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In various fields

Formal logic

Formal logic studies the laws of deductive reasoning, examining the entailment relations between premises and conclusions. It investigates rules of inference, such as modus ponens, which describe the logical structure of deductively valid arguments. Formal logicians develop artificial languages, such as the language of first-order logic, to avoid the ambiguities of natural language and give precise descriptions of the laws of logic. Formal semantics plays a central role in this endeavor for applying the logical insights to natural language arguments. It helps logicians discern the logical form of regular arguments, serving as a crucial step to translate them into logical formulas.

Another key intersection between formal semantics and formal logic concerns the interpretation of artificial logical languages. The semantic of logics examines the construction of mathematical models of formal languages, similar to the mathematical models used used by formal semanticists to study natural language. As such, they typically include abstract objects to represent individuals and sets of individuals as well as an interpretation function that establishes the connection between the symbols in the logical formulas and the abstract objects in the model. A key aspect of this interface is the relation between syntactic entailment and semantic entailment. Syntactic entailment happens on the level of the logical formulas and the rules of inference that allow logicians to draw conclusions from premises. Semantic entailment concerns the level of the mathematical model, expressing that truth is preserved across all possible models.


  • focus on args rather than lang at large[1]
  • about correct args, need to translate to formal lang to assess correctness[1]
  • analysis of meaning of formal lang thr semantics[1]
  • [2]

Computer science

  • programming lang as formal lang, like logic[1]
  • semantics of programming lang[1]
  • relevance of formal semantics to AI & translation[1]
  • AI[3]
  • [4]

Cognitive science

  • interdisciplinary field to study the mind thr info pr. lang imp part of info pr. formal sem to study lang [1]
  • cognitive neuroscience[5]
  • [6]

References

Notes

Citations

  1. ^ a b c d e f g Portner 2005, pp. 214–217.
  2. ^ Barba 2007, pp. 639.
  3. ^ Winter 2016, pp. 4, 233–234.
  4. ^ Stone 2016, pp. 775–776.
  5. ^ Winter 2016, pp. 3.
  6. ^ Baggio, Stenning & van Lambalgen 2016, pp. 756–757.

Sources

  • Baggio, Giosuè; Stenning, Keith; van Lambalgen, Michiel (2016). "24. Semantics and Cognition". In Aloni, Maria; Dekker, Paul (eds.). The Cambridge Handbook of Formal Semantics. Cambridge University Press. pp. 756–774. ISBN 978-1-316-55273-5.
  • Stone, Matthew (2016). "25. Semantics and Computation". In Aloni, Maria; Dekker, Paul (eds.). The Cambridge Handbook of Formal Semantics. Cambridge University Press. pp. 775–800. ISBN 978-1-316-55273-5.
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