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We study a synthetic corpus based approach for language models (LMs) to acquire logical deductive reasoning ability. The previous studies generated deduction examples using specific sets of deduction rules. However, these rules were limited…

Domain Large Language Models (LLMs) are developed for domain-specific tasks based on general LLMs. But it still requires professional knowledge to facilitate the expertise for some domain-specific tasks. In this paper, we investigate into…

Aiming to harmonise finite and infinite model reasoning, we initiate the study of partially finite models, where the reasoning task comes with a formula that specifies a part of the model that must be finite. We focus on the problem of…

Solving constraints involving inductive (aka recursive) definitions is challenging. State-of-the-art SMT/CHC solvers and first-order logic provers provide only limited support for solving such constraints, especially when they involve,…

Effective organization of in-context learning (ICL) demonstrations is key to improving the quality of large language model (LLM) responses. To create better sample-label pairs that instruct LLM understanding, we introduce logit…

This paper presents the DLV system, which is widely considered the state-of-the-art implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel…

The rising popularity of neural networks (NNs) in recent years and their increasing prevalence in real-world applications have drawn attention to the importance of their verification. While verification is known to be computationally…

Differentiable Logics are deployed in neuro-symbolic learning tasks as a way of embedding logical constraints in the training objective of neural networks. A differentiable logic consists of a syntax to write logical properties and a…

While there has been a great deal of work on the development of reasoning algorithms for expressive description logics, in most cases only Tbox reasoning is considered. In this paper we present an algorithm for combined Tbox and Abox…

Constraint Logic Programming (CLP) is a logic programming formalism used to solve problems requiring the consideration of constraints, like resource allocation and automated planning and scheduling. It has previously been extended in…

This paper proposes the use of Constraint Logic Programming (CLP) to model SQL queries in a data-independent abstract layer by focusing on some semantic properties for signalling possible errors in such queries. First, we define a…

Recent studies highlight the effectiveness of using in-context learning (ICL) to steer large language models (LLMs) in processing tabular data, a challenging task given the structured nature of such data. Despite advancements in…

Chase algorithms are indispensable in the domain of knowledge base querying, which enable the extraction of implicit knowledge from a given database via applications of rules from a given ontology. Such algorithms have proved beneficial in…

One of the main reasons to employ a description logic such as EL or EL++ is the fact that it has efficient, polynomial-time algorithmic properties such as deciding consistency and inferring subsumption. However, simply by adding negation of…

To comprehensively evaluate the mathematical reasoning capabilities of Large Language Models (LLMs), researchers have introduced abundant mathematical reasoning datasets. However, most existing datasets primarily focus on linear reasoning,…

In this paper, we study the data complexity of querying inconsistent weighted description logic (DL) knowledge bases under recently-introduced cost-based semantics. In a nutshell, the idea is to assign each interpretation a cost based upon…

Despite their strong performance, large language models (LLMs) face challenges in real-world application of lexical simplification (LS), particularly in privacy-sensitive and resource-constrained environments. Moreover, since vulnerable…

Large language models (LLMs) have shown remarkable improvements in reasoning and many existing benchmarks have been addressed by models such as o1 and o3 either fully or partially. However, a majority of these benchmarks emphasize deductive…

Large Language Models (LLMs) are versatile, yet they often falter in tasks requiring deep and reliable reasoning due to issues like hallucinations, limiting their applicability in critical scenarios. This paper introduces a rigorously…

Fuzzy Description Logics (FDLs) are logic-based formalisms used to represent and reason with vague or imprecise knowledge. It has been recently shown that reasoning in most FDLs using truth values from the interval [0,1] becomes undecidable…