Inquisitive Neighborhood Logic.

Area of Science:

• Logic and Formal Methods
• Theoretical Computer Science
• Philosophy of Language

Background:

• Modal logic provides frameworks for reasoning about various forms of necessity and possibility.
• Neighborhood models offer an alternative semantics for modal logic, focusing on collections of accessible worlds.
• Inquisitive semantics enriches traditional semantics by incorporating questions alongside statements.

Purpose of the Study:

• To introduce and investigate a novel inquisitive modal logic tailored for neighborhood models.
• To define and analyze an inquisitive strict conditional operator and associated neighborhood quantifiers.
• To establish the expressive power, axiomatization, and decidability of the proposed logic.

Main Methods:

• Development of a new modal logic with an inquisitive strict conditional operator ($\Rrightarrow$) and neighborhood quantifiers ($⊞$, ).
• Proof of the logic's expressive power equivalence to bisimilarity in neighborhood models.
• Investigation of language fragments and their invariance properties under neighborhood modifications.
• Construction of a sound and complete axiomatization and proof of decidability via the finite model property.

Main Results:

• The expressive power of the logic matches bisimilarity in neighborhood models.
• The inquisitive conditional ($\Rrightarrow$) is not definable from the neighborhood quantifiers ($⊞$, ), highlighting the indispensability of embedded questions.
• A sound and complete axiomatization is provided for the logic, including specific frame classes.
• Decidability is established through the finite model property.

Conclusions:

• The developed inquisitive modal logic offers a powerful framework for reasoning about neighborhood models, integrating statements and questions.
• The logic's properties, including its expressive power and decidability, make it a valuable tool for formal semantics and theoretical computer science.
• The research clarifies the relationship between inquisitive semantics, neighborhood models, and standard modal logic concepts.