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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 philosophical ...
, simplification of disjunctive antecedents (SDA) is the phenomenon whereby a
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 ...
in the antecedent of a conditional appears to distribute over the conditional as a whole. This inference is shown schematically below: # (A \lor B) \Rightarrow C \models (A \Rightarrow C) \land (B \Rightarrow C) This inference has been argued to be valid on the basis of sentence pairs such as that below, since Sentence 1 seems to imply Sentence 2. # If Yde or Dani had come to the party, it would have been fun. # If Yde had come to the party, it would be been fun and if Dani had come to the party, it would have been fun. The SDA inference was first discussed as a potential problem for the similarity analysis of counterfactuals. In these approaches, a counterfactual (A \lor B) > C is predicted to be true if C holds throughout the
possible world A possible world is a complete and consistent way the world is or could have been. Possible worlds are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional and modal logic. Their me ...
s where A \lor B holds which are most similar to the world of evaluation. On a
Boolean Any kind of logic, function, expression, or theory based on the work of George Boole is considered Boolean. Related to this, "Boolean" may refer to: * Boolean data type, a form of data with only two possible values (usually "true" and "false" ...
semantics for disjunction, A \lor B can hold at a world simply in virtue of A being true there, meaning that the most similar A \lor B-worlds could all be ones where A holds but B does not. If C is also true at these worlds but not at the closest worlds here B is true, then this approach will predict a failure of SDA: (A \lor B) > C will be true at the world of evaluation while (B > C) will be false. In more intuitive terms, imagine that Yde missed the most recent party because he happened to get a flat tire while Dani missed it because she hates parties and is also deceased. In all of the closest worlds where either Yde or Dani comes to the party, it will be Yde and not Dani who attends. If Yde is a fun person to have at parties, this will mean that Sentence 1 above is predicted to be true on the similarity approach. However, if Dani tends to have the opposite effect on parties she attends, then Sentence 2 is predicted false, in violation of SDA. SDA has been analyzed in a variety of ways. One is to derive it as a semantic
entailment Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically ''follows from'' one or more statements. A valid logical argument is one ...
by positing a non-classical treatment of disjunction such as that of alternative semantics or
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 ...
. Another approach also derives it as a semantic
entailment Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically ''follows from'' one or more statements. A valid logical argument is one ...
, but does so by adopting an alternative denotation for conditionals such as the
strict conditional In logic, a strict conditional (symbol: \Box, or ⥽) is a conditional governed by a modal operator, that is, a logical connective of modal logic. It is logically equivalent to the material conditional of classical logic, combined with the necess ...
or any of the options made available in situation semantics. Finally, some researchers have suggested that it can be analyzed as a pragmatic
implicature In pragmatics, a subdiscipline of linguistics, an implicature is something the speaker suggests or implies with an utterance, even though it is not literally expressed. Implicatures can aid in communicating more efficiently than by explicitly say ...
derived on the basis of classical disjunction and a standard semantics for conditionals. SDA is sometimes considered an embedded instance of the
free choice inference Free choice is a phenomenon in natural language where a linguistic disjunction 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 ...
.


See also

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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 ...
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Modal logic Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other ...
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Free choice inference Free choice is a phenomenon in natural language where a linguistic disjunction 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 ...


Notes

Semantics Logic Philosophical logic Mathematical logic Rules of inference {{logic-stub