Related papers: The Modal Logic of Stepwise Removal
We survey dynamic logics for specifying and verifying properties of dynamical systems, including hybrid systems, distributed hybrid systems, and stochastic hybrid systems. A dynamic logic is a first-order modal logic with a pair of…
Large Language Models (LLMs) suffer from critical reasoning gaps, including a tendency to hallucinate and poor accuracy in classifying logical fallacies. This limitation stems from their default System 1 processing, which is fast and…
We investigate the expressive power of the two main kinds of program logics for complex, non-regular program properties found in the literature: those extending propositional dynamic logic (PDL), and those extending the modal mu-calculus.…
This paper presents an efficient approach to image segmentation that approximates the piecewise-smooth (PS) functional in [12] with explicit solutions. By rendering some rational constraints on the initial conditions and the final solutions…
We present a novel and well automatable approach to formal verification of programs with underspecified semantics, i.e., a language semantics that leaves open the order of certain evaluations. First, we reduce this problem to…
The verification community has studied dynamic data structures primarily in a bottom-up way by analyzing pointers and the shapes induced by them. Recent work in fields such as separation logic has made significant progress in extracting…
Symbolic model checking of parallel programs stands and falls with effective methods of dealing with the explosion of interleavings. We propose a dynamic reduction technique to avoid unnecessary interleavings. By extending Lipton's original…
Dynamic logic is a modal logic for reasoning about programs. A cyclic proof system is a proof system that allows proofs containing cycles and is an alternative to a proof system containing (co-)induction. This paper introduces a sequent…
Language models (LMs) are capable of conducting in-context learning for multiple choice reasoning tasks, but the options in these tasks are treated equally. As humans often first eliminate wrong options before picking the final correct…
Machine unlearning (MU) has gained significant attention as a means to remove specific data from trained models without requiring a full retraining process. While progress has been made in unimodal domains like text and image…
We study elementary modal logics, i.e. modal logic considered over first-order definable classes of frames. The classical semantics of modal logic allows infinite structures, but often practical applications require to restrict our…
Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham's modal…
In this paper, we present Modality-Importance-Guided Reasoning (MIGR), a framework designed to improve the reliability of reasoning-based multimodal emotion understanding in multimodal large language models. Although existing methods have…
This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of…
We introduce a modal logic for describing statistical knowledge, which we call statistical epistemic logic. We propose a Kripke model dealing with probability distributions and stochastic assignments, and show a stochastic semantics for the…
We analyze the computational complexity of admissibility and unifiability with parameters in transitive modal logics. The class of cluster-extensible (clx) logics was introduced in the first part of this series of papers. We completely…
As is evident in the programming language literature, many practitioners favor specifying dynamic program behavior using big-step over small-step semantics. Unlike small-step semantics, which must dwell on every intermediate program state,…
Reasoning in language models is difficult to evaluate: natural-language traces are unverifiable, symbolic datasets are too small, and most benchmarks conflate heuristics with inference. We present FOL-Traces, the first large-scale dataset…
We propose a modal logic tailored to describe graph transformations and discuss some of its properties. We focus on a particular class of graphs called termgraphs. They are first-order terms augmented with sharing and cycles. Termgraphs…
Various human activities can be abstracted into a sequence of actions in natural text, i.e. cooking, repairing, manufacturing, etc. Such action sequences heavily depend on the executing order, while disorder in action sequences leads to…