his is a book to broaden the mind. It brings the reader into a world only vaguely imaginable and richly enlightens it with extraordinary attention to interesting historical details. It is beautifully written and endlessly interesting.

In this paper we introduce the notion of filter on the neutrosophic crisp set, then we consider a generalization of the filter’s studies. Afterwards, we present the important neutrosophic crisp filters. We also study several relations between different neutrosophic crisp filters and neutrosophic topologies. Possible applications to database systems are touched upon.

Leibniz filters play a prominent role in the theory of protoalgebraic logics. In [3] the problem of the definability of Leibniz filters is considered. Here we study the definability of Leibniz filters with parameters. The main result of the paper says that a protoalgebraic logic S has its strong version weakly algebraizable iff it has its Leibniz filters explicitly definable with parameters.

We explore the problem of constructing maximal and unbounded filters on computable posets. We obtain both computability results and reverse mathematics results. A maximal filter is one that does not extend to a larger filter. We show that every computable poset has a \Delta^0_2 maximal filter, and there is a computable poset with no \Pi^0_1 or \Sigma^0_1 maximal filter. There is a computable poset on which every maximal filter is Turing complete. We obtain the reverse mathematics result that the (...) principle "every countable poset has a maximal filter" is equivalent to ACA₀ over RCA₀. An unbounded filter is a filter which achieves each of its lower bounds in the poset. We show that every computable poset has a \Sigma^0_1 unbounded filter, and there is a computable poset with no \Pi^0_1 unbounded filter. We show that there is a computable poset on which every unbounded filter is Turing complete, and the principle "every countable poset has an unbounded filter" is equivalent to ACA₀ over RCA₀. We obtain additional reverse mathematics results related to extending arbitrary filters to unbounded filters and forming the upward closures of subsets of computable posets. (shrink)

In Neal Stephenson’s fictional novel, Diamond Age (1995), the protagonist Nell acquires a prototype of what we might today recognise as a highly sophisticated e-reader with a voice-assistant. This e-reader, the “Young Lady’s Illustrated Primer”, uses artificial intelli- gence to serve as Nell’s personal teacher. What is key to the Primer is how it is designed to respond to Nell. The Primer has a theory of Nell – her needs, her real-world situation, her abilities – and it tailors its lessons (...) for her. The Primer is a highly personalised artificially intelligent device. For many readers – myself included – the Primer was a utopian vision of the bespoke digital tutors of the future. The appearance of new media and technologies in the early 2000s all pointed to the near-term reality of devices like Primers. The real-life experience of personalised digital media, though, is so far from Stephen- son’s vision that it is hard to imagine we will ever get there. Nell’s time with the Primer develops her intellectually, emotionally, and physically. Our “bespoke” media experience, by contrast, is more likely to turn us in on ourselves rather than guide us to live well in our societies. Personalised media is making us more like Narcissus: our consumption is driven by personal choices and automated algorithms that reflect what we already want to hear, see, and consume, and we are captivated. Central to our understanding of the problems with the personalisation of digital media are filter bubbles and echo chambers. These phenomena are used interchangeably by some, but in distinct ways by others. I take the position that filter bubbles and echo chambers are distinct phenomena, but ones that raise similar epistemic worries. I begin with a general discussion of filter bubbles and echo chambers, and I introduce the concept of “selective exposure” as central to both phenomena. There is minimal uniformity across uses of the terms “filter bubble” and “echo chamber”. Consequently, I divide the later discussion into two more precise topics: homophily and polarisation. I conclude with some future-looking comments about responsibility and the epistemic risks posed by digital personalisation. (shrink)

A filter of a sentential logic ? is Leibniz when it is the smallest one among all the ?-filters on the same algebra having the same Leibniz congruence. This paper studies these filters and the sentential logic ?+ defined by the class of all ?-matrices whose filter is Leibniz, which is called the strong version of ?, in the context of protoalgebraic logics with theorems. Topics studied include an enhanced Correspondence Theorem, characterizations of the weak algebraizability of ?+ (...) and of the explicit definability of Leibniz filters, and several theorems of transfer of metalogical properties from ? to ?+. For finitely equivalential logics stronger results are obtained. Besides the general theory, the paper examines the examples of modal logics, quantum logics and Łukasiewicz's finitely-valued logics. One finds that in some cases the existence of a weak and a strong version of a logic corresponds to well-known situations in the literature, such as the local and the global consequences for normal modal logics; while in others these constructions give an independent interest to the study of other lesser-known logics, such as the lattice-based many-valued logics. (shrink)

