Logical Properties Research Articles

Testing Cyber–Physical Systems Using a Line-Search Falsification Method

Cyber-physical systems (CPSs) are complex and exhibit both continuous and discrete dynamics, hence it is difficult to guarantee that they satisfy given specifications, i.e., the properties that must be fulfilled by the system. Falsification of temporal logic properties is a testing approach that searches for counterexamples of a given specification that can be used to increase the confidence that a CPS does fulfill its specifications. Falsification can be done using random search methods or optimization methods, both of which have their own benefits and drawbacks. This article introduces two methods that exploit randomness to different degrees: 1) the optimization-free Hybrid-Corner-Random (HCR) and 2) the direct-search method Line-Search Falsification (LSF). HCR combines randomly chosen parameter values with extreme parameter values, which performs surprisingly well on benchmark evaluations. The gradient-free optimization-based LSF optimizes over line segments through a vector of inputs in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> -dimensional parameter space. The two methods are compared to the Nelder-Mead and SNOBFIT methods, using a well-known set of benchmark problems and LSF shows better performance than any of the evaluated methods.

On the complexity of rational verification

Rational verification refers to the problem of checking which temporal logic properties hold of a concurrent/multiagent system, under the assumption that agents in the system choose strategies that form a game theoretic equilibrium. Rational verification can be understood as a counterpart to model checking for multiagent systems, but while classical model checking can be done in polynomial time for some temporal logic specification languages such as CTL, and polynomial space with LTL specifications, rational verification is much harder: the key decision problems for rational verification are 2EXPTIME-complete with LTL specifications, even when using explicit-state system representations. Against this background, our contributions in this paper are threefold. First, we show that the complexity of rational verification can be greatly reduced by restricting specifications to GR(1), a fragment of LTL that can represent a broad and practically useful class of response properties of reactive systems. In particular, we show that for a number of relevant settings, rational verification can be done in polynomial space and even in polynomial time. Second, we provide improved complexity results for rational verification when considering players’ goals given by mean-payoff utility functions—arguably the most widely used approach for quantitative objectives in concurrent and multiagent systems. Finally, we consider the problem of computing outcomes that satisfy social welfare constraints. To this end, we consider both utilitarian and egalitarian social welfare and show that computing such outcomes is either PSPACE-complete or NP-complete.

Outline of a Theory of Reasons

AbstractThis paper investigates the logic of reasons. Its aim is to provide an analysis of the sentences of the form ‘p is a reason for q’ that yields a coherent account of their logical properties. The idea that we will develop is that ‘p is a reason for q’ is acceptable just in case a suitably defined relation of incompatibility obtains between p and ¬q. As we will suggest, a theory of reasons based on this idea can solve three challenging puzzles that concern, respectively, contraposing reasons, conflicting reasons, and supererogatory reasons, and opens a new perspective on some classical issues concerning non-deductive inferences.

Choice logics and their computational properties

Qualitative Choice Logic (QCL) and Conjunctive Choice Logic (CCL) are formalisms for preference handling, with especially QCL being well established in the field of AI. So far, analyses of these logics need to be done on a case-by-case basis, albeit they share several common features. This calls for a more general choice logic framework, with QCL and CCL as well as some of their derivatives being particular instantiations. We provide such a framework, which allows us, on the one hand, to easily define new choice logics and, on the other hand, to examine properties of different choice logics in a uniform setting. In particular, we investigate strong equivalence, a core concept in non-classical logics for understanding formula simplification, and computational complexity. Our analysis also yields new results for QCL and CCL. For example, we show that the main reasoning task regarding preferred models of choice logic formulas is Θ2P-complete for QCL and CCL, while being Δ2P-complete for a newly introduced choice logic. The complexity of preferred model entailment for choice logic theories ranges from coNP to Π2P.

Quantitative evaluation of dissociated optic nerve fibre layer (DONFL) following idiopathic macular hole surgery.

To quantitatively evaluate concentric macular dark spots (CMDS) on spectral-domain optical coherence tomography (SD-OCT) to determine the morphological characteristics of dissociated optic nerve fibre layer (DONFL) following the performance of internal limiting membrane (ILM) peeling in patients with full-thickness idiopathic macular hole (IMH) closure. Retrospective study on patients who underwent a vitrectomy with ILM peeling procedure. BCVA, cross-sectional OCT scans, and three-dimensional reconstructions of en face OCT scans were analysed preoperatively, at 2, 6, 12 months post-operatively. A novel image analysis technique was used to automatically measure DONFL logical properties through the radius, area, the nerve fibre layer dissociation index (NFLDI), and depth of the CMDS. 53 eyes of 51 patients were included, and the mean follow-up was 11.53 ± 6.26 months. CMDS was found in 46 (86.79%) eyes within 2 months after ILM peeling and 50 (94.34%) eyes within 6 months after ILM peeling. CMDS concentrated on the temporal side of the macula in all 50 eyes (100%) at first detection. The area, NFLDI, and depth of CMDS in four quadrants developed significantly during the postoperative 6 months (p < 0.05), and then these changes slowed down and remained unchanged 12 months post-operatively. The morphological changes in the temporal quadrant were significantly greater than those in other quadrants at 2, 6, 12 months (all p < 0.05) post-operatively. CMDS mostly appeared and concentrated on the temporal side of the macula in IMHs within two months after ILM peeling and progressed within 6 months and remained unchanged after 12 months.

