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In this short paper we will discuss the similarities and differences between two semantic approaches to modal logics - non-deterministic semantics and restricted non-deterministic semantics. Generally speaking, both kinds of semantics are similar in the sense that they employ non-deterministic matrices as a starting point but differ significantly in the way extensions of the minimal modal logic M are constructed. Both kinds of semantics are many-valued and truth-values are typically expressed in terms of tuples of 0s and 1s, where each dimension of the tuple represents either truth/falsity, possibility/non-possibility, necessity/non-necessity etc. And while non-deterministic semantics for modal logic offers an intuitive interpretation of the truth-values and the concept of modality, with restricted non-deterministic semantics are more general in terms of providing extensions of M, including normal ones, in an uniform way. On the example of three modal logics, MK, MKT and MKT4, we will show the differences and similarities of those two approaches. Additionally, we will briefly discuss (current) restrictions of both approaches., Comment: In Proceedings NCL'24, arXiv:2412.20053

This paper addresses the integration of \emph{epistemic entrenchment} into paraconsistent belief revision systems based on Logics of Formal Inconsistency (LFIs). While systems like AGMp and AGM$\circ$ adapt AGM principles to paraconsistency, they lack mechanisms to rank beliefs, primarily due to the absence of properties such as the \emph{replacement property} in the underlying logics. We introduce two novel logics, \textbf{Cbr} and \textbf{RCBr}, with the latter extending the former to fully address these limitations given that it is self-extensional. Using \textbf{RCBr}, we define contraction operations via \emph{epistemic entrenchment}, adhering to key rationality principles. Our framework leverages non-deterministic matrix semantics (Nmatrices), providing a robust foundation for paraconsistent reasoning. These contributions advance the theory of paraconsistent belief revision and pave the way for applications in domains such as multi-agent systems and inconsistent knowledge bases.

Adversarial machine learning concerns situations in which learners face attacks from active adversaries. Such scenarios arise in applications such as spam email filtering, malware detection and fake-image generation, where security methods must be actively updated to keep up with the ever improving generation of malicious data.We model these interactions between the learner and the adversary as a game and formulate the problem as a pessimistic bilevel optimisation problem with the learner taking the role of the leader. The adversary, modelled as a stochastic data generator, takes the role of the follower, generating data in response to the classifier. While existing models rely on the assumption that the adversary will choose the least costly solution leading to a convex lower-level problem with a unique solution, we present a novel model and solution method which do not make such assumptions. We compare these to the existing approach and see significant improvements in performance suggesting that relaxing these assumptions leads to a more realistic model., Comment: 27 pages, 5 figures, under review

Graphs and hypergraphs provide powerful abstractions for modeling interactions among a set of entities of interest and have been attracting a growing interest in the literature thanks to many successful applications in several fields. In particular, they are rapidly expanding in domains such as chemistry and biology, especially in the areas of drug discovery and molecule generation. One of the areas witnessing the fasted growth is the chemical reactions field, where chemical reactions can be naturally encoded as directed hyperedges of a hypergraph. In this paper, we address the chemical reaction classification problem by introducing the notation of a Directed Line Graph (DGL) associated with a given directed hypergraph. On top of it, we build the Directed Line Graph Network (DLGNet), the first spectral-based Graph Neural Network (GNN) expressly designed to operate on a hypergraph via its DLG transformation. The foundation of DLGNet is a novel Hermitian matrix, the Directed Line Graph Laplacian, which compactly encodes the directionality of the interactions taking place within the directed hyperedges of the hypergraph thanks to the DLG representation. The Directed Line Graph Laplacian enjoys many desirable properties, including admitting an eigenvalue decomposition and being positive semidefinite, which make it well-suited for its adoption within a spectral-based GNN. Through extensive experiments on chemical reaction datasets, we show that DGLNet significantly outperforms the existing approaches, achieving on a collection of real-world datasets an average relative-percentage-difference improvement of 33.01%, with a maximum improvement of 37.71%.

In this paper, we investigate proof-theoretic aspects of the logics of evidence and truth LETJ and LETF. These logics extend, respectively, Nelson's logic N and the logic of first-degree entailment FDE, also known as Belnap-Dunn four-valued logic, with a classicality operator that recovers classical logic for formulas in its scope. We will present natural deduction and sequent systems for LETJ and LETF, together with proofs of normalization and cut-elimination theorems, respectively. As a corollary, we obtain decidability for both logics.