This article explores what John Dewey’s political philosophy can offer in regard to the current crisis in digital democracy. It focuses on two digital mechanisms, the “filter bubble” and the “echo chamber”. While there is a prominent, Dewey-inspired debate on “digital publics” in the literature, a reconstruction of the Deweyan concepts of the public and of shared experience shows that it does not adequately reflect the aspect of situated and embodied experience. Based on this, it is shown that digital media (...) offerings must also be rooted in local contexts of experience in order to answer the challenge of those two problematic mechanisms. (shrink)

It is often suggested that we are equipped with a set of cognitive tools that help us to filter out unreliable testimony. But are these tools effective? I answer this question in two steps. Firstly, I argue that they are not real-time effective. The process of filtering, which takes place simultaneously with or right after language comprehension, does not prevent a particular hearer on a particular occasion from forming beliefs based on false testimony. Secondly, I argue that they are long-term (...) effective. Some hearers sometimes detect false testimony, which increases speakers’ incentives for honesty and stabilizes the practice of human communication in which deception is risky and costly. In short, filtering prevents us from forming a large number of beliefs based on false testimony, not by turning each of us into a high-functioning polygraph but by turning the social environment of human communication into one in which such polygraphs are not required. Finally, I argue that these considerations support strong anti-reductionism about testimonial entitlement. (shrink)

The Filter Dichotomy says that every uniform nonmeager filter on the integers is mapped by a finite-to-one function to an ultrafilter. The consistency of this principle was proved by Blass and Laflamme. A medial limit is a universally measurable function from [Formula: see text] to the unit interval [0, 1] which is finitely additive for disjoint sets, and maps singletons to 0 and ω to 1. Christensen and Mokobodzki independently showed that the Continuum Hypothesis implies the existence of medial limits. (...) We show that the Filter Dichotomy implies that there are no medial limits. (shrink)

Two countable filters on ω are incompatible if they have no common infinite pseudointersection. Letting α(P f ) denote the minimal size of a maximal uncountable family of pairwise incompatible countable filters on ω, we prove the consistency of t $.

Assuming the consistency of the theory “ZFC + there exists a measurable cardinal”, we construct 1. a model in which the first cardinal κ, such that 2κ > κ+, bears a normal filter F whose associated boolean algebra is κ+-distributive ,2. a model where there is a measurable cardinal κ such that, for every regular cardinal ρ < κ, 2ρ = ρ++ holds,3. a model of “ZFC + GCH” where there exists a non-measurable cardinal κ bearing a normal filter F (...) whose associated boolean algebra is κ+-distributive. (shrink)

Decision-making has a high practical relevance for daily performance. Its relation to other cognitive abilities such as executive control and memory is not fully understood. Here we asked whether training of either attentional filtering or memory storage would influence decision-making as indexed by repetitive assessments of the Iowa Gambling Task (IGT). The IGT was developed to assess and simulate real-life decision-making (Bechara et al., 2005). In this task, participants gain or lose money by developing advantageous or disadvantageous decision strategies. On (...) five consecutive days we trained 29 healthy young adults (20-30 years) either in working memory storage or attentional filtering and measured their IGT scores after each training session. During memory training (MT) subjects performed a computerized delayed match-to-sample task where two displays of bars were presented in succession. During filter training (FT) participants had to indicate whether two simultaneously presented displays of bars matched or not. Whereas in MT the relevant target stimuli stood alone, in FT the targets were embedded within irrelevant distractors (bars in a different color). All subjects within each group improved their performance in the trained cognitive task. For the IGT, we observed an increase over time in the amount of money gained in the FT group only. Decision-making seems to be influenced more by training to filter out irrelevant distractors than by training to store items in working memory. Selective attention could be responsible for the previously noted relationship between IGT performance and working memory and is therefore more important for enhancing efficiency in decision-making. (shrink)

