Related papers: Higher-order Logic as Lingua Franca -- Integrating…

We present an implementation of a probabilistic first-order logic called TensorLog, in which classes of logical queries are compiled into differentiable functions in a neural-network infrastructure such as Tensorflow or Theano. This leads…

Human logic has gradually shifted from intuition-driven inference to rigorous formal systems. Motivated by recent advances in large language models (LLMs), we explore whether LLMs exhibit a similar evolution in the underlying logical…

We establish a novel connection between two research areas in non-classical logics which have been developed independently of each other so far: on the one hand, input/output logic, introduced within a research program developing logical…

The logic programming paradigm provides the basis for a new intensional view of higher-order notions. This view is realized primarily by employing the terms of a typed lambda calculus as representational devices and by using a richer form…

State-of-the-art Datalog engines include expressive features such as ADTs (structured heap values), stratified aggregation and negation, various primitive operations, and the opportunity for further extension using FFIs. Current…

Logicians study and apply a multiplicity of various logical systems. Consequently, there is necessity to build foundations and common grounds for all these systems. This is done in metalogic. Like metamathematics studies formalized…

We study the expressive power of fragments of inclusion and independence logic defined either by restricting the number of universal quantifiers or the arity of inclusion and independence atoms in formulas. Assuming the so-called lax…

Language serves as a vehicle for conveying thought, enabling communication among individuals. The ability to distinguish between diverse concepts, identify fairness and injustice, and comprehend a range of legal notions fundamentally relies…

We propose a purely extensional semantics for higher-order logic programming. In this semantics program predicates denote sets of ordered tuples, and two predicates are equal iff they are equal as sets. Moreover, every program has a unique…

This literature review discovers an implementation of formal logic systems in cyber security by enhancing access control models. We explore the characteristics of the existing access control theories, their limitations and how classical…

Logic rules are powerful for expressing complex reasoning and analysis problems. At the same time, they are inconvenient or impossible to use for many other aspects of applications. Integrating rules in a language with sets and functions,…

To adequately model mathematical arguments the analyst must be able to represent the mathematical objects under discussion and the relationships between them, as well as inferences drawn about these objects and relationships as the…

In this paper we summarized a framework for designing grammar-based procedure for the automatic extraction of the semantic content from spoken queries. Starting with a case study and following an approach which combines the notions of…

This article contains a proposal to add coinduction to the computational apparatus of natural language understanding. This, we argue, will provide a basis for more realistic, computationally sound, and scalable models of natural language…

Large Reasoning Models (LRMs) achieve strong performance on mathematical, scientific, and other question-answering tasks, but their multilingual reasoning abilities remain underexplored. When presented with non-English questions, LRMs often…

High-dimensional distributed semantic spaces have proven useful and effective for aggregating and processing visual, auditory, and lexical information for many tasks related to human-generated data. Human language makes use of a large and…

Recent advances in Large Language Models have demonstrated their capabilities across a variety of tasks. However, automatically extracting implicit knowledge from natural language remains a significant challenge, as machines lack active…

We present a hybrid architecture for agent-augmented strategic reasoning, combining heuristic extraction, semantic activation, and compositional synthesis. Drawing on sources ranging from classical military theory to contemporary corporate…

Contemporary semantic description of logic is based on the ontology of all possible interpretations, an insufficiently clear metaphysical concept. In this article, logic is described as the internal organization of language. Logical…

We define the notion of a model of higher-order modal logic in an arbitrary elementary topos $\mathcal{E}$. In contrast to the well-known interpretation of (non-modal) higher-order logic, the type of propositions is not interpreted by the…