We study the average long-time behavior of the binary opinions of a social group with peer-to-peer interactions under the influence of an external bias and a persuadable leader, a strongly-biased agent with a dynamic opinion with the intention of spreading it across the system. We use a generalized, fully-connected Ising model, with each spin representing the binary opinion of an agent at a given time and a single, super spin representing the opinion of the leader. External fields and interaction constants model the opinion bias and peer-to-peer interactions, respectively, while the temperature $T$ models an idealized social climate, representing an authoritarian regime if $T$ is low or a liberal one if $T$ is high. We derive a mean-field solution for the average magnetization $m$, the "social mood", and investigate how $m$ and the super spin magnetization vary as a function of $T$. We find that, depending on the initial conditions, due to the presence of metastable states, the sign of the average magnetization depends on the temperature. Finally, we verify that this effect is also present even if we consider only nearest-neighbor interactions within the social group.

We introduce QuaterGCN, a spectral Graph Convolutional Network (GCN) with quaternion-valued weights at whose core lies the Quaternionic Laplacian, a quaternion-valued Laplacian matrix by whose proposal we generalize two widely-used Laplacian matrices: the classical Laplacian (defined for undirected graphs) and the complex-valued Sign-Magnetic Laplacian (proposed to handle digraphs with weights of arbitrary sign). In addition to its generality, our Quaternionic Laplacian is the only Laplacian to completely preserve the topology of a digraph, as it can handle graphs and digraphs containing antiparallel pairs of edges (digons) of different weights without reducing them to a single (directed or undirected) edge as done with other Laplacians. Experimental results show the superior performance of QuaterGCN compared to other state-of-the-art GCNs, particularly in scenarios where the information the digons carry is crucial to successfully address the task at hand.

The evolution of the critical superconducting temperature and field, quantum oscillation frequencies and effective mass $m^{*}$ in underdoped YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO) crystals ($p$ = 0.11, with $p$ the hole concentration per Cu atom) points to a partial suppression of the charge orders with increasing pressure up to 7 GPa, mimicking doping. Application of pressures up to 25 GPa pushes the sample to the overdoped side of the superconducting dome. Contrary to other cuprates, or to doping studies on YBCO, the frequency of the quantum oscillations measured in that pressure range do not support the picture of a Fermi-surface reconstruction in the overdoped regime, but possibly point to the existence of a new charge order., Comment: 13 pages, 17 figures

Electric propulsion requires exhaustive ground test campaigns to obtain an accurate characterization of the propulsion devices, or thrusters, used by the spacecraft. Among the many plasma parameters, accurately measured during the tests, that of the ion velocity is key, and can be measured using non-intrusive tools such as Laser-Induced Fluorescence (LIF) diagnostics. The ion velocity is inferred by Doppler shift measurements that presupposes a precise and accurate knowledge of the wavelength of excitation of the ions at rest. Today electric propulsion is moving towards the use of Krypton as a propellant, due to the dramatic increase in cost of the more advantageous Xenon gas propellant, commonly used until now. In this work the 4d$^4D_{7/2}\rightarrow$5p$^4P^\circ_{5/2}$ transition of Kr II is used for LIF diagnostic in hollow cathode discharge., Comment: 6 pages, 5 figures, 26 refs

This paper provides a new decision procedure for intuitionistic propositional logic (IPL) based on a 3-valued restricted non-deterministic matrix and proves its soundness and completeness., Comment: Several typos were corrected. Full proofs of soundness and completeness for S4 and IPL were included. A new section on complexity and an Appendix with some examples were added. The final section was improved

