Evan Goris

A New Principle In The Interpretability Logic Of All Reasonable Arithmetical Theories

The interpretability logic of a mathematical theory describes the structural behavior of interpretations over that theory. Different theories have different logics. This paper from 2011 revolves around the question what logic describes the behavior that is present in all theories with a minimum amount of arithmetic; the intersection over all such theories so to say. We denote this target logic by

Modal Matters for Interpretability Logics

{\textbf{IL}}({\rm All})

Feasible Operations on Proofs: The Logic of Proofs for Bounded Arithmetic

. In this paper we present a new principle

Explicit Proofs in Formal Provability Logic

\sf R

A modal provability logic of explicit and implicit proofs

in

Modal matters in interpretability logics

{\textbf{IL}}({\rm All})

Logic of proofs for bounded arithmetic

. We show that

Two series of formalized interpretability principles for weak systems of arithmetic

\sf R

Self provers and Σ1 sentences

does not follow from the logic

TR-2007005: Interpreting Knowledge into Belief in the Presence of Negative Introspection

{\textbf{IL}}{\sf P_0W^*}