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Akinori Maniwa

Publications and source records attributed to Akinori Maniwa.

2 recordsLinked to original sources
arXiv2026

Bounded Modal Logic: Explicit Scope Dependencies in Multi-Stage Programming

It is widely known that proof systems for modal logic can be interpreted as type systems for multi-stage programming (MSP). However, existing modal-logical foundations for MSP do not fully account for staged programs with complex scoping structures. For example, a modal account of cross-stage persistence, in which free variables in generated code may refer to run-time bindings, has not yet been fully established. This paper presents *Bounded Modal Logic* (BML), a constructive modal logic with modalities bounded by names for scopes and first-order-style quantification over those names. This makes scope dependencies of code fragments explicit, thereby enabling reasoning about staged programs with nontrivial scoping behavior, including cross-stage persistence. We present a natural deduction system and a Kripke semantics for BML, and prove their soundness and completeness. We also provide a computational counterpart of BML as a typed lambda calculus for MSP. In addition to standard metatheoretic properties such as confluence and strong normalization, we develop a staged semantics for the calculus, showing that the type system supports the stage-by-stage execution model required for multi-stage programming.

cs.LO↗
arXiv2024

Syntactic Cut-Elimination for Provability Logic GL via Nested Sequents

The cut-elimination procedure for the provability logic is known to be problematic: a L\"ob-like rule keeps cut-formulae intact on reduction, even in the principal case, thereby complicating the proof of termination. In this paper, we present a syntactic cut-elimination proof based on nested sequents, a generalization of sequents that allows a sequent to contain other sequents as single elements. A similar calculus was developed by Poggiolesi (2009), but there are certain ambiguities in the proof. Adopting the idea of Kushida (2020) into nested sequents, our proof does not require an extra measure on cuts or error-prone, intricate rewriting on derivations, but only straightforward inductions, thus leading to less ambiguity and confusion.

cs.LO↗