Related papers: Automated Reasoning in Modal and Description Logic…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
Large language models (LLMs) can perform complex reasoning in few- and zero-shot settings by generating intermediate chain of thought (CoT) reasoning steps. Further, each reasoning step can rely on external tools to support computation…
An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant…
We approach the task of computing a carefully synchronizing word of minimum length for a given partial deterministic automaton, encoding the problem as an instance of SAT and invoking a SAT solver. Our experimental results demonstrate that…
Answering complex queries over incomplete knowledge graphs (KGs) is a challenging job. Most previous works have focused on learning entity/relation embeddings and simulating first-order logic operators with various neural networks. However,…
Answer Set Programming (ASP), a well-known declarative logic programming paradigm, has recently found practical application in Process Mining. In particular, ASP has been used to model tasks involving declarative specifications of business…
Training large language models (LLMs) with chain-of-thought (CoT) supervision has proven effective for enhancing their reasoning abilities. However, obtaining reliable and accurate reasoning supervision remains a significant challenge. We…
We consider the problem of implementing deontic modal logic. We show how (deontic) modal operators can be elegantly and directly expressed using default negation (negation-as-failure) and strong negation present in answer set programming…
Despite the remarkable success of large language models (LLMs) on traditional natural language processing tasks, their planning ability remains a critical bottleneck in tackling complex multi-step reasoning tasks. Existing approaches mainly…
The standard reasoning problem, concept satisfiability, in the basic description logic ALC is PSPACE-complete, and it is EXPTIME-complete in the presence of unrestricted axioms. Several fragments of ALC, notably logics in the FL, EL, and…
Boolean satisfiability is a propositional logic problem of interest in multiple fields, e.g., physics, mathematics, and computer science. Beyond a field of research, instances of the SAT problem, as it is known, require efficient solution…
In research of manufacturing systems and autonomous robots, the term capability is used for a machine-interpretable specification of a system function. Approaches in this research area develop information models that capture all information…
This survey provides an analysis of current methodologies integrating legal and logical specifications into the perception, prediction, and planning modules of automated driving systems. We systematically explore techniques ranging from…
In the contexts of automated reasoning and formal verification, important decision problems are effectively encoded into Satisfiability Modulo Theories (SMT). In the last decade efficient SMT solvers have been developed for several theories…
While the reasoning capabilities of Large Language Models (LLMs) excel in analytical tasks such as mathematics and code generation, their utility for abstractive summarization remains widely assumed but largely unverified. To bridge this…
Chain-of-Thought (CoT) and Program-Aided Language Models (PAL) represent two distinct reasoning methods, each with its own strengths. CoT employs natural language, offering flexibility and interpretability, while PAL utilizes programming…
We introduce proper display calculi for basic monotonic modal logic, the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
A rational number can be naturally presented by an arithmetic computation (AC): a sequence of elementary arithmetic operations starting from a fixed constant, say 1. The asymptotic complexity issues of such a representation are studied e.g.…
While large language models (LLMs) have demonstrated impressive capabilities across various natural language processing tasks by acquiring rich factual knowledge from their broad training data, their ability to synthesize and logically…
As knowledge and semantics on the web grow increasingly complex, enhancing Large Language Models (LLMs)' comprehension and reasoning capabilities has become particularly important. Chain-of-Thought (CoT) prompting has been shown to enhance…