If $\mathcal{F}$ is a filter on $\omega$, we say that $\mathcal{F}$ is Canjar if the corresponding Mathias forcing does not add a dominating real. We prove that any Borel Canjar filter is $F_{\sigma}$, solving a problem of Hrušák and Minami. We give several examples of Canjar and non-Canjar filters; in particular, we construct a $\mathsf{MAD}$ family such that the corresponding Mathias forcing adds a dominating real. This answers a question of Brendle. Then we prove that in all the “classical” (...) models of $\mathsf{ZFC}$ there are $\mathsf{MAD}$ families whose Mathias forcing does not add a dominating real. We also study ideals generated by branches, and we uncover a close relation between Canjar ideals and the selection principle $S_{\mathrm{fin}}$ on subsets of the Cantor space. (shrink)

To the French critics who originally labelled certain films noir it seemed that a class of Hollywood products had gone darker during the war years – as though a dark filter had been placed over the lens. Films were not designed or marketed as noir, and retrospectively noir's status as a genre is still unsettled. Yet there is widespread interest today in experiencing diverse films as noir, and even in using a Noir Filter in Instagram and video games. Pursuing the (...) filter clue, the noir experience can be thought of as subjection to a dark filtering of narrative. Image filtering styles can help to resolve not only the puzzle of noir's quasi-genre status but also an issue of general interest in aesthetic experience. The use of image filters makes a distinctively powerful contribution to the experience of a work or genre, or to the cultural dominance of an aesthetic regime, due to the unobtrusive formative role it plays in the economy of experience. (shrink)

With the use of a suitable assumption about the structure of the class of experimental filters, it is shown that the sequence of alternating replicas of two filters is their greatest lower bound, as Jauch suggests. A generalization of his suggestion yields the greatest lower bound of a denumerable set of filters. The criteria of admissibility of filters are briefly discussed.

Schemas contribute to adaptation, filtering novelty though knowledge-expectancy structures, the residue of past contingencies and their consequences. Adaptation requires a balance between flexible, dynamic context-sensitivity and the cognitive efficiency that schemas afford in promoting persistent goal pursuit despite distraction. Affects can form and disrupt schemas. Transient affective experiences systematically alter selectivity of attentiveness to the directly experienced present environment, the internal environment, and to the stored experiences of memory. Enduring personal stylistic predispositions, like implicit motives and affective schemas, influence how (...) experience is perceived, responded to, and integrated; they shape memory and influence present experiential patterns, individually and intersubjectively. Such systematic influences are potential sources of error in the study of memory if not mapped; so far, individual personality differences have just been a source of complication in the literature on emotion-congruent perception and memory. I synthesize what findings there are about how personality differences, emotions, and affects contribute to the structuring and integration of perceptions and memories both directly and by way of hot, affectively-anchored schemas. Case studies from experimental and personality psychology highlight a conception of personality and affective experience relevant to memory research and cognitive science. (shrink)

Advances in artificial intelligence, as well as its increased presence in everyday life, have brought the emergence of many new phenomena, including an intriguing appearance of what seems to be a variant of body dysmorphic disorder, coined “Snapchat dysmorphia”. Body dysmorphic disorder is a DSM-5 psychiatric disorder defined as a preoccupation with one or more perceived defects or flaws in physical appearance that are not observable or appear slight to others. Snapchat dysmorphia is fueled by automated selfie filters that (...) reflect unrealistic sociocultural standard. In this paper, we discuss how body dysmorphic disorder and related body image distortions could arise, using the conceptual resources provided by the active inference framework. We suggest that these disorders involve dysfunctional self-modelling which entails maladaptive internalization of sociocultural preferences during adolescent identity formation. Identity formation is hereby described as cycles of interpersonal active inference that arbitrate between identity exploration and commitment. We propose that impaired self-modelling is unable to reduce interpersonal uncertainty during identity exploration, which, over time, degenerates into uncontrollable epistemic habits that isolate the body image from corrective sensory evidence. In light of these insights, we subsequently explore some of the consequences of image-centered social media platforms on the identity formation process. We conclude that heightened interpersonal uncertainty in this novel context could precipitate the onset of body dysmorphic disorder and related body image distortions, particularly when selfie filters are involved. (shrink)

