Merriam Webster defines veridical as truthful, veracious and non illusory. It stems from the Latin "veridicus", composed of Latin verus, meaning "true," and dicere, which means "to say." For example, the statement "Paul saw a snake" asserts the truthfulness of the claim, while "Paul did see a snake" is an even stronger assertion.
The formal definition of veridicality views the context as a propositional operator (Giannakidou 1998).
Negation is veridical, though of opposite polarity, sometimes called antiveridical: "Paul didn't see a snake" asserts that the statement "Paul saw a snake" is false. In English, non-indicative moods or irrealis moods are frequently used in a nonveridical sense: "Paul may have seen a snake" and "Paul would have seen a snake" do not assert that Paul actually saw a snake and the second implies that he did not. "Paul would indeed have seen a snake" is veridical, and some languages have separate veridical conditional moods for such cases.
Nonveridicality has been proposed to be behind the licensing of polarity items such as the English words any and ever, as an alternative to the influential downward entailment theory proposed by Ladusaw (1980). Anastasia Giannakidou (1998) argued that various polarity phenomena observed in language are manifestations of the dependency of polarity items to the (non)veridicality of the context of appearance. The (non)veridical dependency may be positive (licensing), or negative (anti-licensing), and arises from the sensitivity semantics of polarity items. Across languages, different polarity items may show sensitivity to veridicality, anti-veridicality, or non-veridicality.
Nonveridical operators typically license the use of polarity items, which in veridical contexts normally is ungrammatical:
All downward entailing contexts are nonveridical. Because of this, theories based on nonveridicality can be seen as extending those based on downward entailment, allowing more cases of polarity item licensing to be explained.
Quantifiers like exactly three students, nobody but John, and almost nobody are non-monotone (and thus not downward entailing) but nevertheless admit any:
Hardly and barely allow for any despite not being downward entailing.
Polarity items are quite frequent in questions, although questions are not monotone.
Although questions biased towards the negative answer, such as "Do you [even] give a damn about any books?" (tag questions based on negative sentences exhibit even more such bias), can sometimes be seen as downward entailing, this approach cannot account for the general case, such as the above example where the context is perfectly neutral. Neither can it explain why negative questions, which naturally tend to be biased, don't license negative polarity items.
In semantics which treats a question as the set of its true answers, the denotation of a polar question contains two possible answers:
Polarity items appear in future sentences.
According to the formal definition of veridicality for temporal operators, future is nonveridical: that "John will buy a bottle of Merlot" is true now does not entail that "John buys a bottle of Merlot" is true at any instant up to and including now. On the other hand, past is veridical: that "John bought a bottle of Merlot" is true now entails that there is an instant preceding now at which "John buys a bottle of Merlot" is true.
Likewise, nonveridicality of the habitual aspect licenses polarity items.
The habitual aspect is nonveridical because e.g., that "He is usually cheerful" is true over some interval of time does not entail that "He is cheerful" is true over every subinterval of that. This is in contrast to e.g., the progressive aspect, which is veridical and prohibits negative polarity items.
Non-monotone generic sentences accept polarity items.
Modal verbs create generally good environments for polarity items:
Such contexts are nonveridical despite being non-monotone and sometimes even upward entailing ("Mary must tango" entails "Mary must dance").
Imperatives are roughly parallel to modal verbs and intensional contexts in general.