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Subject-matter and intensional operators I: conditional-agnostic analytic implication.

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This study addresses topic-theoretic considerations in logic, particularly for intensional operators like conditionals. It proposes a new framework to define the subject-matter of these operators, enhancing logical expressivity.

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Area of Science:

  • * Formal Logic
  • * Philosophy of Language
  • * Modal Logic

Background:

  • * Traditional logic focuses on alethic (truth-based) considerations.
  • * Topic-theoretic frameworks incorporate subject-matter or topic.
  • * Extending topic to intensional operators like conditionals presents challenges.

Purpose of the Study:

  • * To address the lacuna in defining topics for intensional operators within existing frameworks.
  • * To propose a novel approach for topic-sensitive intentional modals (TSIMs).
  • * To enhance the expressivity of logical theories by defining undefined topics.

Main Methods:

  • * Investigating an analogous problem in Parry-style containment logics.
  • * Introducing a family of subsystems of Parry's .
  • * Developing sound and complete axiomatizations for these subsystems.

Main Results:

  • * A method for defining the subject-matter of intensional conditionals is proposed.
  • * New subsystems of Parry's are introduced.
  • * These subsystems offer fine-grained control over the topics of intensional conditionals.

Conclusions:

  • * The proposed approach successfully fills a gap in topic-theoretic logic.
  • * The new framework enhances the expressivity of TSIMs.
  • * This work provides a foundation for further research in topic-sensitive modal logic.