In view of the poor recommendation performance of traditional resource collaborative filtering recommendation algorithms, this article proposes a collaborative filtering recommendation model based on deep learning for art and MOOC resources. This model first uses embedding vectors based on the context of metapaths for learning. Embedding vectors based on the context of metapaths aggregate different metapath information and different MOOCs may have different preferences for different metapaths. Secondly, to capture this preference drift, the model introduces an attention mechanism, which can (...) improve the interpretability of the recommendation results. Then, by introducing the Laplacian matrix into the prior distribution of the hidden factor feature matrix, the relational network information is effectively integrated into the model. Finally, compared with the traditional model using the scoring matrix, the model in this article using text word vectors effectively alleviates the impact of data sparsity and greatly improves the accuracy of prediction. After analyzing the experimental results, compared with other algorithms, the resource collaborative filtering recommendation model proposed in this article has achieved better recommendation results, with good stability and scalability. (shrink)

An adequate moral theory must – or so many philosophers have argued – be compatible with the attitudes and practical requirements of deep friendship. Bernard Williams suggested that the decision procedure required by both deontology and consequentialism inserts a fetishising filter between the natural moral motivation of any normal person to prioritise friends and the decision to act on it. But this injects ‘one thought too many’ into the moral reaction mechanism. It is standardly assumed that virtue ethics is somehow (...) immune to this objection. The present article explores this assumption and finds it wanting in various respects. Virtue ethics filters friendship throughphronesisand thus inserts an extra thought into the mechanism in question. To escape Williams's curse, the only way is to argue that the extra thought required by virtue ethics is not ‘one thought too many’. The article closes with an attempt to show that, contra deontology, the friendship motivation in virtue ethics is derived from the moral virtue, not the intellectual filter, and, contra consequentialism,phronesisdoes not require the maximisation of value. The presumed advantage of virtue ethics must lie in the content of its filter rather than the filter's non-existence. (shrink)

We analyze combinatorial properties of open covers of sets of real numbers by using filters on the natural numbers. In fact, the goal of this paper is to characterize known properties related to ω-covers of the space in terms of combinatorial properties of filters associated with these ω-covers. As an example, we show that all finite powers of a set R of real numbers have the covering property of Menger if, and only if, each filter on ω associated (...) with its countable ω-cover is a P + filter. (shrink)

With the troubles of core losses and all-state confined to certain limitations which are the innate traits of permanent magnet synchronous motors, this article develops a command filtered adaptive backstepping approach to follow the track of PMSM’s desired rotor position. To begin with, the RBF neural network technique is utilized to get close to the uncharted nonlinear terms which existed in PMSM’s mathematical model. Meanwhile, an advanced adaptive command filter control methodology is constructed to avoid the computing explosion during the (...) process of backstepping design. Furthermore, to make sure that all the state variables are confined into certain ranges, we employed the barrier Lyapunov function at every step of the controllers construction. In addition, an error compensating mechanism is proposed to neutralize filtering errors and only one adaptive law is required. At last, simulation results bear out the superiority of the aforementioned control scheme. (shrink)

In this paper, we introduce the notions of -fuzzy filters and -fuzzy Boolean filters in R0-algebras and investigate some of their related properties. Some characterization theorems of these generalized fuzzy filters are derived. In particular, we prove that a fuzzy set in R0-algebras is an -fuzzy Boolean filter if and only if it is an -fuzzy implicative filter. Finally, we consider the concepts of implication-based fuzzy Boolean filters of R0-algebras.

This personal account traces a series of studies that led from DNA physical chemistry to anticancer drug mechanisms. Chemical crosslinking as a basis for anticancer drug actions had been suspected since the time of the first clinical reports of the effectiveness of nitrogen mustard in 1946. After the elucidation of the DNA helix‐coil transition, several nearly concurrent findings in the early 1960s established the paradigm of DNA interstrand crosslinking. The DNA filter elution phenomenon was discovered in the early 1970s, and (...) lent itself to the development of practical assays for DNA crosslinks and other DNA lesions in mammalian cells. The assays allowed studies of the effects of DNA damaging agents at pharmacologically or toxicologically relevant doses, and have been widely applied in studies of mutagenic and chemotherapeutic agents. During the period 1979–1986, DNA filter elution studies led to the paradigm of DNA topoisomerases as targets of anticancer drug action, and this has become one of the most active areas of anticancer drug development. (shrink)

