Related papers: Some observations about generalized quantifiers in…
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…
We present alternative definitions of the first-order stable model semantics and its extension to incorporate generalized quantifiers by referring to the familiar notion of a reduct instead of referring to the SM operator in the original…
We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series…
First Order Team Semantics is a generalization of Tarskian Semantics in which formulas are satisfied with respect to sets of assignments. In Team Semantics, it is possible to extend First Order Logic via new types of atoms that describe…
The entanglement theory in quantum systems with internal symmetries is rich due to the spontaneous creation of entangled pairs of charge/anti-charge particles at the entangling surface. We call these pair creation operators the bi-local…
There have been a huge number of benchmarks proposed to evaluate how large language models (LLMs) behave for logic inference tasks. However, it remains an open question how to properly evaluate this ability. In this paper, we provide a…
We study the expressive power of fragments of inclusion and independence logic defined by restricting the number k of universal quantifiers in formulas. Assuming the so-called strict semantics for these logics, we relate these fragments of…
As a part of the construction of an information theory based on general probabilistic theories, we propose and investigate the several distinguishability measures and "entropies" in general probabilistic theories. As their applications,…
Team Semantics is a generalization of Tarskian Semantics that can be used to add to First Order Logic atoms and connectives expressing dependencies between the possible values of variables. Some of these extensions are more expressive than…
We provide two proofs of the compactness theorem for extensions of first-order logic based on team semantics. First, we build upon L\"uck's ultraproduct construction for team semantics and prove a suitable version of {\L}o\'s' Theorem.…
We contribute to the refined understanding of the language-logic-algebra interplay in the context of first-order properties of countable words. We establish decidable algebraic characterizations of one variable fragment of FO as well as…
We argue that in some KR applications, we want to quantify over sets of concepts formally represented by symbols in the vocabulary. We show that this quantification should be distinguished from second-order quantification and…
This note contributes to the understanding of generalized entropy power inequalities. Our main goal is to construct a counter-example regarding monotonicity and entropy comparison of weighted sums of independent identically distributed…
This paper surveys the common approach to quantification and generalised quantification in formal linguistics and philosophy of language. We point out how this general setting departs from empirical linguistic data, and give some hints for…
A novel measure, quantumness of correlations is introduced here for bipartite states, by incorporating the required measurement scheme crucial in defining any such quantity. Quantumness coincides with the previously proposed measures in…
We consider a family U of finite universes. The second order quantifier Q_R, means for each u in U quantifying over a set of n(R)-place relations isomorphic to a given relation. We define a natural partial order on such quantifiers called…
In this paper, a new approximate syllogistic reasoning schema is described that expands some of the approaches expounded in the literature into two ways: (i) a number of different types of quantifiers (logical, absolute, proportional,…
Observational entropy is interpreted as the uncertainty an observer making measurements associates with a system. So far, properties that make such an interpretation possible rely on the assumption of ideal projective measurements. We show…
Markov categories are a novel framework to describe and treat problems in probability and information theory. In this work we combine the categorical formalism with the traditional quantitative notions of entropy, mutual information, and…
The main formal structures of Generalized Quantum Theory are summarized. Recent progress has sharpened some of the concepts, in particular the notion of an observable, the action of an observable on states (putting more emphasis on the role…