modality the manner in which a proposition (or statement) describes or applies to its subject matter. Derivatively ‘modality’ refers to characteristics of entities or states of affairs described by modal propositions.
Modalities are classified as follows: Assertoric propositions are expressions of mere fact. Alethic modalities include necessity and possibility (the latter two sometimes are referred to respectively as the apodictic and problematic modalities). The causal modalities include causal (or empirical) necessity and possibility, whereas the deontic modalities include obligation and permittedness. There are epistemic modalities such as knowing that and doxastic ones such as believing that.
Following medieval logicians, propositions can be distinguished on the basis of whether the modality is introduced via adverbial modification of the copula or verb (sensus divisus) or via a modal operator that modifies the proposition (sensus compositus). Today many deny the distinction or confine attention just to modal operators. Modal operators in non-assertoric propositions are said to produce referential opacity or oblique contexts in which truth is not preserved under substitution of extensionally equivalent expressions. Modal and deontic logics provide formal analyses of various modalities. Intensional logics investigate the logic of oblique contexts. Modal logicians have produced possible worlds semantics interpretations wherein propositions MP with modal operator M are true provided P is true in all suitable (e.g., logically possible, causally possible, morally permissible, rationally acceptable) possible worlds. Modal realism grants ontological status to possible worlds other than the actual world or otherwise commits to objective modalities in nature or reality. See also INTENSIONAL LOGIC, MODAL LOGIC , QUANTIFYING I. F.S.