Related papers: Fixpoint Semantics for DatalogMTL with Negation
The supervaluationist approach to fixed-point semantics is, arguably, the most celebrated and studied competitor to the Strong Kleene approach within Kripkean truth. In this paper, we show how to obtain supervaluationist fixed-point…
Counterfactual explanations (CFEs) provide actionable recourse, but most methods assume a static framework with fixed data and a trained classifier. This assumption breaks in evolving data environments, such as data streams, where online…
Datalog$^\neg$ is a central formalism used in a variety of domains ranging from deductive databases and abstract argumentation frameworks to answer set programming. Its model theory is the finite counterpart of the logical semantics…
One of possible ways of obtaining continuous-space sentence representations is by training neural machine translation (NMT) systems. The recent attention mechanism however removes the single point in the neural network from which the source…
We give a sufficient condition for Kripke completeness of modal logics enriched with the transitive closure modality. More precisely, we show that if a logic admits what we call definable filtration (ADF), then such an expansion of the…
Negation is a common linguistic feature that is crucial in many language understanding tasks, yet it remains a hard problem due to diversity in its expression in different types of text. Recent work has shown that state-of-the-art NLP…
In the literature on Kleene algebra, a number of variants have been proposed which impose additional structure specified by a theory, such as Kleene algebra with tests (KAT) and the recent Kleene algebra with observations (KAO), or make…
As Artificial Intelligence (AI) integrates deeper into diverse sectors, the quest for powerful models has intensified. While significant strides have been made in boosting model capabilities and their applicability across domains, a glaring…
We present a theoretical framework in which a document and an AI model engage in a transfinite fixed-point interaction that leads to stable semantic alignment. Building on the foundations of Alpay Algebra, we introduce a functorial system…
Nonnegative matrix factorization (NMF), which is the approximation of a data matrix as the product of two nonnegative matrices, is a key issue in machine learning and data analysis. One approach to NMF is to formulate the problem as a…
We study modal team logic MTL, the team-semantical extension of modal logic ML closed under Boolean negation. Its fragments, such as modal dependence, independence, and inclusion logic, are well-understood. However, due to the unrestricted…
We develop team semantics for Linear Temporal Logic (LTL) to express hyperproperties, which have recently been identified as a key concept in the verification of information flow properties. Conceptually, we consider an asynchronous and a…
Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling and evaluating argumentation allowing general logical satisfaction conditions. Different criteria used to settle the acceptance of arguments are called…
We present a new metric temporal logic HornMTL over dense time and its datalog extension datalogMTL. The use of datalogMTL is demonstrated in the context of ontology-based data access over meteorological data. We show decidability of…
Model checking and automated theorem proving are two pillars of formal methods. This paper investigates model checking from an automated theorem proving perspective, aiming at combining the expressiveness of automated theorem proving and…
Recently many efforts have been devoted to interpreting the black-box NMT models, but little progress has been made on metrics to evaluate explanation methods. Word Alignment Error Rate can be used as such a metric that matches human…
Quantified CTL (QCTL) is a well-studied temporal logic that extends CTL with quantification over atomic propositions. It has recently come to the fore as a powerful intermediary framework to study logics for strategic reasoning. We extend…
Defeasible logic is an efficient logic for defeasible reasoning. It is defined through a proof theory and, until now, has had no model theory. In this paper a model-theoretic semantics is given for defeasible logic. The logic is sound and…
We present team semantics for two of the most important linear and branching time specification languages, Linear Temporal Logic (LTL) and Computation Tree Logic (CTL). With team semantics, LTL is able to express hyperproperties, which have…
We propose a novel framework for ontology-based access to temporal log data using a datalog extension datalogMTL of a Horn fragment of the metric temporal logic MTL. We show that datalogMTL is ExpSpace-complete even with punctual intervals,…