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The result of the evaluation is called the modal force. [2]: 649 For example, the utterance in (4) expresses that, according to what the speaker has observed, it is necessary to conclude that John has a rather high income: (4) John must be earning a lot of money. The modal base here is the knowledge of the speaker, the modal force is necessity.
In modal logic, a regular modal logic is a modal logic containing (as axiom or theorem) the duality of the modal operators:
In modal logic, a classical modal logic L is any modal logic containing (as axiom or theorem) the duality of the modal operators
A modal verb is a type of verb that contextually indicates a modality such as a likelihood, ability, permission, request, capacity, suggestion, order, obligation, necessity, possibility or advice. Modal verbs generally accompany the base (infinitive) form of another verb having semantic content. [1]
When a Sahlqvist formula is used as an axiom in a normal modal logic, the logic is guaranteed to be complete with respect to the basic elementary class of frames the axiom defines. This result comes from the Sahlqvist completeness theorem [Modal Logic, Blackburn et al., Theorem 4.42]. But there is also a converse theorem, namely a theorem that ...
The following table lists several common normal modal systems. The notation refers to the table at Kripke semantics § Common modal axiom schemata.Frame conditions for some of the systems were simplified: the logics are sound and complete with respect to the frame classes given in the table, but they may correspond to a larger class of frames.
A class of modal logics that include the necessitation rule and the distribution axiom, allowing for the derivation of necessary truths from given axioms and rules of inference. NP A complexity class (nondeterministic polynomial time) that includes decision problems for which a 'yes' answer can be verified in polynomial time by a deterministic ...
A non-normal modal logic is a variant of modal logic that deviates from the basic principles of normal modal logics. Normal modal logics adhere to the distributivity axiom ( ( p → q ) → ( p → q ) {\displaystyle \Box (p\to q)\to (\Box p\to \Box q)} ) and the necessitation principle which states that "a tautology must be necessarily true ...