Related papers: Dualized Simple Type Theory

We introduce a new matrix model that describes Causal Dynamical Triangulations (CDT) in two dimensions. In order to do so, we introduce a new, simpler definition of 2D CDT and show it to be equivalent to the old one. The model makes use of…

Large Language Models (LLMs) often exhibit misalignment between the quality of their generated responses and the confidence estimates they assign to them. Bayesian treatments, such as marginalizing over a reliable weight posterior or over…

We introduce a temporal logic to reason on global applications in an asynchronous setting. First, we define the Distributed States Logic (DSL), a modal logic for localities that embeds the local theories of each component into a theory of…

We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is…

In Linear Logic ($\mathsf{LL}$), the exponential modality $!$ brings forth a distinction between non-linear proofs and linear proofs, where linear means using an argument exactly once. Differential Linear Logic ($\mathsf{DiLL}$) is an…

Dynamic topological logic ($\mathbf{DTL}$) is a trimodal logic designed for reasoning about dynamic topological systems. It was shown by Fern\'andez-Duque that the natural set of axioms for $\mathbf{DTL}$ is incomplete, but he provided a…

This article presents a bidirectional type system for the Calculus of Inductive Constructions (CIC). It introduces a new judgement intermediate between the usual inference and checking, dubbed constrained inference, to handle the presence…

In this paper, we introduce Linear Logic with a nondeterministic facility, which has a self-dual additive connective. In the system the proof net technology is available in a natural way. The important point is that nondeterminism in the…

$\tau$-tilting theory can be thought of as a generalization of the classical tilting theory which allows mutations at any indecomposable summand of a support $\tau$-tilting pair. Indeed, for any algebra $\Lambda$ its tilting modules…

This paper presents \tdl, a typed feature-based representation language and inference system. Type definitions in \tdl\ consist of type and feature constraints over the boolean connectives. \tdl\ supports open- and closed-world reasoning…

Dependent Object Types (DOT) is a calculus with path dependent types, intersection types, and object self-references, which serves as the core calculus of Scala 3. Although the calculus has been proven sound, it remains open whether type…

Type-free systems of logic are designed to consistently handle significant instances of self-reference. Some consistent type-free systems also have the feature of allowing the sort of general abstraction or comprehension principle that…

We introduce Probabilistic Dependent Type Systems (PDTS) via a functional language based on a subsystem of intuitionistic type theory including dependent sums and products, which is expanded to include stochastic functions. We provide a…

The integration of reasoning, learning, and decision-making is key to build more general artificial intelligence systems. As a step in this direction, we propose a novel neural-logic architecture, called differentiable logic machine (DLM),…

Several different proof translations exist between classical and intuitionistic logic (negative translations), and intuitionistic and linear logic (Girard translations). Our aims in this paper are (1) to consider extensions of…

Conventional test-time adaptation (TTA) approaches typically adapt the model using only a small fraction of test samples, often those with low-entropy predictions, thereby failing to fully leverage the available information in the test…

This paper presents Non-Axiomatic Term Logic (NATL) as a theoretical computational framework of humanlike symbolic reasoning in artificial intelligence. NATL unites a discrete syntactic system inspired from Aristotle's term logic and a…

This paper proposes a specification test for the conventional distributional assumptions of error terms in binary choice models, focusing on its tail properties. Based on extreme value theory, we first establish that the tail index of the…

The task of Long-tailed Class Incremental Learning (LT-CIL) addresses the sequential learning of new classes from datasets with imbalanced class distributions. This scenario intensifies the fundamental problem of catastrophic forgetting,…

This thesis deals with Double Field Theory (DFT), an effective field theory capturing the low energy dynamics of closed strings on a torus. It renders T-duality on a torus manifest by adding $D$ winding coordinates in addition to the $D$…