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  3. Update Rules And Semantic Universals.
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Update rules and semantic universals.

Luca Incurvati1, Giorgio Sbardolini1

  • 1ILLC and Philosophy, University of Amsterdam, Amsterdam, The Netherlands.

Linguistics and Philosophy
|March 28, 2023

View abstract on PubMed

Summary
This summary is machine-generated.

Natural languages only lexicalize a few logical operators, like "and" and "or". This study explains these lexical gaps and the Monotonicity Universal using dynamic logic and update potentials.

Keywords:
ConnectivesContext change potentialsLexicalizationMonotonicityQuantifiersSemantic universalsUpdate semantics

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Area of Science:

  • Linguistics
  • Formal Semantics
  • Logic

Background:

  • Natural languages exhibit lexical gaps, omitting many logically possible operators.
  • Lexicalized logical operators (connectives, quantifiers) adhere to the Monotonicity Universal (upward or downward monotonicity).

Purpose of the Study:

  • To provide a logical explanation for lexical gaps in natural language.
  • To explain the Monotonicity Universal based on the dynamic behavior of logical operators.

Main Methods:

  • Defining 'update potentials' for logical operators as procedures to modify conversational context.
  • Analyzing how updates depend on an operator's logical form and the speech act (assertion/rejection).

Main Results:

  • The study proposes that the adequacy of update potentials limits which logical operators become lexicalized.
  • The Monotonicity Universal is shown to follow logically from the properties of these operator updates.

    • Conclusions:

    • Update potentials offer a framework for understanding the constraints on lexicalizing logical operators.
    • The dynamic behavior of operators, specifically their update potentials, explains observed patterns in natural language.