The aim of this paper is to combine several Ivlev-like modal systems characterized by 4-valued non-deterministic matrices (Nmatrices) with IDM4, a 4-valued expansion of Belnap-Dunn's logic FDE with an implication introduced by Pynko in 1999. In order to do this, we introduce a new methodology for combining logics which are characterized by means of swap structures, based on what we call superposition of snapshots. In particular, the combination of IDM4 with Tm, the 4-valued Ivlev's version of KT, will be analyzed with more details. From the semantical perspective, the idea is to combine the 4-valued swap structures (Nmatrices) for Tm (and several of its extensions) with the 4-valued twist structure (logical matrix) for IDM4. This superposition produces a universe of 6 snapshots, with 3 of them being designated. The multioperators over the new universe are defined by combining the specifications of the given swap and twist structures. This gives rise to 6 different paradefinite Ivlev-like modal logics, each one of them characterized by a 6-valued Nmatrix, and conservatively extending the original modal logic and IDM4. This important feature allows to consider the proposed construction as a genuine technique for combining logics. In addition, it is possible to define in the combined logics a classicality operator in the sense of logics of evidence and truth (LETs). A sound and complete Hilbert-style axiomatization is also presented for the 6 combined systems, as well as a Prolog program which implements the swap structures semantics for the 6 systems, producing a decision procedure for satisfiability, refutability and validity of formulas in these logics., Comment: Definition of hyperintensionality on p.2 was corrected

Tetravalent modal logic (T ML) was introduced by Font and Rius in 2000; and it is an expansion of the Belnap-Dunn four{valued logic FOUR, a logical system that is well{known for the many applications it has been found in several fields. Besides, T ML is the logic that preserve degrees of truth with respect to Monteiro's tetravalent modal algebras. Among other things, Font and Rius showed that T ML has a strongly adequate sequent system, but unfortunately this system does not enjoy the cut-elimination property. However, in [16], it was presented a sequent system for T ML with the cut{elimination property. Besides, in this same work, it was also presented a sound and complete natural deduction system for this logic. In the present work, we continue with the study of T ML under a proof-theoretic perspective. In first place, we show that the natural deduction system given in [16] admits a normalization theorem. In second place, taking advantage of the contrapositive implication for the tetravalent modal algebras introduced in [17], we define a decidable tableau system adequate to check validity in the logic T ML. Finally, we provide a sound and complete tableau system for T ML in the original language.These two tableau systems constitute new (proof-theoretic) decision procedures for checking validity in the variety of tetravalent modal algebras., Comment: arXiv admin note: text overlap with arXiv:2101.09724

Significant information on the dynamics of the plasma constituents in Hall effect thrusters can be obtained using minimally-intrusive techniques such as laser-induced fluorescence (LIF) diagnostics. Indeed, LIF provides an excellent tool to determine the ion velocity distribution function with high spatial resolution. Even in a steady-state operation, recording time-resolved maps of the velocity distribution is relevant due to persisting time-dependent features of the thruster discharge. One of the preeminent phenomena that renders the ion velocity distribution time dependent is commonly attributed to the breathing mode, characterized by pronounced oscillations in the discharge current. The goal of this work is to propose a new technique for plasma dynamic studies based on LIF spectroscopy with phase-resolution during the breathing period. To this purpose, the Hilbert transform is used to define the instantaneous phase of oscillation of the thruster current. Ion velocity distribution modification, over assigned phases of oscillation, is measured simultaneously and in real-time thanks to fully numerical analysis of the data., Comment: 8 pages, 12 figures, 34 references

We present in this paper an adaptation of the process of combination of logics known as fibring introduced by D. Gabbay. We are focused on the combination of two logics defined by matrix semantics, and based on pairs of functions that relate the logics to be combined. A number of technical results are proved. Among them, we demonstrate that the fibring of two matrix logics is also a matrix one. In addition, we prove that fibring is a (weak) conservative extension of the original logics, and we give conditions for such extension to be strong. We also study the case of fibring identifying two connectives as being the same. Several examples referred to fibring of some well-known matrix logics are shown along this paper., Comment: 28 pages

Belnap-Dunn's relevance logic, BD, was designed seeking a suitable logical device for dealing with multiple information sources which sometimes may provide inconsistent and/or incomplete pieces of information. BD is a four-valued logic which is both paraconsistent and paracomplete. On the other hand, De and Omori while investigating what classical negation amounts to in a paracomplete and paraconsistent four-valued setting, proposed the expansion BD2 of the four valued Belnap-Dunn logic by a classical negation. In this paper, we reintroduce the logic BD2 by means of a primitive weak consistency operator $\copyright$. This approach allows us to state in a direct way that this is not only a Logic of Formal Inconsistency (LFI) but also a Logic of Formal Underterminedness (LFU). After presenting a natural Hilbert-style characterization of BD2 obtained by means of twist-structures semantics, we propose a first-order version of BD2 called QBD2, with semantics based on an appropriate notion of partial structures. We show that in QBD2, $\exists$ and $\forall$ are interdefinable in terms of the paracomplete and paraconsistent negation, and not by means of the the classical negation. Finally, a Hilbert-style calculus for QBD2 is presented, proving the corresponding and soundness and completeness theorems., Comment: 29 pages

