arXiv subjects

Nachiappan Valliappan

Publications and source records attributed to Nachiappan Valliappan.

5 recordsLinked to original sources

arXiv2026

Cover Semantics for Intuitionistic Modalities

Intuitionistic modal logic (IML) has inspired several developments in programming languages including modal type systems for staging, computational effects and language-based security. IMLs are typically studied using Kripke-style relational semantics, which simplifies proofs of meta-theoretic properties, such as completeness and consistency, by making it easy to construct models. Kripke-style relational semantics, however, relies upon classical reasoning principles, which makes it unappealing from a computational perspective and unsuitable for formalization in a constructive type theory. Goldblatt provides an alternative semantics for IMLs by extending Beth-Kripke-Joyal-style "cover" semantics for intuitionistic propositional logic with relations to support modalities. Goldblatt's "relational cover" semantics overcomes classical reasoning but introduces a new limitation: it relies upon a "modal localization" condition that restricts the class of models and complicates model construction. Goldblatt bypasses this restriction by using intricate order-theoretic completion arguments to prove completeness. In this article, we present a conservative extension of relational cover semantics that alleviates this restriction and is amenable to simpler and standard model construction techniques. We formalize our semantics in Agda and prove completeness constructively in the style of Normalization by Evaluation for a variety of IMLs featuring independent box and diamond modalities.

cs.LO↗

arXiv2025

Lax Modal Lambda Calculi

Intuitionistic modal logics (IMLs) extend intuitionistic propositional logic with modalities such as the box and diamond connectives. Advances in the study of IMLs have inspired several applications in programming languages via the development of corresponding type theories with modalities. Until recently, IMLs with diamonds have been misunderstood as somewhat peculiar and unstable, causing the development of type theories with diamonds to lag behind type theories with boxes. In this article, we develop a family of typed-lambda calculi corresponding to sublogics of a peculiar IML with diamonds known as Lax logic. These calculi provide a modal logical foundation for various strong functors in typed-functional programming. We present possible-world and categorical semantics for these calculi and constructively prove normalization, equational completeness and proof-theoretic inadmissibility results. Our main results have been formalized using the proof assistant Agda.

cs.LO↗

arXiv2024

UniAR: A Unified model for predicting human Attention and Responses on visual content

Progress in human behavior modeling involves understanding both implicit, early-stage perceptual behavior, such as human attention, and explicit, later-stage behavior, such as subjective preferences or likes. Yet most prior research has focused on modeling implicit and explicit human behavior in isolation; and often limited to a specific type of visual content. We propose UniAR -- a unified model of human attention and preference behavior across diverse visual content. UniAR leverages a multimodal transformer to predict subjective feedback, such as satisfaction or aesthetic quality, along with the underlying human attention or interaction heatmaps and viewing order. We train UniAR on diverse public datasets spanning natural images, webpages, and graphic designs, and achieve SOTA performance on multiple benchmarks across various image domains and behavior modeling tasks. Potential applications include providing instant feedback on the effectiveness of UIs/visual content, and enabling designers and content-creation models to optimize their creation for human-centric improvements.

cs.CV↗

arXiv2022

Differentially Private Heatmaps

We consider the task of producing heatmaps from users' aggregated data while protecting their privacy. We give a differentially private (DP) algorithm for this task and demonstrate its advantages over previous algorithms on real-world datasets. Our core algorithmic primitive is a DP procedure that takes in a set of distributions and produces an output that is close in Earth Mover's Distance to the average of the inputs. We prove theoretical bounds on the error of our algorithm under a certain sparsity assumption and that these are near-optimal.

cs.DS↗

arXiv2022

Normalization for Fitch-Style Modal Calculi

Fitch-style modal lambda calculi enable programming with necessity modalities in a typed lambda calculus by extending the typing context with a delimiting operator that is denoted by a lock. The addition of locks simplifies the formulation of typing rules for calculi that incorporate different modal axioms, but each variant demands different, tedious and seemingly ad hoc syntactic lemmas to prove normalization. In this work, we take a semantic approach to normalization, called normalization by evaluation (NbE), by leveraging the possible-world semantics of Fitch-style calculi to yield a more modular approach to normalization. We show that NbE models can be constructed for calculi that incorporate the K, T and 4 axioms of modal logic, as suitable instantiations of the possible-world semantics. In addition to existing results that handle beta-equivalence, our normalization result also considers eta-equivalence for these calculi. Our key results have been mechanized in the proof assistant Agda. Finally, we showcase several consequences of normalization for proving meta-theoretic properties of Fitch-style calculi as well as programming-language applications based on different interpretations of the necessity modality.

cs.LO↗