Logics L F (M) are considered, in which M ("most") is a new first-order quantifier whose interpretation depends on a given filter F of subsets of ω. It is proved that countable compactness and axiomatizability are each equivalent to the assertion that F is not of the form $\{(\bigcap F) \cup X:|\omega - X| with $|\omega - \bigcap F| = \omega$ . Moreover the set of validities of L F (M) and even of L F ω 1 ω (M) depends (...) only on a few basic properties of F. Similar characterizations are given of the class of filters F for which L F (M) has the interpolation or Robinson properties. An omitting types theorem is also proved. These results sharpen the corresponding known theorems on weak models (U, q), where the collection q is allowed to vary. In addition they provide extensions of first-order logic which possess some nice properties, thus escaping from contradicting Lindstrom's Theorem [1969] only because satisfaction is not isomorphism-invariant (as it is tied to the filter F). However, Lindstrom's argument is applied to characterize the invariant sentences as just those of first-order logic. (shrink)

In this paper, we study (open) filters and deductive systems of self-distributive weak Heyting algebras (SDWH-algebras) and obtain some results which determine the relationship between them. We show that the variety of SDWH-algebras is not weakly regular and every open filter is the kernel of at least one congruence relation. Then it presents necessary and sufficient conditions for the existence of a one to one correspondence between open filters and congruence relations.

For a free filter F on $$\omega $$, let $$N_F=\omega \cup \{p_F\}$$, where $$p_F\not \in \omega $$, be equipped with the following topology: every element of $$\omega $$ is isolated whereas all open neighborhoods of $$p_F$$ are of the form $$A\cup \{p_F\}$$ for $$A\in F$$. The aim of this paper is to study spaces of the form $$N_F$$ in the context of the Nikodym property of Boolean algebras. By $$\mathcal{A}\mathcal{N}$$ we denote the class of all those ideals $$\mathcal {I}$$ on (...) $$\omega $$ such that for the dual filter $$\mathcal {I}^*$$ the space $$N_{\mathcal {I}^*}$$ carries a sequence $$\langle \mu _n:n\in \omega \rangle $$ of finitely supported signed measures such that $$\Vert \mu _n\Vert \rightarrow \infty $$ and $$\mu _n(A)\rightarrow 0$$ for every clopen subset $$A\subseteq N_{\mathcal {I}^*}$$. We prove that $$\mathcal {I}\in \mathcal{A}\mathcal{N}$$ if and only if there exists a density submeasure $$\varphi $$ on $$\omega $$ such that $$\varphi (\omega )=\infty $$ and $$\mathcal {I}$$ is contained in the exhaustive ideal $$\text{ Exh }(\varphi )$$. Consequently, we get that if $$\mathcal {I}\subseteq \text{ Exh }(\varphi )$$ for some density submeasure $$\varphi $$ on $$\omega $$ such that $$\varphi (\omega )=\infty $$ and $$N_{\mathcal {I}^*}$$ is homeomorphic to a subspace of the Stone space $$St(\mathcal {A})$$ of a given Boolean algebra $$\mathcal {A}$$, then $$\mathcal {A}$$ does not have the Nikodym property. We observe that each $$\mathcal {I}\in \mathcal{A}\mathcal{N}$$ is Katětov below the asymptotic density zero ideal $$\mathcal {Z}$$, and prove that the class $$\mathcal{A}\mathcal{N}$$ has a subset of size $$\mathfrak {d}$$ which is dominating with respect to the Katětov order $$\le _K$$, but $$\mathcal{A}\mathcal{N}$$ has no $$\le _K$$ -maximal element. We show that, when $$\mathcal {I}$$ is a density ideal, $$\mathcal {I}\not \in \mathcal{A}\mathcal{N}$$ holds if and only if $$\mathcal {I}$$ is totally bounded if and only if the Boolean algebra $$\mathcal {P}(\omega )/\mathcal {I}$$ contains a countable splitting family. Our results shed some new light on differences between the Nikodym property and the Grothendieck property of Boolean algebras. (shrink)

