Neighborhood Frames Research Articles

Some Logics in the Vicinity of Interpretability Logics

In this paper we shall define semantically some families of propositional modal logics related to the interpretability logic \(\mathbf{IL}\). We will introduce the logics \(\mathbf{BIL}\) and \(\mathbf{BIL}^{+}\) in the propositional language with a modal operator \(\square\) and a binary operator \(\Rightarrow\) such that \(\mathbf{BIL}\subseteq\mathbf{BIL}^{+}\subseteq\mathbf{IL}\). The logic \(\mathbf{BIL}\) is generated by the relational structures \(\left<X,R,N\right>\), called basic frames, where \(\left<X,R\right>\) is a Kripke frame and \(\left<X,N\right>\) is a neighborhood frame. We will prove that the logic \(\mathbf{BIL}^{+}\) is generated by the basic frames where the binary relation \(R\) is definable by the neighborhood relation \(N\) and, therefore, the neighborhood semantics is suitable to study the logic \(\mathbf{BIL}^{+}\) and its extensions. We shall also study some axiomatic extensions of \(\mathsf{\mathbf{BIL}}\) and we will prove that these extensions are sound and complete with respect to a certain classes of basic frames. Finally, we prove that the logic BIL+ and some of its extensions are complete respect with the class of neighborhood frames.

Global Appeal: Colorblindness, Neoliberalism, and Neighborhood Branding

Using content analysis of Buffalo media and 20 semi-structured interviews, I document the use of immigrant entrepreneurialism as a neoliberal urban governance strategy. Racism evasiveness is central to this strategy. I observe that immigrants and refugees are treated as symbolic capital as part of a neighborhood branding strategy that involves parlaying diversity into material benefits. I call this strategy global appeal. Buffalo’s resurgence is a feel-good story that draws on neoliberal market logics, colorblindness, and diversity ideology. These stories allow Whites to evade racism when discussing neighborhood renewal and racist comments. Drawing on Bourdieu’s theory of symbolic capital, Bell’s concept of neighborhood frames, and Beeman’s theory of racism evasiveness, I argue that immigrants and refugees are used as symbolic capital to construct a neighborhood brand. This is part of a strategy of roll out neoliberalism that relies on two neighborhood frames: revitalization and diversity. The revitalization frame credits immigrants and refugees with contributing to the neighborhood through homeownership, entrepreneurialism, and school enrollment. The diversity frame celebrates people of different races, cultures, and ethnicities coming together while both evading and obscuring racism.

Intuitionistic Logics of Confirmation and Discouragement

We analyse intuitionistic logics of confirmation and discouragement. This means that our acceptance of some formula φ in a possible world w gets an additional support or disapprovement. We use pre-ordered neighbourhood frames to model this situation. Our systems have certain connection with so-called logics of false belief and unknown truths.

A Coalgebraic Approach to Dualities for Neighborhood Frames

We develop a uniform coalgebraic approach to J\'onsson-Tarski and Thomason type dualities for various classes of neighborhood frames and neighborhood algebras. In the first part of the paper we construct an endofunctor on the category of complete and atomic Boolean algebras that is dual to the double powerset functor on $\mathsf{Set}$. This allows us to show that Thomason duality for neighborhood frames can be viewed as an algebra-coalgebra duality. We generalize this approach to any class of algebras for an endofunctor presented by one-step axioms in the language of infinitary modal logic. As a consequence, we obtain a uniform approach to dualities for various classes of neighborhood frames, including monotone neighborhood frames, pretopological spaces, and topological spaces. In the second part of the paper we develop a coalgebraic approach to J\'{o}nsson-Tarski duality for neighborhood algebras and descriptive neighborhood frames. We introduce an analogue of the Vietoris endofunctor on the category of Stone spaces and show that descriptive neighborhood frames are isomorphic to coalgebras for this endofunctor. This allows us to obtain a coalgebraic proof of the duality between descriptive neighborhood frames and neighborhood algebras. Using one-step axioms in the language of finitary modal logic, we restrict this duality to other classes of neighborhood algebras studied in the literature, including monotone modal algebras and contingency algebras. We conclude the paper by connecting the two types of dualities via canonical extensions, and discuss when these extensions are functorial.

