Related papers: An optimized KE-tableau-based system for reasoning…
We give an optimal (EXPTIME), sound and complete tableau-based algorithm for deciding satisfiability for propositional dynamic logic with converse (CPDL) which does not require the use of analytic cut. Our main contribution is a sound…
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…
In this paper, we present a novel diagnostic framework that integrates Knowledge Graphs (KGs) and Large Language Models (LLMs) to support system diagnostics in high-reliability systems such as nuclear power plants. Traditional diagnostic…
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…
In this paper we present a theorem proving methodology for a restricted but significant fragment of the conditional language made up of (boolean combinations of) conditional statements with unnested antecedents. The method is based on the…
There have been several recent suggestions for tableau systems for deciding satisfiability in the practically important branching time temporal logic known as CTL*. In this paper we present a streamlined and more traditional tableau…
Large Language Models (LLMs) struggle with multi-step reasoning over structured tables. The primary reason is the lack of explicit supervision for intermediate reasoning states. Existing learned reward models or executor-based verifiers are…
This paper introduces an explanation framework designed to enhance the quality of rules in knowledge-based reasoning systems based on dataset-driven insights. The traditional method for rule induction from data typically requires…
We propose a new declarative planning language, called K, which is based on principles and methods of logic programming. In this language, transitions between states of knowledge can be described, rather than transitions between completely…
Representation of defeasible information is of interest in description logics, as it is related to the need of accommodating exceptional instances in knowledge bases. In this direction, in our previous works we presented a datalog…
Table reasoning tasks have shown remarkable progress with the development of large language models (LLMs), which involve interpreting and drawing conclusions from tabular data based on natural language (NL) questions. Existing solutions…
This thesis concerns the development of a framework that facilitates the design and analysis of formal systems. Specifically, this framework provides a specification language which supports the concise and direct description of formal…
We reformulate Pratt's tableau decision procedure of checking satisfiability of a set of formulas in PDL. Our formulation is simpler and more direct for implementation. Extending the method we give the first EXPTIME (optimal) tableau…
We introduce $\mathcal{DLR}^+$, an extension of the n-ary propositionally closed description logic $\mathcal{DLR}$ to deal with attribute-labelled tuples (generalising the positional notation), projections of relations, and global and local…
Recently, the description logic LE-ALC was introduced for reasoning in the semantic environment of the enriched formal contexts, and a tableaux algorithm was developed for checking the consistency of ABoxes in this logic. In this paper, we…
Prior work has combined chain-of-thought prompting in large language models (LLMs) with programmatic representations to perform effective and transparent reasoning. While such an approach works well for tasks that only require forward…
This paper describes an architecture that combines the complementary strengths of declarative programming and probabilistic graphical models to enable robots to represent, reason with, and learn from, qualitative and quantitative…
Reasoning over knowledge graphs (KGs) is a challenging task that requires a deep understanding of the complex relationships between entities and the underlying logic of their relations. Current approaches rely on learning geometries to…
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…
The KLM approach to defeasible reasoning introduces a weakened form of implication into classical logic. This allows one to incorporate exceptions to general rules into a logical system, and for old conclusions to be withdrawn upon learning…