Related papers: Algorithmic correspondence for relevance logics, b…

Considering the limited internal parametric knowledge, retrieval-augmented generation (RAG) has been widely used to extend the knowledge scope of large language models (LLMs). Despite the extensive efforts on RAG research, in existing…

The emergence of tools based on artificial intelligence has also led to the need of producing explanations which are understandable by a human being. In most approaches, the system is considered a black box, making it difficult to generate…

We propose a new formalism for specifying and reasoning about problems that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and connections between them. The essence…

Relational program verification is a variant of program verification where one can reason about two programs and as a special case about two executions of a single program on different inputs. Relational program verification can be used for…

Properties such as provable security and correctness for randomized programs are naturally expressed relationally as approximate equivalences. As a result, a number of relational program logics have been developed to reason about such…

Efficiently reranking documents retrieved from information retrieval (IR) pipelines to enhance overall quality of Retrieval-Augmented Generation (RAG) system remains an important yet challenging problem. Recent studies have highlighted the…

Reinforcement learning (RL) is a versatile framework for optimizing long-term goals. Although many real-world problems can be formalized with RL, learning and deploying a performant RL policy requires a system designed to address several…

We show how to transform any set of prioritized propositional defaults into an equivalent set of parallel (i.e., unprioritized) defaults, in circumscription. We give an algorithm to implement the transform. We show how to use the transform…

Causal representation learning (CRL) has garnered increasing interest from the causal inference and artificial intelligence communities due to its potential to disentangle complex data-generating mechanism into causally interpretable latent…

This paper presents a novel simplification calculus for propositional logic derived from Peirce's existential graphs' rules of inference and implication graphs. Our rules can be applied to propositional logic formulae in nested form, are…

Real-world data is frequently noisy and ambiguous. In crowdsourcing, for example, human annotators may assign conflicting class labels to the same instances. Partial-label learning (PLL) addresses this challenge by training classifiers when…

This paper presents the development of a software tool that enables the translation of first-order predicate logic with at most three variables into relation algebra. The tool was developed using the Z3 theorem prover, leveraging its…

A new algebraic object is introduced - recurrent fractions, which is an n-dimensional generalization of continued fractions. It is used to describe an algorithm for rational approximations of algebraic irrational numbers. Some…

Capturing complex user preferences from sparse behavioral sequences remains a fundamental challenge in sequential recommendation. Recent latent reasoning methods have shown promise by extending test-time computation through multi-step…

In many probabilistic first-order representation systems, inference is performed by "grounding"---i.e., mapping it to a propositional representation, and then performing propositional inference. With a large database of facts, groundings…

When proving theorems from large sets of logical assertions, it can be helpful to restrict the search for a proof to those assertions that are relevant, that is, closely related to the theorem in some sense. For example, in the Watson…

Inference in natural language often involves recognizing lexical entailment (RLE); that is, identifying whether one word entails another. For example, "buy" entails "own". Two general strategies for RLE have been proposed: One strategy is…

Many machine learning applications require the ability to learn from and reason about noisy multi-relational data. To address this, several effective representations have been developed that provide both a language for expressing the…

Recently, dense passage retrieval has become a mainstream approach to finding relevant information in various natural language processing tasks. A number of studies have been devoted to improving the widely adopted dual-encoder…

Functional programming comes in two flavours: one where ``functions are first-class citizens'' (we call this applicative) and one which is based on equations (we call this declarative). In relational programming clauses play the role of…