# What are the various interpretations of modal logic?

Wikipedia lists the following interpretations of modal logic:

• Alethic: fundamental conditions of possible worlds, causality, time-space parameters, and the action capacity of persons. Indicates the possibility, impossibility and necessity of actions, states of affairs, events, people, and qualities in the possible worlds.

• Deontic modal operators influence the construction of possible worlds as proscriptive or prescriptive norms, i.e. they indicate what is prohibited, obligatory, or permitted.

• Axiological modal operators transform the world's entities into values and disvalues as seen by a social group, a culture, or a historical period.

• Epistemic modal operators reflect the level of knowledge, ignorance and belief in the possible world.

• Doxastic modal operators express belief in statements.

Are you aware of more?

It seems that more interpretations may be constructed through the Categories of Being.

James Garson also lists the following in his summary of modal logics which may qualify:

In temporal logic (also known as tense logic), there are two basic operators, G for the future, and H for the past. G is read ‘it always will be that’ and the defined operator F (read ‘it will be the case that’) can be introduced by FA=∼G∼A.

The founder of modal logic, C. I. Lewis, defined a series of modal logics which did not have □ as a primitive symbol. Lewis was concerned to develop a logic of conditionals that was free of the so called Paradoxes of Material Implication...

Provability logics are systems where the propositional variables p,q,r, etc. range over formulas of some mathematical system, for example Peano’s system PA for arithmetic.

There may be others.

Garson, James, "Modal Logic", The Stanford Encyclopedia of Philosophy (Fall 2018 Edition), Edward N. Zalta (ed.), URL = https://plato.stanford.edu/archives/fall2018/entries/logic-modal/.