Youan Su | Searcharxiv

arXiv2026

Uniform Agent-interpolation of Distributed Knowledge

Uniform interpolation property (UIP) is a strengthening of Craig interpolation property. It can be understood as the definability of propositional quantifiers. This paper develops the sequent calculi provided in Murai and Sano (2020), combining with the methods studied by B{\'\i}lkov{\'a} (2007) to show the uniform interpolation for epistemic logic $\mathbf{K}$, $\mathbf{KD}$ and $\mathbf{KT}$ with distributed knowledge. A purely syntactic algorithm is presented to determine a uniform interpolant formula. In the definition of an interpolant formula, not only propositional variables but also agent symbols are taken into consideration.

cs.LO↗

arXiv2025

A proof-theoretic approach to uniform interpolation property of multi-agent modal logic

Uniform interpolation property (UIP) is a strengthening of Craig interpolation property. It was first established by Pitts(1992) based on a pure proof-theoretic method. UIP in multi-modal $\mathbf{K_n}$, $\mathbf{KD_n}$ and $\mathbf{KT_n}$ logic have been established by semantic approaches, however, a proof-theoretic approach is still lacking. B\'ilkov\'a (2007) develops the method in Pitts (1992) to show UIP in classical modal logic $\mathbf{K}$ and $\mathbf{KT}$. This paper further extends B\'ilkov\'a (2007)'s systems to establish the UIP in multi-agent modal logic $\mathbf{K_n}$, $\mathbf{KD_n}$ and $\mathbf{KT_n}$. A purely syntactic algorithm is presented to determine a uniform interpolant formula. It is also shown that quantification over propositional variables can be modeled by UIP in these systems. Furthermore, a direct argument to establish UIP without using second-order quantifiers is also presented.

cs.LO↗