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Chapter 2 Kearns: Reading guide

Make sure you know what the following concepts mean and how to use them appropriately:

  • proposition
  • propositional logic
  • logical connective (also the specific connectives: conjunction, negation, disjunction, material implication, biconditional)
  • antecedent and consequent of a material implication
  • exclusive vs. inclusive disjunction
  • truth table
  • logical equivalence
  • predicate logic
  • predicate
  • argument
  • logical constant, logical variable
  • logical quantifier (also the specific quantifiers: universal and existential)
  • bound variable
  • scopal ambiguity
Make sure you understand:
  • the difference between propositional logic and predicate logic
  • the relationship between material implication in logic and conditional sentences in natural language
  • that logical quantifiers bind variables; that variables must be bound by quantifiers (remember, otherwise the formula is "naked")
  • why determiners like every or some in English are analyzed as logical quantifiers binding variables
  • that we are aiming at defining the truth conditions beyond the formula corresponding to a natural language sentence or phrase
Make sure you know how to:
  • build a truth table for a formula
  • formalize sentences in English as formulae in propositional and predicate logic, respecting the rules of the logic
  • state the truth conditions of sentences expressed as logical formulae
  • determine whether two formulae are logically equivalent (see p. 27 and exercise B)
  • determine how many arguments a predicate representing a word has, depending on the meaning of the word (verb, noun, adjective, preposition, etc.) and its linguistic behavior in natural language
  • determine the order of the arguments (and stay consistent)
  • argue for a given formalization of an English sentence over possible alternatives
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