Related papers: On Linear Information Systems
This paper revisits the definition of linear time-invariant (LTI) stochastic process within a behavioral systems framework. Building on [Willems, 2013], we derive a canonical representation of an LTI stochastic process and a physically…
Semantic Knowledge Graphs (SKG) face challenges with scalability, flexibility, contextual understanding, and handling unstructured or ambiguous information. However, they offer formal and structured knowledge enabling highly interpretable…
In this paper we introduce Epistemic Strategy Logic (ESL), an extension of Strategy Logic with modal operators for individual knowledge. This enhanced framework allows us to represent explicitly and to reason about the knowledge agents have…
The theory of bounded, distributive lattices provides the appropriate language for describing directionality and asymptotics in dynamical systems. For bounded, distributive lattices the general notion of `set-difference' taking values in a…
Linear time-invariant (LTI) systems appear frequently in natural sciences and engineering contexts. Many LTI systems are described by ordinary differential equations (ODEs). For example, biological gene regulation, analog filter circuits,…
Differential Linear Logic enriches Linear Logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. We present a proof-net syntax for Differential Linear Logic…
We classify the possible Scott complexities for models of Peano arithmetic. We construct models of particular complexities by first giving a complete Scott analysis of colored linear orderings and constructing models of Peano arithmetic…
Curry-Howard correspondences between Linear Logic (LL) and session types provide a firm foundation for concurrent processes. As the correspondences hold for intuitionistic and classic versions of LL (ILL and CLL), we obtain two different…
Time series classification is a task of paramount importance, as this kind of data often arises in safety-critical applications. However, it is typically tackled with black-box deep learning methods, making it hard for humans to understand…
Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. They have been used to reason about beliefs, lies, and group epistemic behaviour inspired by social…
This work presents a novel systematic methodology to analyse the capabilities and limitations of Large Language Models (LLMs) with feedback from a formal inference engine, on logic theory induction. The analysis is complexity-graded w.r.t.…
The field of statistical relational learning aims at unifying logic and probability to reason and learn from data. Perhaps the most successful paradigm in the field is probabilistic logic programming: the enabling of stochastic primitives…
We characterize regular string transductions as programs in a linear $\lambda$-calculus with additives. One direction of this equivalence is proved by encoding copyless streaming string transducers (SSTs), which compute regular functions,…
Quantum information has suggested new forms of quantum logic, called quantum computational logics, where meanings of sentences are represented by pieces of quantum information (generally, density operators of some Hilbert spaces), which can…
Ontology Learning (OL) is the computational task of generating a knowledge base in the form of an ontology given an unstructured corpus whose content is in natural language (NL). Several works can be found in this area most of which are…
Cognitive BASIC is a minimal, BASIC-style prompting language and in-model interpreter that structures large language model (LLM) reasoning into explicit, stepwise execution traces. Inspired by the simplicity of retro BASIC, we repurpose…
Message Sequence Charts & Sequence Diagrams are graphical models that represent the behavior of distributed and concurrent systems via the scheduling of discrete and local emission and reception events. We propose an Interaction Language…
The ability to summarize and organize knowledge into abstract concepts is key to learning and reasoning. Many industrial applications rely on the consistent and systematic use of concepts, especially when dealing with decision-critical…
Chase algorithms are indispensable in the domain of knowledge base querying, which enable the extraction of implicit knowledge from a given database via applications of rules from a given ontology. Such algorithms have proved beneficial in…
Standard epistemic logics introduce a modal operator K to represent knowledge, but in doing so they presuppose the logical apparatus they aim to explain. By contrast, this paper explores how logic may be derived from the structure of…