Related papers: Generalised Information Systems Capture L-Domains
Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…
The proliferation of large language models (LLMs) has significantly transformed the digital information landscape, making it increasingly challenging to distinguish between human-written and LLM-generated content. Detecting LLM-generated…
The ordinary Structure Identity Principle states that any property of set-level structures (e.g., posets, groups, rings, fields) definable in Univalent Foundations is invariant under isomorphism: more specifically, identifications of…
Signed systems were introduced as a general, syntax-independent framework for paraconsistent reasoning, that is, non-trivialised reasoning from inconsistent information. In this paper, we show how the family of corresponding paraconsistent…
By nature, transmissible human knowledge is enumerable: every sentence, movie, audio record can be encoded in a sufficiently long string of 0's and 1's. The works of G\"odel, Turing and others showed that there are inherent limits and…
Every countable structure has a sentence of the infinitary logic $\mathcal{L}_{\omega_1 \omega}$ which characterizes that structure up to isomorphism among countable structures. Such a sentence is called a Scott sentence, and can be thought…
Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…
We present a model-theoretic property of finite structures, that can be seen to be a finitary analogue of the well-studied downward L\"owenheim-Skolem property from classical model theory. We call this property as the…
We prove the finiteness of $B$-representations of generalised log canonical pairs. As a consequence, we prove that, the (relative) abundance for a generalised semi-log canonical pair is implied by the abundance for its normalisation.…
We generalise the distribution semantics underpinning probabilistic logic programming by distilling its essential concept, the separation of a free random component and a deterministic part. This abstracts the core ideas beyond logic…
Previous studies have relied on existing question-answering benchmarks to evaluate the knowledge stored in large language models (LLMs). However, this approach has limitations regarding factual knowledge coverage, as it mostly focuses on…
A crucial step in the history of General Relativity was Einstein's adoption of the principle of general covariance which demands a coordinate independent formulation for our spacetime theories. General covariance helps us to disentangle a…
The multivariate covering lemma states that given a collection of $k$ codebooks, each of sufficiently large cardinality and independently generated according to one of the marginals of a joint distribution, one can always choose one…
The widely considered assertion is that the unitarity of quantum mechanical evolution assures the preservation of information. It is even promoted in popular literature as an established fact. (Susskind, 2008) Yet, a simple chain of…
The analysis of concurrent and reactive systems is based to a large degree on various notions of process equivalence, ranging, on the so-called linear-time/branching-time spectrum, from fine-grained equivalences such as strong bisimilarity…
A universal quantum computing scheme, with a universal set of logical gates, is proposed based on networks of 1D quantum systems. The encoding of information is in terms of universal features of gapped phases, for which effective field…
To adapt effectively to dynamic real-world environments, intelligent systems must continually acquire new skills while generalizing them to diverse, unseen scenarios. Here, we introduce a novel and realistic setting named domain…
Dependence logic provides an elegant approach for introducing dependencies between variables into the object language of first-order logic. In [1] generalized quantifiers were introduced in this context. However, a satisfactory account was…
This paper discusses the extension of the Prototype Verification System (PVS) sub-theory for rings, part of the PVS algebra theory, with theorems related to the division algorithm for Euclidean rings and Unique Factorization Domains that…
We generalize the information lattice, originally defined for one-dimensional open-boundary chains, to characterize quantum many-body states in higher-dimensional geometries. In one dimension, the information lattice provides a position-…