Monotone Subintuitionistic Logic: Duality and Transfer Results

We consider subintuitionistic logics as an extension of positive propositional logic with a binary modality, interpreted over ordered and unordered monotone neighborhood frames, with a range of frame conditions. This change in perspective allows us to apply tools and techniques from the modal setting to subintuitionistic logics. We provide a Priestley-style duality, and transfer results from the (classical) logic of monotone neighborhood frames to obtain completeness, conservativity, and a finite model property for the basic logic, extended with a number of axioms.

A Non-Uniform Continuous Cellular Automata for Analyzing and Predicting the Spreading Patterns of COVID-19

During the COVID-19 outbreak, modeling the spread of infectious diseases became a challenging research topic due to its rapid spread and high mortality rate. The main objective of a standard epidemiological model is to estimate the number of infected, suspected, and recovered from the illness by mathematical modeling. This model does not capture how the disease transmits between neighboring regions through interaction. A more general framework such as Cellular Automata (CA) is required to accommodate a more complex spatial interaction within the epidemiological model. The critical issue of modeling in the spread of diseases is how to reduce the prediction error. This research aims to formulate the influence of the interaction of a neighborhood on the spreading pattern of COVID-19 using a neighborhood frame model in a Cellular-Automata (CA) approach and obtain a predictive model for the COVID-19 spread with the error reduction to improve the model. We propose a non-uniform continuous CA (N-CCA) as our contribution to demonstrate the influence of interactions on the spread of COVID-19. The model has succeeded in demonstrating the influence of the interaction between regions on the COVID-19 spread, as represented by the coefficients obtained. These coefficients result from multiple regression models. The coefficient obtained represents the population’s behavior interacting with its neighborhood in a cell and influences the number of cases that occur the next day. The evaluation of the N-CCA model is conducted by root mean square error (RMSE) for the difference in the number of cases between prediction and real cases per cell in each region. This study demonstrates that this approach improves the prediction of accuracy for 14 days in the future using data points from the past 42 days, compared to a baseline model.

Basic modal congruent and monotonic multilattice logics

Abstract In the paper, we introduce multilattice versions of the basic congruent and monotonic modal logics. In the case of congruent and monotonic ones, we also study their extensions by Gödel’s rule. We formulate these logics in the form of sequent calculi and prove syntactic embedding theorems (as a consequence, we obtain cut admissibility and decidability). Then we present them algebraically and semantically: via modal multilattices and via general and descriptive neighbourhood frames. We show the dual equivalency of the categories of modal multilattices and descriptive neighbourhood frames. Using Lindenbaum–Tarski algebras, we prove that the sequent calculi under consideration are sound and complete with respect to modal multilattices.

An enhanced model for Rosenkranz’s logic of justification

Rosenkranz (2021) devised two bimodal epistemic logics: an idealized one and a realistic one. The former is shown to be sound with respect to a class of neighborhood frames called i-frames. Rosenkranz designed a specific i-frame able to invalidate a series of undesired formulas, proving that these are not theorems of the idealized logic. Nonetheless, an unwanted formula and an unwanted rule of inference are not invalidated. Invalidating the former guarantees the distinction between the two modal operators characteristic of the logic, while invalidating the latter is crucial in order to deal with the problem of logical omniscience. In this paper, I present an i-frame able to invalidate all the undesired formulas already invalidated by Rosenkranz, together with the missing formula and rule of inference.

An extension of Jónsson‐Tarski representation and model existence in predicate non‐normal modal logics

AbstractWe give an extension of the Jónsson‐Tarski representation theorem for both normal and non‐normal modal algebras so that it preserves countably many infinite meets and joins. In order to extend the Jónsson‐Tarski representation to non‐normal modal algebras we consider neighborhood frames instead of Kripke frames just as Došen's duality theorem for modal algebras, and to deal with infinite meets and joins, we make use of Q‐filters, which were introduced by Rasiowa and Sikorski, instead of prime filters. By means of the extended representation theorem, we show that every predicate modal logic, whether it is normal or non‐normal, has a model defined on a neighborhood frame with constant domains, and we give a completeness theorem for some predicate modal logics with respect to classes of neighborhood frames with constant domains. Similarly, we show a model existence theorem and a completeness theorem for infinitary modal logics which allow conjunctions of countably many formulas.

Neighbourhood Semantics for Graded Modal Logic

We introduce a class of neighbourhood frames for graded modal logic embedding Kripke frames into neighbourhood frames. This class of neighbourhood frames is shown to be first-order definable but not modally definable. We also obtain a new definition of graded bisimulation with respect to Kripke frames by modifying the definition of monotonic bisimulation.