ON THE UNCOUNTABILITY OF

AbstractCantor’s first set theory paper (1874) establishes the uncountability of ${\mathbb R}$ . We study this most basic mathematical fact formulated in the language of higher-order arithmetic. In particular, we investigate the logical and computational properties of ${\mathsf {NIN}}$ (resp. ${\mathsf {NBI}}$ ), i.e., the third-order statement there is no injection resp. bijection from $[0,1]$ to ${\mathbb N}$ . Working in Kohlenbach’s higher-order Reverse Mathematics, we show that ${\mathsf {NIN}}$ and ${\mathsf {NBI}}$ are hard to prove in terms of (conventional) comprehension axioms, while many basic theorems, like Arzelà’s convergence theorem for the Riemann integral (1885), are shown to imply ${\mathsf {NIN}}$ and/or ${\mathsf {NBI}}$ . Working in Kleene’s higher-order computability theory based on S1–S9, we show that the following fourth-order process based on ${\mathsf {NIN}}$ is similarly hard to compute: for a given $[0,1]\rightarrow {\mathbb N}$ -function, find reals in the unit interval that map to the same natural number.

Parameterized Complexity of Elimination Distance to First-Order Logic Properties

The elimination distance to some target graph property P is a general graph modification parameter introduced by Bulian and Dawar. We initiate the study of elimination distances to graph properties expressible in first-order logic. We delimit the problem’s fixed-parameter tractability by identifying sufficient and necessary conditions on the structure of prefixes of first-order logic formulas. Our main result is the following meta-theorem: For every graph property P expressible by a first order-logic formula \( \varphi \in \Sigma _3 \) , that is, of the form \( \begin{equation*} \varphi =\exists x_1\exists x_2\cdots \exists x_r\ \ \forall y_{1}\forall y_{2}\cdots \forall y_{s}\ \ \exists z_1\exists z_2\cdots \exists z_t~~ \psi ,\end{equation*} \) where \( \psi \) is a quantifier-free first-order formula, checking whether the elimination distance of a graph to P does not exceed \( k \) , is fixed-parameter tractable parameterized by \( k \) . Properties of graphs expressible by formulas from \( \Sigma _3 \) include being of bounded degree, excluding a forbidden subgraph, or containing a bounded dominating set. We complement this theorem by showing that such a general statement does not hold for formulas with even slightly more expressive prefix structure: There are formulas \( \varphi \in \Pi _3 \) , for which computing elimination distance is \( {\sf W}[2] \) -hard.

Graph data temporal evolutions: From conceptual modelling to implementation

Graph data management systems are designed for managing highly interconnected data. However, most of the existing work on the topic does not take into account the temporal dimension of such data, even though they may change over time: new interconnections, new internal characteristics of data (etc.). For decision makers, these data changes provide additional insights to explain the underlying behaviour of a business domain. The objective of this paper is to propose a complete solution to manage temporal interconnected data. To do so, we propose a new conceptual model of temporal graphs. It has the advantage of being generic as it captures the different kinds of changes that may occur in interconnected data. We define a set of translation rules to convert our conceptual model into the logical property graph. Based on the translation rules, we implement several temporal graphs according to benchmark and real-world datasets in the Neo4j data store. These implementations allow us to carry out a comprehensive study of the feasibility and usability (through business analyses), the efficiency (saving up to 99% query execution times comparing to classic approaches) and the scalability of our solution.

Anti-exceptionalism about logic as tradition rejection

While anti-exceptionalism about logic (AEL) is now a popular topic within the philosophy of logic, there’s still a lack of clarity over what the proposal amounts to. currently, it is most common to conceive of AEL as the proposal that logic is continuous with the sciences. Yet, as we show here, this conception of AEL is unhelpful due to both its lack of precision, and its distortion of the current debates. Rather, AEL is better understood as the rejection of certain traditional properties of logic. The picture that results is not of one singular position, but rather a cluster of often connected positions with distinct motivations, understood in terms of their rejection of clusters of the various traditional properties. In order to show the fruitfulness of this new conception of AEL, we distinguish between two prominent versions of the position, metaphysical and epistemological AEL, and show how the two positions need not stand or fall together.

