I study

My research field is mathematical logic. In particular, my current primary research interest is hybrid logic.

Hybrid Logic

Hybrid logic is an extension of modal logic. We introduce, in addition to the usual propositional variables, a special propositional variable that "holds only in one of the possible worlds" (this is called nominal). Nominals and some operators associated with them provides the following advantages.

• Nominals correspond to various concepts in the real world. For example, a moment in the concept of time or an individual in human relationships can be represented by a nominal. In fact, there is a study that gives a model of friendship using hybrid logic (Seligman et al., 2011).
• We can characterize more properties of the Kripke model. For example, irreflexivity (no possible world can reach itself) cannot be characterized by formulas of modal logic, but can be by hybrid logic. Some studies have also taken this advantage to analyze graph theory using hybrid logic (Benevides & Schechter, 2009).
• With appropriate restrictions, decidability holds for hybrid logic. If whether any formula is a theorem of a logic or not can be determined in finite time, then the logic is called decidable. Since basic modal logic has the decidability, it can be said to be a good extension of modal logic in this sense. Note that first-order logic, which possesses far greater expressive power than modal or hybrid logic, is known to be undecidable.

For more detail, see the following page.

Hybrid Logic (Stanford Encyclopedia of Philosophy)

My current work

My current research is to develop proof systems for hybrid logic. In hybrid logic, the proof system known as tableau calculus is extensively studied, and my work follows this general trend. Tableau calculus is a tool that can provide proofs for provable propositions and countermodels for unprovable ones. Furthermore, it is distinguished by being an accessible proof technique that follows a clear algorithm.

In addition, leveraging the insights gained from my research on tableau calculus, I am working on providing proof systems for various non-classical logics. I have a broad interest in various non-classical logics, starting with modal logic.

In the future, I would like to conduct research that expresses various structures in the world, including language, through the logic. I believe that hybrid logic is a very useful tool for this purpose.