Related papers: Sequent Calculi for Data-Aware Modal Logics
Large pretrained language models and neural reasoning systems have advanced many natural language tasks, yet they remain challenged by knowledge-intensive queries that require precise, structured multi-hop inference. Knowledge graphs…
Differentiable logics are a family of quantitative logics originated in the machine learning literature. Because of their origin, differentiable logics often come equipped with analytic properties that guarantee that they are…
The sequent calculus is a proof system which was designed as a more symmetric alternative to natural deduction. The {\lambda}{\mu}{\mu}-calculus is a term assignment system for the sequent calculus and a great foundation for compiler…
Recursive query processing has experienced a recent resurgence, as a result of its use in many modern application domains, including data integration, graph analytics, security, program analysis, networking and decision making. Due to the…
We present a uniform characterisation of three-valued logics by means of the bisequent calculus (BSC). It is a generalised form of a sequent calculus (SC) where rules operate on the ordered pairs of ordinary sequents. BSC may be treated as…
Non-normal modal logics, interpreted on neighbourhood models which generalise the usual relational semantics, have found application in several areas, such as epistemic, deontic, and coalitional reasoning. We present here preliminary…
Querying and exploring massive collections of data sources, such as data lakes, has been an essential research topic in the database community. Although many efforts have been paid in the field of data discovery and data integration in data…
We introduce the first cut-free nested sequent systems for first-order modal logics that admit increasing, decreasing, constant, and empty domains along with so-called general path conditions and seriality. We obtain such systems by means…
Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…
Hybrid computation combines discrete and continuous dynamics in the form of an entangled mixture inherently present both in various natural phenomena, and in applications ranging from control theory to microbiology. The emergent behaviours…
Current Retrieval-Augmented Generation (RAG) systems primarily operate on unimodal textual data, limiting their effectiveness on unstructured multimodal documents. Such documents often combine text, images, tables, equations, and graphs,…
This paper considers two logics. The first one, $\mathbf{K}\mathsf{G}_\mathsf{inv}$, is an expansion of the G\"odel modal logic $\mathbf{K}\mathsf{G}$ with the involutive negation $\sim_\mathsf{i}$ defined as…
We introduce a complete many-valued semantics for two normal lattice-based modal logics. This semantics is based on reflexive many-valued graphs. We discuss an interpretation and possible applications of this logical framework in the…
Modality is the linguistic ability to describe events with added information such as how desirable, plausible, or feasible they are. Modality is important for many NLP downstream tasks such as the detection of hedging, uncertainty,…
We introduce a cyclic proof system for the two-way alternation-free modal $\mu$-calculus. The system manipulates one-sided Gentzen sequents and locally deals with the backwards modalities by allowing analytic applications of the cut rule.…
This technical report provides some lightweight introduction motivating the definition of an alignment of log traces against Data-Aware Declare Models potentially containing correlation conditions. This technical report is only providing…
We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path…
Graph-based data models allow for flexible data representation. In particular, semantic data based on RDF and OWL fuels use cases ranging from general knowledge graphs to domain specific knowledge in various technological or scientific…
In this paper, we revisit Moggi's celebrated calculus of computational effects from the perspective of logic of monoidal action (actegory). Our development takes the following steps. Firstly, we perform proof-theoretic reconstruction of…
We define a new kind of automata recognizing properties of data words or data trees and prove that the automata capture all queries definable in Regular XPath. We show that the automata-theoretic approach may be applied to answer…