Related papers: The Modal Logic of Stepwise Removal
The central open question in Descriptive Complexity is whether there is a logic that characterizes deterministic polynomial time (PTIME) on relational structures. Towards this goal, we define a logic that is obtained from first-order logic…
This article presents modal versions of resource-conscious logics. We concentrate on extensions of variants of Linear Logic with one minimal non-normal modality. In earlier work, where we investigated agency in multi-agent systems, we have…
Real-world multimodal learning is often hindered by missing modalities. While Incomplete Multimodal Learning (IML) has gained traction, existing methods typically rely on the unrealistic assumption of full-modal availability during training…
We introduce a geometric model of shallow multiplicative exponential linear logic (MELL) using the Hilbert scheme. Building on previous work interpreting multiplicative linear logic proofs as systems of linear equations, we show that…
Epistemic logic programs constitute an extension of the stable models semantics to deal with new constructs called subjective literals. Informally speaking, a subjective literal allows checking whether some regular literal is true in all…
Intuitionistic grammar logics fuse constructive and multi-modal reasoning while permitting the use of converse modalities, serving as a generalization of standard intuitionistic modal logics. In this paper, we provide definitions of these…
Appel and McAllester's "step-indexed" logical relations have proven to be a simple and effective technique for reasoning about programs in languages with semantically interesting types, such as general recursive types and general reference…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
The fuzzy modality `probably` is interpreted over probabilistic type spaces by taking expected truth values. The arising probabilistic fuzzy description logic is invariant under probabilistic bisimilarity; more informatively, it is…
Aristotle's discussions on modal syllogistic have often been viewed as error-prone and have garnered significant attention in the literature due to historical and philosophical interests. However, from a contemporary standpoint, they also…
Reinforcement Learning with Verifiable Rewards (RLVR) elicits long chain-of-thought reasoning in large language models (LLMs), but outcome-based rewards lead to coarse-grained advantage estimation. While existing approaches improve RLVR via…
Extending and generalizing the approach of 2-sequents (Masini, 1992), we present sequent calculi for the classical modal logics in the K, D, T, S4 spectrum. The systems are presented in a uniform way-different logics are obtained by tuning…
Large language models demonstrate limited capability in proficiency-controlled sentence simplification, particularly when simplifying across large readability levels. We propose a framework that decomposes complex simplifications into…
We present a non-deterministic semantic framework for all modal logics in the modal cube, extending prior works by Kearns and others. Our approach introduces modular and uniform multi-valued non-deterministic matrices (Nmatrices) for each…
For lack of general algorithmic methods that apply to wide classes of logics, establishing a complexity bound for a given modal logic is often a laborious task. The present work is a step towards a general theory of the complexity of modal…
Logical reasoning is a crucial task for Large Language Models (LLMs), enabling them to tackle complex problems. Among reasoning tasks, multi-step reasoning poses a particular challenge. Grounded in the theory of formal logic, we have…
Step-wise explanations can explain logic puzzles and other satisfaction problems by showing how to derive decisions step by step. Each step consists of a set of constraints that derive an assignment to one or more decision variables.…
Polyhedral semantics is a recently introduced branch of spatial modal logic, in which modal formulas are interpreted as piecewise linear subsets of an Euclidean space. Polyhedral semantics for the basic modal language has already been well…
Multi-step reasoning instruction, such as chain-of-thought prompting, is widely adopted to explore better language models (LMs) performance. We report on the systematic strategy that LMs employ in such a multi-step reasoning process. Our…
Classical logics of knowledge and belief are usually interpreted on Kripke models, for which a mathematically well-developed model theory is available. However, such models are inadequate to capture dynamic phenomena. Therefore, epistemic…