Related papers: Algebraic Semantics of Datalog with Equality
PRholog is an experimental extension of logic programming with strategic conditional transformation rules, combining Prolog with Rholog calculus. The rules perform nondeterministic transformations on hedges. Queries may have several results…
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…
The syntactic nature of logic and computation separates them from other fields of mathematics. Nevertheless, syntax has been the only way to adequately capture the dynamics of proofs and programs such as cut-elimination, and the finiteness…
The healthcare sector has experienced a rapid accumulation of digital data recently, especially in the form of electronic health records (EHRs). EHRs constitute a precious resource that IS researchers could utilize for clinical applications…
While pre-trained language models (PLMs) are the go-to solution to tackle many natural language processing problems, they are still very limited in their ability to capture and to use common-sense knowledge. In fact, even if information is…
A systematic algebraic framework for composing and decomposing logic programs is currently missing, limiting our ability to analyze and construct programs in a modular way. In this paper, we introduce set-like operations for (propositional…
While Large Language Models (LLM) enable non-experts to specify open-world multi-robot tasks, the generated plans often lack kinematic feasibility and are not efficient, especially in long-horizon scenarios. Formal methods like Linear…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…
This paper proves a homomorphism between extensional formal semantics and distributional vector space semantics, demonstrating structural compatibility. Formal semantics models meaning as reference, using logical structures to map…
Probabilistic logical models are a core component of neurosymbolic AI and are important in their own right for tasks that require high explainability. Unlike neural networks, logical theories that underlie the model are often handcrafted…
In the setting of modern mathematical logic and model theory, classification theory has been one of the landmark achievements of the field. Likewise, the classification of UHF-algebras and AF-algebras were substantial contributions to the…
Logic has proved essential for formally modeling software based systems. Such formal descriptions, frequently called specifications, have served not only as requirements documentation and formalisation, but also for providing the…
Epistemic Logic Programs (ELPs), extend Answer Set Programming (ASP) with epistemic operators. The semantics of such programs is provided in terms of world views, which are sets of belief sets, i.e., syntactically, sets of sets of atoms.…
Using the programming language Haskell, we introduce an implementation of propositional calculus, number theory, and a simple imperative language that can evaluate arithmetic and boolean expressions. Finally, we provide an implementation of…
As a core cognitive skill that enables the transferability of information across domains, analogical reasoning has been extensively studied for both humans and computational models. However, while cognitive theories of analogy often focus…
Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…
This work revisits operator learning from a spectral perspective by introducing Polar Linear Algebra, a structured framework based on polar geometry that combines a linear radial component with a periodic angular component. Starting from…
We present a simple technique for semantic, open logical relations arguments about languages with recursive types, which, as we show, follows from a principled foundation in categorical semantics. We demonstrate how it can be used to give a…
Data analysis at the LHC has a very steep learning curve, which erects a formidable barrier between data and anyone who wishes to analyze data, either to study an idea or to simply understand how data analysis is performed. To make analysis…
The BHK interpretation interprets propositional statements as descriptions of the world of proofs; a world which is hierarchical in nature. It consists of different layers of the concept of proof; the proofs, the proofs about proofs and so…