I study

Here is an introduction to my research.

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 logical symbols associated with them provides the following advantages.

• 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).
• 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).
• 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.

For more detail, see the following page.

Hybrid Logic (Stanford Encyclopedia of Philosophy)

My current work

My current research is to check, for various hybrid logics, whether they are decidable or not.

There are various ways to investigate the decidability of logic. I take the approach of showing decidability by constructing a tableau calculus. A tableau calculus is a tool that can provide proofs for provable propositions and counterexample models for unprovable. It is also an excellent proof system in that it can easily give proof.

In the future, I want to conduct research that constructs new logics that reflects various mechanisms in the world. I believe that hybrid logic is a very useful tool for this purpose.