$$\Box A \rightarrow \Diamond B \Rightarrow \Box(\Box A \rightarrow \Diamond B)$$ First I tried to create a proof tree to find a counterexample, but that got very complicated to comprehend very quickly. A solid background in first-order logic is essential. (An Introduction to Modal Logic, London: Methuen, 1968; A Compan-ion to Modal Logic, London: Methuen, 1984), and E. J. Lemmon (An Introduction to Modal Logic, Oxford: Blackwell, 1977). Modal Metalogic: Modal Metalogic: Completeness (PDF) 12–13: Glimpses Beyond: Counterfactuals, Neighborhood Semantics, Probability, Predicative Necessity, etc. Wikipedia has some examples in its article modal logic: Versions of temporal logic can be used in computer science to model computer operations and prove theorems about them. Modal logic is the logic of necessity and possibility, and by extension of analogously paired notions like validity and consistency, obligation and permission, the known and the not-ruled-out. corrections. These are examples of logic models that other people have found effective. As I'm new to modal logic, I wanted to check whether my counter examples for the given formula is right. Mathematical Modal Logic: A View of its Evolution 3 about when, where or how Sis true, or about the circumstances under which S may be true. And modal logic can be given a topological semantics, so it can also This a first course in the area. Further inspiration and examples have been drawn from a variety of sources, including the course notes Intensional Logic by F. Veltman and D. de Jongh, Basic Concepts in Modal Logic by E. Zalta, the textbook Modal Logic by P. Blackburn, M. de Rijke, and Y. Venema  and Modal Logic for Open Minds by J. van Benthem . Tense logic, brings in propositional operators F and P, corresponding to whether a given proposition … Modal logic is the logic of necessity and possibility, and by extension of analogously paired notions like validity and consistency, obligation and permission, the known and the not-ruled-out. Dynamic logic is an extension of modal logic originally intended for reasoning about computer programs and later applied to more general complex behaviors arising in linguistics, philosophy, AI, and other fields. First we take a look at basic modal logic. 8. Epistemic logic, for example, includes a propositional operator K, which symbolizes that that proposition is known. result = svelte.compile(source, { generate: "dom" "ssr", dev: false, css: false, hydratable: false, customElement: false, immutable: false, legacy: false}); This a first course in the area. 2 Basic Modal Logic 2.1 Syntax We will develop a general framework in which we will be able to reason about situations as the ones above. as in the rst example, possible worlds as in the second example or states of knowledge of a person/agent as in the last two examples. There are other systems of modal logic as well. Please note, however, that no other person's or group's logic model can serve as template for your own; even if your initiative is similar, the forces of change and other important details for each effort will differ.