The main aim of this paper is to introduce the logics of evidence and truth LETK+ and LETF+ together with a sound, complete, and decidable six-valued deterministic semantics for them. These logics extend the logics LETK and LETF- with rules of propagation of classicality, which are inferences that express how the classicality operator o is transmitted from less complex to more complex sentences, and vice-versa. The six-valued semantics here proposed extends the 4 values of Belnap-Dunn logic with 2 more values that intend to represent (positive and negative) reliable information. A six-valued non-deterministic semantics for LETK is obtained by means of Nmatrices based on swap structures, and the six-valued semantics for LETK+ is then obtained by imposing restrictions on the semantics of LETK. These restrictions correspond exactly to the rules of propagation of classicality that extend LETK. The logic LETF+ is obtained as the implication-free fragment of LETK+. We also show that the 6 values of LETK+ and LETF+ define a lattice structure that extends the lattice L4 defined by the Belnap-Dunn four-valued logic with the 2 additional values mentioned above, intuitively interpreted as positive and negative reliable information. Finally, we also show that LETK+ is Blok-Pigozzi algebraizable and that its implication-free fragment LETF+ coincides with the degree-preserving logic of the involutive Stone algebras., Comment: 38 pages

It is well known that there is a correspondence between sets and complete, atomic Boolean algebras (CABA's) taking a set to its power-set and, reciprocally, a complete, atomic Boolean algebra to its set of atomic elements. Of course, such a correspondence induces an equivalence between the opposite category of $\textbf{Set}$ and the category of CABA's. We extend this result by taking multialgebras over a signature $\Sigma$, specifically those whose non-deterministic operations cannot return the empty-set, to CABA's with their zero element removed and a structure of $\Sigma$-algebra compatible with its order; reciprocally, one of these "almost Boolean" $\Sigma$-algebras is taken to its set of atomic elements equipped with a structure of multialgebra over $\Sigma$. This leads to an equivalence between the category of $\Sigma$-multialgebras and a category of ordered $\Sigma$-algebras. The intuition, here, is that if one wishes to do so, non-determinism may be replaced by a sufficiently rich ordering of the underlying structures.

This paper introduces SigMaNet, a generalized Graph Convolutional Network (GCN) capable of handling both undirected and directed graphs with weights not restricted in sign nor magnitude. The cornerstone of SigMaNet is the Sign-Magnetic Laplacian ($L^{\sigma}$), a new Laplacian matrix that we introduce ex novo in this work. $L^{\sigma}$ allows us to bridge a gap in the current literature by extending the theory of spectral GCNs to (directed) graphs with both positive and negative weights. $L^{\sigma}$ exhibits several desirable properties not enjoyed by other Laplacian matrices on which several state-of-the-art architectures are based, among which encoding the edge direction and weight in a clear and natural way that is not negatively affected by the weight magnitude. $L^{\sigma}$ is also completely parameter-free, which is not the case of other Laplacian operators such as, e.g., the Magnetic Laplacian. The versatility and the performance of our proposed approach is amply demonstrated via computational experiments. Indeed, our results show that, for at least a metric, SigMaNet achieves the best performance in 15 out of 21 cases and either the first- or second-best performance in 21 cases out of 21, even when compared to architectures that are either more complex or that, due to being designed for a narrower class of graphs, should -- but do not -- achieve a better performance., Comment: 22 pages, 6 tables

The aim of this article is to generalize logics of formal inconsistency ($\textbf{LFI}$s) to systems dealing with the concept of incompatibility, expressed by means of a binary connective. The basic idea is that having two incompatible formulas to hold trivializes a deduction, and as a special case, a formula becomes consistent (in the sense of $\textbf{LFI}$s) when it is incompatible with its own negation. We show how this notion extends that of consistency in a non-trivial way, presenting conservative translations for many simple $\textbf{LFI}$s into some of the most basic logics of incompatibility, what evidences in a precise way how the notion of incompatibility generalizes that of consistency. We provide semantics for the new logics, as well as decision procedures, based on restricted non-deterministic matrices. The use of non-deterministic semantics with restrictions is justified by the fact that, as proved here, these systems are not algebraizable according to Blok-Pigozzi nor are they characterizable by finite Nmatrices. Finally, we briefly compare our logics to other systems focused on treating incompatibility, specially those pioneered by Brandom and further developed by Peregrin.

