In natural language, we create sentences to refer to a state of reality. While the state of reality presented by the sentence is called the truth of the sentence, a modal is therefore anything that qualifies the truth of a sentence (similar to the concept of a vector’s module, which is used to measure the length of a vector regardless of its direction, or the extent to which a vector expands in a certain direction). For example, to refer to someone’s current state of mind, say embarrassed, sentences with different types of modals can be “someone is probably embarrassed”, “someone is caught to be embarrassed”, or “someone will be embarrassed”, to name just a few.
Different types of modals are supported by different types of modal logic, which captures meaning beyond objects. It often reflects possibility, desirability, causality, validity or some other sought goal (and simultaneously the restrictions on pursuing that goal), the kind of knowledge that someone has about what they are saying, that cannot be embedded meaningfully in the statement of the fact itself, but can only be alluded to. Some commonly used modal logic and their expressions in natural languages are:
tense modal logic: henceforth, eventually, hitherto, previously, now, tomorrow, yesterday, since, until, inevitably, finally, ultimately, endlessly, it will have been, it is being,...
epistemic modal logic: it is known to a that, it is common knowledge that
doxastic modal logic: it is believed that, it is highly probable that, the probability is greater than r that, it is commonly believed that..
deontic modal logic: it is obligatory/forbidden permitted/unlawful that
dynamic modal logic: after the program/computation/action finishes, the program enables, throughout the computation
geometric modal logic: it is locally the case that
Despite being an important component in philosophy, semantics, mathematics, and linguistics, modal logic also applies to multiple aspects of our daily life. For instance, the control of traffic lights and Model checking in computer science.
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