Epistemic modality

Epistemic modality is a sub-type of linguistic modality that encompasses knowledge, belief, or credence in a proposition. Epistemic modality is exemplified by the English modals "may", "might", "must". However, it occurs cross-linguistically, encoded in a wide variety of lexical items and grammatical structures. Epistemic modality has been studied from many perspectives within linguistics and philosophy. It is one of the most studied phenomena in formal semantics.
Non-canonical environments and objective epistemic modality.
Lyons 1977 started a long discussion regarding in which environments epistemic modal operators can be embedded and from which environments they are banned. He argues that epistemic modal operators compete for the same position as illocutionary operators, such as the assertion operator, question operator or imperative operator. According to him this explains why most epistemic modals in English are not acceptable embedded under questions or negation.
As Lyons finds single lexemes of epistemic modals in English that are used in questions and under negation, he assumes that they must be part of a separate class of epistemic modality–the so called "objective" epistemic modality, in contrast to "subjective" epistemic modality—whose operators are considered to be taking the same position in the clause as illocutionary operators.
Which modal lexemes convey an `objective' epistemic interpretation is subject to much controversy. So far most of the authors who are in favour of a distinct class of objective epistemic modal verbs have not explicitly stated which verbs can be interpreted in an `objective' epistemic way and which can only be interpreted in an `subjective' epistemic way.
It is often assumed that, for languages such as English, Hungarian, Dutch and German, epistemic adverbs only involve a subjective epistemic interpretation and can never be interpreted in an objective epistemic way.
Since the publication of Lyons' work, a range environments have been suggested from which (subjective) epistemic modals are assumed to be banned. Most of these non-canonical environments were motivated by data from English:
However, taking a look into languages which have a more productive inflectional morphology such as German, there is solid corpus data that epistemic modal verbs do occur in many of these environments. The only environments in which epistemic modal verbs do not occur in German are as follows.
This corpus data further shows that there is no consistent class of objective epistemic modal verbs, neither in English, nor in German. Each of the assumed objective epistemic modals is acceptable in a different range of environments which are actually supposed to hold for the entire stipulated class of objective epistemic modality.
The table below illustrates in which environments the most frequent epistemic modals in German, "kann" `can', "muss" `must', "dürfte" `be.probable', "mögen" `may' are attested in corpora (yes), or yield ungrammatical judgements (no). The lower part makes reference to classifications by various authors, which of these epistemic modal verb come with a objective epistemic interpretation and which are only restricted to subjective epistemic modality.
Link to evidentiality.
Many linguists have considered possible links between epistemic modality and evidentiality, the grammatical marking of a speaker's evidence or information source. However, there is no consensus about what such a link consists of. Some work takes epistemic modality as a starting point and tries to explain evidentiality as a subtype. Others work in the other direction, attempting to reduce epistemic modality to evidentiality. Still others recognize epistemic modality and evidentiality as two fundamentally separate categories, and posit that particular lexical items may have both an epistemic and an evidential component to their meanings. However, other linguists feel that evidentiality is distinct from and not necessarily related to modality. Some languages mark evidentiality separately from epistemic modality.