Metal-insulator transitions in clean, crystalline solids can be driven by two distinct mechanisms. In a conventional insulator, the charge carrier concentration vanishes, when an energy gap separates filled and unfilled electronic states. In the established picture of a Mott insulator, by contrast, electronic interactions cause coherent charge carriers to slow down and eventually stop in electronic grid-lock without materially affecting the carrier concentration itself. This description has so far escaped experimental verification by quantum oscillation measurements, which directly probe the velocity distribution of the coherent charge carriers. By extending this technique to high pressure we were able to examine the evolution of carrier concentration and velocity in the strongly correlated metallic state of the clean, crystalline material NiS$_2$, while tuning the system towards the Mott insulating phase. Our results confirm that pronounced electronic slowing down indeed governs the approach to the insulating state. However, the critical point itself, at which the carrier velocity would reach zero and the effective carrier mass diverge, is concealed by the insulating sector of the phase diagram. In the resulting, more nuanced view of Mott localisation, the inaccessibility of the low temperature Mott critical point resembles that of the threshold of magnetic order in clean metallic systems, where criticality is almost universally interrupted by first order transitions, tricritical behaviour or novel emergent phases such as unconventional superconductivity., Comment: 8 pages, 3 figures

Ivlev's pioneering work started in the 1970's showed a new and promissory way in the study of modal logic from the perspective of many-valued logics. Continuing our previous work on Ivlev-like non-normal modal logics with non-deterministic semantics, we present in this paper tableau systems for Tm, S4m and S5m, the non-normal versions of T, S4 and S5, respectively, as well as for their corresponding first-order extensions Tm*, S4m* and S5m*., Comment: 26 pages

In a previous article we introduced the concept of restricted Nmatrices (in short, RNmatrices), which generalize Nmatrices in the following sense: a RNmatrix is a Nmatrix together with a {\em subset} of valuations over it, from which the consequence relation is defined. Within this semantical framework we have characterized each paraconsistent logic $C_{n}$ in the hierarchy of da Costa by means of a $(n+2)$-valued RNmatrix, which also provides a relatively simple decision procedure for each calculus (recalling that $C_1$ cannot be characterized by a single finite Nmatrix). In this paper we extend such RNmatrices for $C_{n}$ by means of what we call {\em restricted swap-structures} over arbitrary Boolean algebras, obtaining so a class of non-deterministic semantical structures which characterizes da Costa's systems. We give a brief algebraic and combinatorial description of the elements of the underlying RNmatrices. Finally, by presenting a notion of category of RNmatrices, we show that the category of RNmatrices for $C_{n}$ is in fact isomorphic to the category of non-trivial Boolean algebras., Comment: 24 pages. arXiv admin note: text overlap with arXiv:2011.10151

CeOs$_4$Sb$_{12}$, a member of the skutterudite family, has an unusual semimetallic low-temperature $\cal{L}$-phase that inhabits a wedge-like area of the field $H$ - temperature $T$ phase diagram. We have conducted measurements of electrical transport and megahertz conductivity on CeOs$_4$Sb$_{12}$ single crystals under pressures of up to 3 GPa and in high magnetic fields of up to 41 T to investigate the influence of pressure on the different $H$-$T$ phase boundaries. While the high-temperature valence transition between the metallic $\cal{H}$-phase and the $\cal{L}$-phase is shifted to higher $T$ by pressures of the order of 1 GPa, we observed only a marginal suppression of the $\cal{S}$-phase that is found below 1 K for pressures of up to 1.91 GPa. High-field quantum oscillations have been observed for pressures up to 3.0 GPa and the Fermi surface of the high-field side of the $\cal{H}$-phase is found to show a surprising decrease in size with increasing pressure, implying a change in electronic structure rather than a mere contraction of lattice parameters. We evaluate the field-dependence of the effective masses for different pressures and also reflect on the sample dependence of some of the properties of CeOs$_4$Sb$_{12}$ which appears to be limited to the low-field region., Comment: 13 pages, 6 figures