Related papers: Reflection calculus and conservativity spectra
We define an extension of lambda-calculus with dependents types that enables us to encode transparent and opaque probabilistic programs and prove a strong normalisation result for it by a reducibility technique. While transparent…
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…
Large language models have recently demonstrated significant gains in reasoning ability, often attributed to their capacity to generate longer chains of thought and engage in reflective reasoning. However, the contribution of reflections to…
We discuss reflection factors for purely elastic scattering theories and relate them to perturbations of specific conformal boundary conditions, using recent results on exact off-critical g-functions. For the non-unitary cases, we support…
Circuit representations are becoming the lingua franca to express and reason about tractable generative and discriminative models. In this paper, we show how complex inference scenarios for these models that commonly arise in machine…
We present a sequent calculus for abstract focussing, equipped with proof-terms: in the tradition of Zeilberger's work, logical connectives and their introduction rules are left as a parameter of the system, which collapses the synchronous…
We study differential forms invariant under a finite reflection group over a field of arbitrary characteristic. In particular, we prove an analogue of Saito's freeness criterion for invariant differential 1-forms. We also discuss how…
Persistence modules are representations of products of totally ordered sets in the category of vector spaces. They appear naturally in the representation theory of algebras, but in recent years they have also found applications in other…
This thesis concerns the development of a framework that facilitates the design and analysis of formal systems. Specifically, this framework provides a specification language which supports the concise and direct description of formal…
We specify the operational semantics and bisimulation relations for the finite pi-calculus within a logic that contains the nabla quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the…
In this note we give a simplified ordinal analysis of first-order reflection. An ordinal notation system $OT$ is introduced based on $\psi$-functions. Provable $\Sigma_{1}$-sentences on $L_{\omega_{1}^{CK}}$ are bounded through…
We use ring-theoretic methods and methods from the theory of skew braces to produce set-theoretic solutions to the reflection equation. We also use set-theoretic solutions to construct solutions to the parameter-dependent reflection…
We study structural limitations of purely algebraic reasoning in the analysis of arithmetic dynamical systems. Rather than addressing the truth of specific conjectures, we introduce a fragment - relative notion of algebraic refutability for…
In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…
The general solutions of the reflection equation associated with Temperley-Lieb $R$-matrices are constructed. Their parametrization is defined and the Hamiltonians of corresponding integrable spin systems are given.
Free-text rationales play a pivotal role in explainable NLP, bridging the knowledge and reasoning gaps behind a model's decision-making. However, due to the diversity of potential reasoning paths and a corresponding lack of definitive…
Computability logic is a formal theory of computability. The earlier article "Introduction to cirquent calculus and abstract resource semantics" by Japaridze proved soundness and completeness for the basic fragment CL5 of computability…
We present role logic, a notation for describing properties of relational structures in shape analysis, databases, and knowledge bases. We construct role logic using the ideas of de Bruijn's notation for lambda calculus, an encoding of…
Introduced in 2006 by Japaridze, cirquent calculus is a refinement of sequent calculus. The advent of cirquent calculus arose from the need for a deductive system with a more explicit ability to reason about resources. Unlike the more…
Java reflection has been increasingly used in a wide range of software. It allows a software system to inspect and/or modify the behaviour of its classes, interfaces, methods and fields at runtime, enabling the software to adapt to…