Shedding Light on the “Eclipse” Narrative: Some Notes on Pragmatism in the Twentieth Century

Shedding Light on the “Eclipse” Narrative: Some Notes on Pragmatism in the Twentieth Century

Logical and algebraic properties of generalized orthomodular posets

Abstract Generalized orthomodular posets were introduced recently by D. Fazio, A. Ledda and the first author of the present paper in order to establish a useful tool for studying the logic of quantum mechanics. They investigated structural properties of these posets. In the present paper, we study logical and algebraic properties of these posets. In particular, we investigate conditions under which they can be converted into operator residuated structures. Further, we study their representation by means of algebras (directoids) with everywhere defined operations. We prove congruence properties for the class of algebras assigned to generalized orthomodular posets and, in particular, for a subvariety of this class determined by a simple identity. Finally, in contrast to the fact that the Dedekind-MacNeille completion of an orthomodular poset need not be an orthomodular lattice, we show that the Dedekind-MacNeille completion of a stronger version of a generalized orthomodular poset is nearly an orthomodular lattice.

WHAT IS KINSHIP ALL ABOUT? AGAIN. CRITIQUE OF THE CAMBRIDGE HANDBOOK OF KINSHIP, EDITED BY SANDRA BAMFORD

The world of anthropology has witnessed a recurring rhetorical title:“What Is Kinship All About?” and now this article titles itself “What is Kinship All About? Again.” Why? Whereas we have over a century’s worth of ethnography and theory focusing on the centrality of kinship in human society and in anthropological theory, in 2019 a Handbook is published that names itself “Kinship” but, despite its claim and to the contrary, it is not about kinship at all. The Handbook editor explicitly states that it is about “conceiving kinship,” with kinship reduced to gendered social relatedness. In response, we re-affirm the centrality of kinship as a domain universal in human societies by way of a critique of the Handbook and a comprehensive review of its contributing chapters. Countering the Handbook’s denialist — or in Harold Scheffler’s famous term, dismantling — position, we bring to the fore the already determined universal properties that define the boundaries of the kinship domain and the logical properties that uni-versally define the category of kinship.

Belief contraction and erasure in fragments of propositional logic

Abstract Recently, belief change within the framework of fragments of propositional logic has gained attention. In the context of revision, it has been proposed to refine existing operators so that they operate within propositional fragments and that the result of revision remains in the fragment under consideration. Later, this notion of refinement was generalized to belief change operators. Whereas refinement allowed one to define concrete rational operators adapted to propositional fragments in the context of revision and update, it has to be specified for contraction and erasure. We propose a specific notion of refinement for contraction and erasure operators, called reasonable refinement. This allows us to provide refined contraction and erasure operators that satisfy the basic postulates. We study the logical properties of reasonable refinement of two model-based contraction operators and two model-based erasure operators. Our approach is not limited to the Horn fragment but applicable to many fragments of propositional logic, like Krom and affine fragments.

What is Kinship About? Again. Critique of the Cambridge Handbook of Kinship, Edited by Sandra Bamford

The world of anthropology has witnessed a recurring rhetorical title:“What Is Kinship All About?” and now this article titles itself “What is Kinship All About? Again.” Why? Whereas we have over a century’s worth of ethnography and theory focusing on the centrality of kinship in human society and in anthropological theory, in 2019 a Handbook is published that names itself “Kinship” but, despite its claim and to the contrary, it is not about kinship at all. The Handbook editor explicitly states that it is about “conceiving kinship,” with kinship reduced to gendered social relatedness. In response, we re-affirm the centrality of kinship as a domain universal in human societies by way of a critique of the Handbook and a comprehensive review of its contributing chapters. Countering the Handbook’s denialist — or in Harold Scheffler’s famous term, dismantling — position, we bring to the fore the already determined universal properties that define the boundaries of the kinship domain and the logical properties that uni-versally define the category of kinship.

Countable sets versus sets that are countable in reverse mathematics

The program Reverse Mathematics (RM for short) seeks to identify the axioms necessary to prove theorems of ordinary mathematics, usually working in the language of second-order arithmetic L 2 . A major theme in RM is therefore the study of structures that are countable or can be approximated by countable sets. Now, countable sets must be represented by sequences here, because the higher-order definition of ‘countable set’ involving injections/bijections to N cannot be directly expressed in L 2 . Working in Kohlenbach’s higher-order RM, we investigate various central theorems, e.g. those due to König, Ramsey, Bolzano, Weierstrass, and Borel, in their (often original) formulation involving the definition of ‘countable set’ based on injections/bijections to N. This study turns out to be closely related to the logical properties of the uncountably of R, recently developed by the author and Dag Normann. Now, ‘being countable’ can be expressed by the existence of an injection to N (Kunen) or the existence of a bijection to N (Hrbacek–Jech). The former (and not the latter) choice yields ‘explosive’ theorems, i.e. relatively weak statements that become much stronger when combined with discontinuous functionals, even up to Π 2 1 - CA 0 . Nonetheless, replacing ‘sequence’ by ‘countable set’ seriously reduces the first-order strength of these theorems, whatever the notion of ‘set’ used. Finally, we obtain ‘splittings’ involving e.g. lemmas by König and theorems from the RM zoo, showing that the latter are ‘a lot more tame’ when formulated with countable sets.

