Free choice is a phenomenon in natural language where a linguistic
disjunction
In logic, disjunction is a logical connective typically notated as \lor and read aloud as "or". For instance, the English language sentence "it is raining or it is snowing" can be represented in logic using the disjunctive formula R \lor S ...
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 because they are not
valid in classical systems of
modal logic. If they were valid, then the semantics of natural language would validate the ''Free Choice Principle''.
# ''Free Choice Principle'':
This symbolic logic formula above is not valid in classical
modal logic: Adding this principle as an axiom to standard modal logics would allow one to conclude
from
, for any
and
. 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 dynam ...
,
linear logic,
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 "Le ...
, and
inquisitive semantics
Inquisitive semantics is a framework in logic and 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 raises. The framework provides ...
.
Others have proposed ways of deriving free choice inferences as
scalar implicatures 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 has occurred
*Conditional proof, in logic: a proof that asserts a co ...
, and other kinds of operators.
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 In phonology, a natural class is a set of phonemes in a language that share certain distinctive features. A natural class is determined by participation in shared phonological processes, described using the minimum number of features necessary for d ...
with disjunctive free choice.
See also
*
Deontic logic
Deontic logic is the field of philosophical logic that is concerned with obligation, permission, and related concepts. Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts. It ...
*
Disjunction
In logic, disjunction is a logical connective typically notated as \lor and read aloud as "or". For instance, the English language sentence "it is raining or it is snowing" can be represented in logic using the disjunctive formula R \lor S ...
*
Hans Kamp
Johan Anthony Willem "Hans" Kamp (born 5 September 1940) is a Dutch philosopher and Linguistics, linguist, responsible for introducing discourse representation theory (DRT) in 1981.
Kamp was born in Den Burg. He received a Ph.D. in UCLA Departmen ...
*
Modal logic
*
Ross's paradox
*
Simplification of disjunctive antecedents
*
Sluicing
In syntax, sluicing is a type of Ellipsis (linguistics), ellipsis that occurs in both direct and indirect interrogative clauses. The ellipsis is introduced by a ''wh''-expression, whereby in most cases, everything except the ''wh''-expression is e ...
Notes
Semantics
Logic
Philosophical logic
Mathematical logic
Rules of inference
Formal semantics (natural language)
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