can be constructed from the constants and function symbols in the formulas.

  1. True
  2. False
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