Design of multifunctional spin logic gates based on manganese porphyrin molecules connected to graphene electrodes.

The spin-resolved transport properties of molecular logic devices composed of two Mn porphyrin molecules connected to each other via a six-carbon atomic chain were studied using the non-equilibrium Green's function combined with density functional theory. The molecules were symmetrically connected to armchair graphene nanoribbon electrodes through four-carbon atomic chains on the left- and right-hand sides. Our calculations revealed that the spin-resolved current-voltage curves depend on the initial spin setting of the transition metal Mn atoms and carbon atoms on the zigzag edges where the electrodes come in contact with the molecule. By simultaneously regulating the spin orientations of the intermediate functional molecules and the zigzag edges of the armchair graphene nanoribbon electrodes, seven spin polarization configurations were obtained. These configurations were examined in this study considering the spin-related symmetry of molecular junctions. By meticulously selecting different combinations according to the specific input and output signals, YES, NOT, OR, NOR, and XOR multifarious spin logic devices were created. The findings of this study are expected to contribute toward the extension of molecular junction functions in future spintronic integrated circuit design and further miniaturization.

Satisfiability in a Temporal Multi-valueted Logic Based on Z

In this paper we continue the series of papers by V. V. Rybakov devoted to properties of multi-valueted logics and where he propose a new approach for modelling knowledge and reasoning of agents in a multi-agent system. We prove that the satisfiability problem is decidable in a temporal multi-valueted logic based on Z

A Bounded Model Checker for Timed Automata and Its Application to LTL Properties

Model checking with a time aspect is often used in verification on hardware and embedded systems. Timed automata are often used for such models. UPPAAL is a world-wide famous model checking tool for timed automata; however, UPPAAL is a Computational Tree Logic (CTL)-based model checking tool and cannot use Linear Temporal Logic (LTL) properties. Bounded model checking uses LTL (Linear Time Logic) for a checking formula. Bounded model checking specifies a boundary k and obtains counterexamples by searching from the initial state of a system to states reachable by k-steps. There are several studies on bounded model checking. Sorea has proposed a concrete algorithm for a timed automaton. There are, however, no clear details on how to implement bounded model checking tools for timed automata, and study the performance. Another problem is that the timed automaton covered by the method does not support general variables except for clock variables. The objective of this study is to implement a bounded model checking tool using LTL for timed automata. We also improve Sorea's method so that it can handle extended timed automata that handle general variables. This paper also presents some LTL examples from texts on requirement specifications for embedded systems and the results of applying the tool to them.

Invariant of Enhanced AES Algorithm Implementations Against Power Analysis Attacks

The security of Internet of Things (IoT) is a challenging task for researchers due to plethora of IoT networks. Side Channel Attacks (SCA) are one of the major concerns. The prime objective of SCA is to acquire the information by observing the power consumption, electromagnetic (EM) field, timing analysis, and acoustics of the device. Later, the attackers perform statistical functions to recover the key. Advanced Encryption Standard (AES) algorithm has proved to be a good security solution for constrained IoT devices. This paper implements a simulation model which is used to modify the AES algorithm using logical masking properties. This invariant of the AES algorithm hides the array of bits during substitution byte transformation of AES. This model is used against SCA and particularly Power Analysis Attacks (PAAs). Simulation model is designed on MATLAB simulator. Results will give better solution by hiding power profiles of the IoT devices against PAAs. In future, the lightweight AES algorithm with false key mechanisms and power reduction techniques such as wave dynamic differential logic (WDDL) will be used to safeguard IoT devices against side channel attacks by using Arduino and field programmable gate array (FPGA).

Determination of Fetal sex by Fetal anatomy parameters using a Fuzzy C-Mean Cluster

This paper proposes a new approach to determining the sex of the fetus using the measurement of dimensions of the head. The research attempted to use one of the techniques of fuzzy logic in the field of medicine, and here it was dealt with the visual properties designed to mix the properties of fuzzy logic (FL) and feature images. The results that some traits cannot give good results such as the results obtained from the local binary pattern (LBP) algorithm and the power and superiority of the results of hybrid filters because the ultrasound images have a special color spectrum. The results also showed the ability of the fuzzy logic proposed by using the characteristics derived from the hybrid filter to deal with the study of images and to achieve a better diagnosis of the gender of the fetus through measuring the dimensions of the head.