Duality for $$\kappa $$-additive complete atomic modal algebras

In this paper, we give a duality theorem between the category of $\kappa$-additive complete atomic modal algebras and the category of $\kappa$-downward directed multi-relational Kripke frames, for any cardinal number $\kappa$. Multi-relational Kripke frames are not Kripke frames for multi-modal logic, but frames for monomodal logics in which the modal operator $\Diamond$ does not distribute over (possibly infinite) disjunction, in general. We first define homomorphisms of multi-relational Kripke frames, and then show the equivalence between the category of $\kappa$-downward directed multi-relational Kripke frames and the category $\kappa$-complete neighborhood frames, from which the duality theorem follows. We also present another direct proof of this duality based on the technique given by Minari.

CARNAP’S PROBLEM FOR MODAL LOGIC

AbstractWe take Carnap’s problem to be to what extent standard consequence relations in various formal languages fix the meaning of their logical vocabulary, alone or together with additional constraints on the form of the semantics. This paper studies Carnap’s problem for basic modal logic. Setting the stage, we show that neighborhood semantics is the most general form of compositional possible worlds semantics, and proceed to ask which standard modal logics (if any) constrain the box operator to be interpreted as in relational Kripke semantics. Except when restricted to finite domains, no modal logic characterizes exactly the Kripkean interpretations of $\Box $ . Moreover, we show that, in contrast with the case of first-order logic, the obvious requirement of permutation invariance is not adequate in the modal case. After pointing out some known facts about modal logics that nevertheless force the Kripkean interpretation, we focus on another feature often taken to embody the gist of modal logic: locality. We show that invariance under point-generated subframes (properly defined) does single out the Kripkean interpretations, but only among topological interpretations, not in general. Finally, we define a notion of bisimulation invariance—another aspect of locality—that, together with a reasonable closure condition, gives the desired general result. Along the way, we propose a new perspective on normal neighborhood frames as filter frames, consisting of a set of worlds equipped with an accessibility relation, and a free filter at every world.

Positive Monotone Modal Logic

Positive monotone modal logic is the negation- and implication-free fragment of monotone modal logic, i.e., the fragment with connectives and . We axiomatise positive monotone modal logic, give monotone neighbourhood semantics based on posets, and prove soundness and completeness. The latter follows from the main result of this paper: a (categorical) duality between so-called $$M^+$$ -spaces (poset-based monotone neighbourhood frames with extra structure) and the algebraic semantics of positive monotone modal logic. The main technical tool is the use of coalgebra.

Learning Spatiotemporal Features for Esophageal Abnormality Detection From Endoscopic Videos.

Esophageal cancer is categorized as a type of disease with a high mortality rate. Early detection of esophageal abnormalities (i.e. precancerous and early cancerous) can improve the survival rate of the patients. Recent deep learning-based methods for selected types of esophageal abnormality detection from endoscopic images have been proposed. However, no methods have been introduced in the literature to cover the detection from endoscopic videos, detection from challenging frames and detection of more than one esophageal abnormality type. In this paper, we present an efficient method to automatically detect different types of esophageal abnormalities from endoscopic videos. We propose a novel 3D Sequential DenseConvLstm network that extracts spatiotemporal features from the input video. Our network incorporates 3D Convolutional Neural Network (3DCNN) and Convolutional Lstm (ConvLstm) to efficiently learn short and long term spatiotemporal features. The generated feature map is utilized by a region proposal network and ROI pooling layer to produce a bounding box that detects abnormality regions in each frame throughout the video. Finally, we investigate a post-processing method named Frame Search Conditional Random Field (FS-CRF) that improves the overall performance of the model by recovering the missing regions in neighborhood frames within the same clip. We extensively validate our model on an endoscopic video dataset that includes a variety of esophageal abnormalities. Our model achieved high performance using different evaluation metrics showing 93.7% recall, 92.7% precision, and 93.2% F-measure. Moreover, as no results have been reported in the literature for the esophageal abnormality detection from endoscopic videos, to validate the robustness of our model, we have tested the model on a publicly available colonoscopy video dataset, achieving the polyp detection performance in a recall of 81.18%, precision of 96.45% and F-measure 88.16%, compared to the state-of-the-art results of 78.84% recall, 90.51% precision and 84.27% F-measure using the same dataset. This demonstrates that the proposed method can be adapted to different gastrointestinal endoscopic video applications with a promising performance.

