Free choice is a phenomenon in natural language where a linguistic

disjunction In logic, disjunction (also known as logical disjunction, logical or, logical addition, or inclusive disjunction) is a logical connective typically notated as \lor and read aloud as "or". For instance, the English language sentence "it is ...

appears to receive a logical conjunctive interpretation when it interacts with a modal operator. For example, the following English sentences can be interpreted to mean that the addressee can watch a movie ''and'' that they can also play video games, depending on their preference: # You can watch a movie or play video games. # You can watch a movie or you can play video games. Free choice inferences are a major topic of research in formal semantics and

philosophical logic Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. Some theorists conceive philosophic ...

because they are not valid in classical systems of

modal logic Modal logic is a kind of logic used to represent statements about Modality (natural language), necessity and possibility. In philosophy and related fields it is used as a tool for understanding concepts such as knowledge, obligation, and causality ...

. If they were valid, then the semantics of natural language would validate the ''Free Choice Principle''. # ''Free Choice Principle'':

\Diamond( P \lor Q) \rightarrow (\Diamond P \land \Diamond Q)

This symbolic logic formula above is not valid in classical

: Adding this principle as an axiom to standard modal logics would allow one to conclude

\Diamond Q

from

\Diamond P

, for any

P

and

Q

. This observation is known as the ''Paradox of Free Choice''. To resolve this paradox, some researchers have proposed analyses of free choice within nonclassical frameworks such as

dynamic semantics Dynamic semantics is a framework in logic and natural language semantics that treats the meaning of a sentence as its potential to update a context. In static semantics, knowing the meaning of a sentence amounts to knowing when it is true; in dyna ...

linear logic Linear logic is a substructural logic proposed by French logician Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the dualities of the former with many of the constructive properties of the latter. Although the ...

alternative semantics Alternative semantics (or Hamblin semantics) is a framework in formal semantics and logic. In alternative semantics, expressions denote ''alternative sets'', understood as sets of objects of the same semantic type. For instance, while the word "L ...

, and

inquisitive semantics Inquisitive semantics is a framework in logic and Formal semantics (linguistics), natural language semantics. In inquisitive semantics, the semantic content of a sentence captures both the information that the sentence conveys and the issue that it ...

. Others have proposed ways of deriving free choice inferences as

scalar implicature In pragmatics, scalar implicature, or quantity implicature, is an implicature that attributes an ''implicit'' meaning beyond the explicit or ''literal'' meaning of an utterance, and which suggests that the utterer had a reason for not using a more ...

s which arise on the basis of classical lexical entries for disjunction and modality. Free choice inferences are most widely studied for deontic modals, but also arise with other flavors of modality as well as imperatives,

conditionals Conditional (if then) may refer to: *Causal conditional, if X then Y, where X is a cause of Y *Conditional probability, the probability of an event A given that another event B *Conditional proof, in logic: a proof that asserts a conditional, a ...

, and other kinds of operators. Indefinite noun phrases give rise to a similar inference which is also referred to as "free choice" though researchers disagree as to whether it forms a natural class with disjunctive free choice.

Notes

Semantics Deontic logic Philosophical logic Mathematical logic Rules of inference Formal semantics (natural language) {{Formal semantics

See also

Notes