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Exercise A

Avg difficulty 3.0

Present counter-interpretations to the following:

  1. ¬P⊨K¬◊P\neg P\vDash_{\mathbf{K}}\neg\Diamond P

  2. □(P∨Q)⊨K□P∨□Q\Box(P\vee Q)\vDash_{\mathbf{K}}\Box P\vee\Box Q

  3. ⊨K¬□(A∧¬A)\vDash_{\mathbf{K}}\neg\Box(A\wedge\neg A)

  4. □A⊨KA\Box A\vDash_{\mathbf{K}}A

Magnus et al., forall x: Calgary, Modal logic, Semantics for ML, Exercise A

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Adapted from forall x: Calgary © 2025 P. D. Magnus, Tim Button, Robert Trueman, and Richard Zach. Licensed under CC BY 4.0. Source: forall x: Calgary. Imported at revision ec34df8.