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In various fields

Formal logic

Formal logic studies the laws of deductive reasoning, focusing the entailment relations between premises and conclusions rather than analyzing language at large. 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.[1]

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

Computational semantics is an interdisciplinary field at the [intersection] of computer science and formal semantics. It studies how computation processes can be utilized to deal with linguistic meaning. One of its key concerns is the analysis of natural language sentences through computational processes to discern their logical structure, understand their meaning, and extract information. This form of inquiry has various applications to areas of artificial intelligence, such as automatic reasoning, machine learning, and machine translation. Difficulties in this process come from the ambiguity, vagueness, and context-dependence of natural language expressions.[1][3][4][5][6]

Another intersection concerns the analysis of meaning of programming languages. A programming language is an artificial language designed to give instructions or describe computations to be performed by computers. A formal semantics of a programming language is a mathematical model of how it works. Its goal is to help computer scientists understand, analyze, and verify program behavior.[7][8][1] Static semantics describes the process of compilation or how a high-level programming language is translated into binary machine code.[9] Dynamic semantics examines run time behavior or what happens during the execution of instructions.[10] The main approaches to dynamic semantics are denotational, axiomatic, and operational semantics. Denotational semantics describes the effects of code elements, axiomatic semantics examines the conditions before and after code execution, and operational semantics interprets code execution as a series of state transitions.[11]

  • semantics of programming lang, computational semantics, AI
  • programming lang as formal lang, like logic[1]
  • semantics of programming lang[1]
  • relevance of formal semantics to AI & translation[1]
  • AI[12]
  • [13]

Cognitive science

Cognitive sciences studies the mind by focusing on how it represents and transforms information. It is an interdisciplinary field that integrates research from diverse fields, ranging from psychology and neuroscience to philosophy, artificial intelligence, and linguistics.[14] Various researchers emphasize the central role of language for understanding the human mind and rely on formal semantics to provide an abstract model for analyzing how linguistic meaning is constructed and interpreted.[1][15][16]

Cognitive neuroscience, for example, seeks to explain the biological processes underlying cognition. One approach uses brain imaging techniques to visualize brain activity and employs mathematical models to link this data to cognitive processes. Insights from formal semantics can refine these models and formulate testable predictions. For instance, researchers can examine semantic cognition by presenting a person with semantically slightly different sentences and measuring how the brain reponds to the difference.[17][18]

References

Notes

Citations

  1. ^ a b c d e f g h i j Portner 2005, pp. 214–217.
  2. ^ Barba 2007, pp. 639.
  3. ^ Geeraerts 2010, p. 118.
  4. ^ Bunt & Muskens 1999, pp. 1–2.
  5. ^ Erk 2018, Summary.
  6. ^ Stone 2016, pp. 775–777, 799–800.
  7. ^ Fernández 2014, pp. 14–16.
  8. ^ Winskel 1993, pp. xv–xvi.
  9. ^
  10. ^
  11. ^
  12. ^ Winter 2016, pp. 4, 233–234.
  13. ^ Stone 2016, pp. 775–776.
  14. ^ Portner 2005, pp. 216–217.
  15. ^ Partee 2008, p. 10.
  16. ^ Partee 1995, pp. 311–360.
  17. ^ Winter 2016, pp. 3–4.
  18. ^ Baggio, Stenning & van Lambalgen 2016, pp. 756–757, 761–762, 773–774.

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.
  • Winskel, Glynn (1993). The Formal Semantics of Programming Languages: An Introduction. MIT Press. ISBN 978-0-262-23169-5.
  • Partee, Barbara H. (2008). Compositionality in Formal Semantics: Selected Papers. John Wiley & Sons. ISBN 978-0-470-75129-9.
  • Partee, Barbara H. (1995). "11. Lexical Semantics and Compositionality". In Osherson, Daniel N.; Gleitman, Lila R. (eds.). An Invitation to Cognitive Science: Language. MIT Press. ISBN 978-0-262-65044-1.
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