Social media have undoubtedly changed our ways of living. Their presence concerns an increasing number of users (over 4,74 billion) and pervasively expands in the most diverse areas of human life. Marketing, education, news, data, and sociality are just a few of the many areas in which social media play now a central role. Recently, some attention toward the link between social media and political participation has emerged. Works in the field of artificial intelligence have already pointed out that there (...) is a close link between the use of machine learning algorithms in social media and possible epistemic isolation, which could lead to political radicalization. The idea supporting this paper is that artificial intelligence for social media can actively put users’ deliberative capacity at risk and foster political extremism. To prove these claims, I proceed along two lines of inquiry. First, I focus on filter bubbles, namely the result of selections made by algorithms that recommend contents that meet users’ expectations and opinions. To analyze this phenomenon, I refer to the Deweyan model of experience. Second, I connect the filter bubbles problem to the Deweyan idea of deliberative and participatory democracy and Nussbaum’s concept of political compassion. The purpose of this paper is to provide a philosophical foundation that can both (1) effectively serve as a method for analyzing machine learning algorithms and their potential problems in relation to political extremism, and (2) be adopted as a standard to counter the danger of extremism associated with social media experience. (shrink)

We characterize (both from a syntactic and an algebraic point of view) the normal K4-logics for which unification is filtering. We also give a sufficient semantic criterion for existence of most general unifiers, covering natural extensions of K4.2⁺ (i.e., of the modal system obtained from K4 by adding to it, as a further axiom schemata, the modal translation of the weak excluded middle principle).

Rough set theory is an excellent mathematical tool for the analysis of a vague description of actions in decision problems. Now, in this paper by considering the notion of an equality algebra, the notion of the lower and the upper approximations are introduced and some properties of them are given. Moreover, it is proved that the lower and the upper approximations define an interior operator and a closure operator, respectively. Also, using D-lower and D-upper approximation, conditions for a nonempty subset (...) to be definable are provided and investigated that under which condition D-lower and D-upper approximation can be filter. (shrink)

This report brings out a simple observation on the close connection of lters with algebraic closure systems. In [1], Orrin Frink gave a general denition of ideals in ordered sets. Here, we use the dual notion of lter and apply it to preordered sets. When referring to nite sets fc1; : : : ; ckg we often omit the brackets. The symbol ; denotes the empty set and, X f Y means that X is a nite subset of Y.

We find some characterizations of the Axiom of Choice in terms of certain families of open sets in T1 spaces.

We propose a model of uncertain belief. This models coherent beliefs by a filter, ????, on the set of probabilities. That is, it is given by a collection of sets of probabilities which are closed under supersets and finite intersections. This can naturally capture your probabilistic judgements. When you think that it is more likely to be sunny than rainy, we have{????|????(????????????????????)>????(????????????????????)}∈????. When you think that a gamble ???? is desirable, we have {????|Exp????[????]>0}∈????. It naturally extends the model of credal (...) sets; and we will show it captures all the expressive power of the desirable gambles model. It also captures the expressive power of sets of desirable gamble sets (with a mixing axiom, but no Archimadean axiom). (shrink)

In this essay, I explore ethical considerations that might arise from the use of collaborative filtering algorithms on dating apps. Collaborative filtering algorithms can predict the preferences of a target user by looking at the past behavior of similar users. By recommending products through this process, they can influence the news we read, the movies we watch, and more. They are extremely powerful and effective on platforms like Amazon and Google. Recommender systems on dating apps are likely to group people (...) by race, since they exhibit similar patterns of behavior: users on dating platforms seem to segregate themselves based on race, exclude certain races from romantic and sexual consideration, and generally show a preference for white men and women. As collaborative filtering algorithms learn from these patterns to predict preferences and build recommendations, they can homogenize the behavior of dating app users and exacerbate biased sexual and romantic behavior. (shrink)

We investigate club guessing sequences and filters. We prove that assuming V=L, there exists a strong club guessing sequence on μ if and only if μ is not ineffable for every uncountable regular cardinal μ. We also prove that for every uncountable regular cardinal μ, relative to the existence of a Woodin cardinal above μ, it is consistent that every tail club guessing ideal on μ is precipitous.

