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The rapid advancement of large language models (LLMs) such as GPT-3, PaLM, and Llama has significantly transformed natural language processing, showcasing remarkable capabilities in understanding and generating language. However, a…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
Satisfiability modulo theories (SMT) solving has become a critical part of many static analyses, including symbolic execution, refinement type checking, and model checking. We propose Formulog, a domain-specific language that makes it…
We study the problem of rewriting an ontology O1 expressed in a DL L1 into an ontology O2 in a Horn DL L2 such that O1 and O2 are equisatisfiable when extended with an arbitrary dataset. Ontologies that admit such rewritings are amenable to…
Regular expression (regex) matching is fundamental in many applications, especially in web services. However, matching by backtracking -- preferred by most real-world implementations for its practical performance and backward compatibility…
Document Reading Order Recovery is a fundamental task in document image understanding, playing a pivotal role in enhancing Retrieval-Augmented Generation (RAG) and serving as a critical preprocessing step for large language models (LLMs).…
Reducing the non-Clifford cost of fault-tolerant quantum circuits is a central challenge in quantum compilation, since T gates are typically far more expensive than Clifford operations in error-corrected architectures. For Clifford+T…
The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…
The paper considers recovery of signals from incomplete observations and a problem of determination of the allowed quantity of missed observations, i.e. the problem of determination of the size of the uniqueness sets for a given data…
We introduce a novel model-theoretic framework inspired from graph modification and based on the interplay between model theory and algorithmic graph minors. The core of our framework is a new compound logic operating with two types of…
Retrieval augmented generation (RAG) enhances the accuracy and reliability of generative AI models by sourcing factual information from external databases, which is extensively employed in document-grounded question-answering (QA) tasks.…
We show that, for OWL 2 QL ontology-mediated queries with (i) ontologies of bounded depth and conjunctive queries of bounded treewidth, (ii) ontologies of bounded depth and bounded-leaf tree-shaped conjunctive queries, and (iii) arbitrary…
In many scenarios, complete and incomplete information coexist. For this reason, the knowledge representation and database communities have long shown interest in simultaneously supporting the closed- and the open-world views when reasoning…
The superiorization methodology is intended to work with input data of constrained minimization problems, i.e., a target function and a constraints set. However, it is based on an antipodal way of thinking to the thinking that leads…
In ontology-based data access (OBDA), the classical database is enhanced with an ontology in the form of logical assertions generating new intensional knowledge. A powerful form of such logical assertions is the tuple-generating…
This paper presents a comprehensive analysis of the well-known extragradient (EG) method for solving both equations and inclusions. First, we unify and generalize EG for [non]linear equations to a wider class of algorithms, encompassing…
Adding rewriting to a proof assistant based on the Curry-Howard isomorphism, such as Coq, may greatly improve usability of the tool. Unfortunately adding an arbitrary set of rewrite rules may render the underlying formal system undecidable…
Like the notion of computation via (strong) monads serves to classify various flavours of impurity, including exceptions, non-determinism, probability, local and global store, the notion of guardedness classifies well-behavedness of cycles…
The trend towards large language models (LLMs) for guardrailing against undesired behaviors is increasing and has shown promise for censoring user inputs. However, increased latency, memory consumption, hosting expenses and non-structured…
Replication ensures data availability in fault-prone distributed systems. The celebrated CAP theorem stipulates that replicas cannot guarantee both strong consistency and availability under network partitions. A popular alternative, adopted…