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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