Truthmaker Semantics for Intuitionistic Modal Logic

Area of Science:

• Logic
• Philosophy of Mathematics
• Modal Logic

Background:

• Truthmaker semantics provides a way to understand truth in terms of objects that make propositions true.
• Existing truthmaker semantics primarily focus on intuitionistic logic, leaving modal extensions less explored.
• The concept of 'exactness' in truthmaking, where truthmakers contain only relevant information, is crucial for fine-grained analysis.

Purpose of the Study:

• To extend Fine's truthmaker semantics for intuitionistic logic to handle necessitated propositions in intuitionistic modal logic.
• To develop an exact truthmaker semantics for intuitionistic modal logic.
• To investigate the differences in truthmaking between intuitionistic and classical logic, particularly concerning the T and B axioms.

Main Methods:

• Extending Fine's truthmaker semantics framework.
• Developing a formal system for exact truthmaker semantics in intuitionistic modal logic.
• Analyzing the truthmakers for necessitated propositions within this new framework.

Main Results:

• Successfully extended Fine's truthmaker semantics to intuitionistic modal logic.
• Provided a method for determining exact truthmakers for necessitated propositions.
• Demonstrated how classical and intuitionistic logic exhibit distinct truthmaking conditions, illuminating the T and B axioms.

Conclusions:

• The developed exact truthmaker semantics offers a novel approach to understanding modal truths in intuitionistic logic.
• The findings provide new insights into the philosophical underpinnings of modal logic and the nature of truth.
• This work bridges truthmaker semantics and modal logic, offering a foundation for further research in philosophical logic.