Volume-based inter difference XOR pattern: a new pattern for pulmonary nodule detection in CT images

The pulmonary nodule identification which paves the path to the cancer diagnosis is a challenging task today. The proposed work, volume-based inter difference XOR pattern (VIDXP) provides an efficient lung nodule detection system using a 3D texture-based pattern which is formed by XOR pattern calculation of inter-frame grey value differences among centre frame with its neighbourhood frames in rotationally clockwise direction, for every segmented nodule. Different classifiers such as random forest (RF), decision tree (DT) and AdaBoost are used with ten trails of five-fold cross validation test for classification. The experimental analysis in the public database, lung image database consortium-image database resource initiative (LIDC-IDRI) shows that proposed scheme gives better accuracy while comparing with existing approaches. Further, the proposed scheme is enhanced by combining shape information using histogram of oriented gradient (HOG) which improves the classification accuracy.

Volume-based inter difference XOR pattern: a new pattern for pulmonary nodule detection in CT images

The pulmonary nodule identification which paves the path to the cancer diagnosis is a challenging task today. The proposed work, volume-based inter difference XOR pattern (VIDXP) provides an efficient lung nodule detection system using a 3D texture-based pattern which is formed by XOR pattern calculation of inter-frame grey value differences among centre frame with its neighbourhood frames in rotationally clockwise direction, for every segmented nodule. Different classifiers such as random forest (RF), decision tree (DT) and AdaBoost are used with ten trails of five-fold cross validation test for classification. The experimental analysis in the public database, lung image database consortium-image database resource initiative (LIDC-IDRI) shows that proposed scheme gives better accuracy while comparing with existing approaches. Further, the proposed scheme is enhanced by combining shape information using histogram of oriented gradient (HOG) which improves the classification accuracy.

Research on small moving target detection algorithm based on complex scene

In recent years, small moving target detection based on complex scenes is widely used in many fields, such as computer vision, image processing and pattern recognition. It is widely used in military navigation, intelligent video monitoring system, video retrieval and other fields. Due to the dynamic background in the complex scene, the moving object has the characteristics of long distance, small area, unclear texture and color features, and partial loss of detail features. Therefore, how to extract small moving objects quickly, accurately and completely from complex scenes is the key of subsequent image analysis and processing. Aiming at the problem of strong background noise in more complex scenes, this paper proposes a neighborhood frame search denoising algorithm based on time consistency, which can effectively remove the strong background noise disturbance. The experimental results show that the algorithm can effectively remove strong background noise.

Correspondence, Canonicity, and Model Theory for Monotonic Modal Logics

We investigate the role of coalgebraic predicate logic, a logic for neighborhood frames first proposed by Chang, in the study of monotonic modal logics. We prove analogues of the Goldblatt-Thomason Theorem and Fine's Canonicity Theorem for classes of monotonic neighborhood frames closed under elementary equivalence in coalgebraic predicate logic. The elementary equivalence here can be relativized to the classes of monotonic, quasi-filter, augmented quasi-filter, filter, or augmented filter neighborhood frames, respectively. The original, Kripke-semantic versions of the theorems follow as a special case concerning the classes of augmented filter neighborhood frames.

Located Institutions: Neighborhood Frames, Residential Preferences, and the Case of Policing

How do parents weigh police presence and police activity in their assessments of a neighborhood’s suitability for raising children? How do place-bound institutions relate to neighborhood frames? This article introduces located institutions as a way of articulating how certain institutions—here, the police—become a lens through which parents make meaning of places and thus express preferences for particular neighborhoods or communities. By drawing from 73 interviews with a diverse sample of parents in Cuyahoga County, Ohio, this article shows how parents draw on their perceptions of the police as an attractive amenity or a public nuisance as a way of articulating neighborhood frames and making sense of their residential preferences. More broadly, this article envisions the perception of institutions as a key mechanism that shapes neighborhood frames and residential preferences.

Proof theory for quantified monotone modal logics

Abstract This paper provides a proof-theoretic study of quantified non-normal modal logics (NNML). It introduces labelled sequent calculi based on neighbourhood semantics for the first-order extension, with both varying and constant domains, of monotone NNML, and studies the role of the Barcan formulas in these calculi. It will be shown that the calculi introduced have good structural properties: invertibility of the rules, height-preserving admissibility of weakening and contraction and syntactic cut elimination. It will also be shown that each of the calculi introduced is sound and complete with respect to the appropriate class of neighbourhood frames. In particular, the completeness proof constructs a formal derivation for derivable sequents and a countermodel for non-derivable ones, and gives a semantic proof of the admissibility of cut.