My primary area of research is paraconsistent logic, which is a branch of non-classical logic. Although there are many different systems and approaches to paraconsistent logic, they are all broadly characterized by the fact that they break the principle of explosion. Hence, unlike classical logic, paraconsistent logics allow for non-trivial consequence relations and inferences to be drawn from some inconsistent formula sets.
Specifically, I focus on various multi-valued paraconsistent logics (including the three-valued system LP) and preservaitonist logics. My interest in multi-valued paraconsistent logic is concerned with its application in first-order arithmetic. My undergraduate honours thesis “Paraconsistent Logics and Model-Theoretic Applications of LP” was an analysis of this very application and investigated the resulting “collapse models” of arithmetic.
My interest in preservationist logic on the other hand is not concerned with theories of arithmetic, but rather, theories of consequence (i.e., provability and entailment). Preservationist logics are an important branch of paraconsistent logics, but rather than extending the set of values of the underlying metalanguage of classical logic (as multi-valued logics do), preservationist logics develop paraconsistent consequence relations by extending the concept of consequence itself. This is typically accomplished by drawing from various concepts in set theory, combinatorics, and topology, as a means to impose measures on formula sets that extend beyond that of consistency and satisfiability.
I also have interest in the general philosophy of science, including the work of Karl Popper, Pierre Duhem, and Willard van Orman Quine. I am also interested in the history of analytic philosophy, including the works of Rudolf Carnap and Ludwig Wittgenstein.