When confronting the unexplained, it is helpful to consider it from many different points of view. In an essay published in 2004, entitled "Sensors, Filters, and the Source of Reality," Robert Jahn and Brenda Dunne of Princeton University's PEAR laboratory proposed that consciousness constructs its reality by ordering the information it derives from the external world through an array of physiological, psychological, and cultural filters. This thesis has now been considered by nineteen distinguished scholars who here present their (...) commentaries from a broad spectrum of professional and personal perspectives. Drawn from such diverse backgrounds as art, Buddhism, evolutionary biology, fantasy, out-of-body experiences, philosophy, physics, psychology, semiotics, and systems engineering, among others, these contributions offer an assortment of unique and fascinating glimpses of how our experiences and their styles of representation are reflected through these filters of consciousness. (shrink)

The present paper is thought as a formal study of distributive closure systems which arise in the domain of sentential logics. Special stress is laid on the notion of a C-filter, playing the role analogous to that of a congruence in universal algebra. A sentential logic C is called filter distributive if the lattice of C-filters in every algebra similar to the language of C is distributive. Theorem IV.2 in Section IV gives a method of axiomatization of those filter (...) distributive logics for which the class Matr (C) prime of C-prime matrices (models) is axiomatizable. In Section V, the attention is focused on axiomatic strengthenings of filter distributive logics. The theorems placed there may be regarded, to some extent, as the matrix counterparts of Baker's well-known theorem from universal algebra [9, § 62, Theorem 2]. (shrink)

We recall some notions introduced and developed by António Aniceto Monteiro, and show how these notions have been used and generalised, thus establishing a direct and indirect influence of Monteiro’s work that extends to this day.

I argue that classical counterfactual semantics in the style of Stalnaker, Lewis, and Kratzer validates an inference pattern that is disconfirmed in natural language. The solution is to alter the algorithm we use to handle inconsistency in premise sets: rather than checking all maximally consistent fragments of a premise sets, as in Krazter’s semantics, we selectively remove some of the premises. The proposed implementation starts from standard premise semantics and involves a new ‘filtering’ operation that achieves just this removal. The (...) resulting semantics is interestingly related to the semantics for counterfactuals emerging from Judea Pearl’s causal models framework in computer science: in particular, filtering is a possible worlds semantics counterpart of Pearl’s interventions. (shrink)

Online information intermediaries such as Facebook and Google are slowly replacing traditional media channels thereby partly becoming the gatekeepers of our society. To deal with the growing amount of information on the social web and the burden it brings on the average user, these gatekeepers recently started to introduce personalization features, algorithms that filter information per individual. In this paper we show that these online services that filter information are not merely algorithms. Humans not only affect the design of the (...) algorithms, but they also can manually influence the filtering process even when the algorithm is operational. We further analyze filtering processes in detail, show how personalization connects to other filtering techniques, and show that both human and technical biases are present in today’s emergent gatekeepers. We use the existing literature on gatekeeping and search engine bias and provide a model of algorithmic gatekeeping. (shrink)

The purpose of this paper is to compare the notion of a Grzegorczyk point introduced in [19] (and thoroughly investigated in [3, 14, 16, 18]) to the standard notions of a filter in Boolean algebras and round filter in Boolean contact algebras. In particular, we compare Grzegorczyk points to filters and ultrafilters of atomic and atomless algebras. We also prove how a certain extra axiom influences topological spaces for Grzegorczyk contact algebras. Last but not least, we do not refrain (...) from a philosophical interpretation of the results from the paper. (shrink)

We introduce the property “F-linked” of subsets of posets for a given free filter F on the natural numbers, and define the properties “μ-F-linked” and “θ-F-Knaster” for posets in a natural way. We show that θ-F-Knaster posets preserve strong types of unbounded families and of maximal almost disjoint families. Concerning iterations of such posets, we develop a general technique to construct θ-Fr-Knaster posets (where Fr is the Frechet ideal) via matrix iterations of <θ-ultrafilter-linked posets (restricted to some level of the (...) matrix). This is applied to prove consistency results about Cichoń's diagram (without using large cardinals) and to prove the consistency of the fact that, for each Yorioka ideal, the four cardinal invariants associated with it are pairwise different. At the end, we show that three strongly compact cardinals are enough to force that Cichoń's diagram can be separated into 10 different values. (shrink)