Related papers: A Two-Watched Literal Scheme for First-Order Logic
Four algorithms for propositional forgetting are compared. The first performs all possible resolutions and deletes the clauses containing a variable to forget. The second forgets a variable at time by resolving and then deleting all clauses…
Large language models (LLMs) have shown promise in formal theorem proving, but their token-level processing often fails to capture the inherent hierarchical nature of mathematical proofs. We introduce \textbf{Hierarchical Attention}, a…
Classical planning representation languages based on first-order logic have preliminarily been used to model and solve robotic task planning problems. Wider adoption of these representation languages, however, is hindered by the limitations…
Large language models perform well on many logical reasoning benchmarks, but it remains unclear which core logical skills they truly master. To address this, we introduce LogicSkills, a benchmark that isolates three fundamental logical…
Learning semantic-rich representations from raw unlabeled time series data is critical for downstream tasks such as classification and forecasting. Contrastive learning has recently shown its promising representation learning capability in…
Distributed First Order Logic (DFOL) has been introduced more than ten years ago with the purpose of formalising distributed knowledge-based systems, where knowledge about heterogeneous domains is scattered into a set of interconnected…
We study the problem of deriving policies, or rules, that when enacted on a complex system, cause a desired outcome. Absent the ability to perform controlled experiments, such rules have to be inferred from past observations of the system's…
In solving a query, the SLD proof procedure for definite programs sometimes searches an infinite space for a non existing solution. For example, querying a planner for an unreachable goal state. Such programs motivate the development of…
Reified Input/Output (I/O) logic[21] has been recently proposed to model real-world norms in terms of the logic in [11]. This is massively grounded on the notion of reification, and it has specifically designed to model meaning of natural…
Logical reasoning is a pivotal component in the field of artificial intelligence. Proof planning, particularly in contexts requiring the validation of explanation accuracy, continues to present challenges. The recent advancement of large…
We give an algorithm for the class of second order unification problems in which second order variables have at most one occurrence.
We present a polymorphic linear lambda-calculus as a proof language for second-order intuitionistic linear logic. The calculus includes addition and scalar multiplication, enabling the proof of a linearity result at the syntactic level.
On the Semantic Web, metadata and ontologies are used to enable computers to read data. The Web Ontology Language (OWL) has been proposed as a standard ontological language, and various inference systems for this language have been studied.…
This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the…
At present, the deep end-to-end method based on supervised learning is used in entity recognition and dependency analysis. There are two problems in this method: firstly, background knowledge cannot be introduced; secondly, multi…
This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and first-order constructs together with…
We show that large language models (LLMs) exhibit an $\textit{internal chain-of-thought}$: they sequentially decompose and execute composite tasks layer-by-layer. Two claims ground our study: (i) distinct subtasks are learned at different…
Distributed processing over networks relies on in-network processing and cooperation among neighboring agents. Cooperation is beneficial when agents share a common objective. However, in many applications agents may belong to different…
We present PDLP, a practical first-order method for linear programming (LP) that can solve to the high levels of accuracy that are expected in traditional LP applications. In addition, it can scale to very large problems because its core…
The recently proposed Successive-Cancellation List Flip (SCLF) decoding algorithm for polar codes improves the error-correcting performance of state-of-the-art SC List (SCL) decoding. However, it comes at the cost of a higher complexity. In…