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Understanding Modal Logic: Semantic Analysis and Language Variations

Explore truth conditions in sentences like "You must not smoke here" vs. "You may not smoke here," formalize statements using logic symbols, and delve into modal and perfect verb ambiguities. Investigate cross-linguistic data on deontic and epistemic modals, and grapple with epistemic vs. counterfactual possibilities in natural language.

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Understanding Modal Logic: Semantic Analysis and Language Variations

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  1. Lecture 6 Ling 442

  2. Exercises (part 1) • Why do the following two sentences have the same truth conditions? • You must not smoke here. • You may not smoke here.

  3. Exercises (part 2) ⟡ • Formalize the following using ⃟⃞. • Necessarily, a bachelor is unmarried. • A child could have invented the mousetrap. • The lake is sure to freeze tonight. • Right-turning traffic must give way. • Discuss the differences between 1 and 2 • If Cain didn’t kill Abel, then someone else did. • If Cain hadn’t killed Abel, then someone else would have.

  4. Cross-linguistic data • In Japanese, the concepts associated with deontic must/may and epistemic must/may are conveyed by two separate forms: (approximate translations into English) Deontic must: If you do not do it, it is no good. Epistemic must: It is not wrong that S. Deontic may: Even if you do it, it is good. Epistemic may: It is not known if S. • How about your language (if it is not English)?

  5. Modal + Perfect • In principle, any modal verb is ambiguous between epistemic and deontic readings. But complex forms (modal + perfect) often lack deontic readings. In order to take Ling 479, You must have taken L442. (deontic – ok) ?? An applicant to our graduate program may have been a member of another program. (deontic – presumably impossible)

  6. Epistemic vs. Counterfactual Possibilities Nice example from the text • She might have fallen down the cliff. (Ambiguous between an epistemic reading and a counterfactual (Kearns calls it “logical”) reading. If you have difficulty finding two readings, then try using could. • She could have fallen down the cliff.

  7. Counterfactual conditions in more detail • The semantics of counterfactual conditionals cannot be stated in terms of the truth values of the component sentences. • You need to say something like the following: • ⟦If S1, then S2⟧= true iff in all possible worlds w most similar to the actual world among those in which ⟦S1⟧ = true, ⟦S2⟧ = true as well.

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