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The single-valued neutrosophic set (\(\mathcal {SVNS}\)) defined to incorporate the indeterminate, imprecise, and inconsistent data in real-life scientific and engineering problems. The uncertain information is significantly measured by similarity and dissimilarity measures. The similarity and dissimilarity measures are employed to depict the closeness and differences among SVNSs and have many applications in real-life situations like medical diagnosis, data mining, decision making, classification, and pattern recognition. This paper investigates the new similarity and dissimilarity measures for the SVNS. Additional properties of the newly proposed similarity and dissimilarity measures are focused. Their corresponding weighted similarity and dissimilarity measures are discussed on. It can be seen that the newly proposed similarity and dissimilarity measures respect all the axioms of similarity and dissimilarity definitions. The notion of \(\simeq ^{\alpha }\) similar relation is defined and it can be seen that the \(\simeq ^{\alpha }\) similar relation is reflective and symmetric but not transitive. The numerical examples are provided for the explanations.

George Kelly introduced the notion of formulation in his personal construct psychology and its associated form of psychotherapy. The process of assessing and sharing the formulation, in which the clinician attempts to construe the construction processes of the client using a set of diagnostic constructs, is an example of what Kelly termed sociality. Psychological disorders are viewed as personal constructions which are used in spite of consistent invalidation and may involve the use of strategies to avoid invalidation. Later developments have given somewhat greater attention to the relational and developmental aspects of disorders. Four principal features of the personal construct approach to formulation are worthy of note: the diagnostic constructs refer to processes that are neither healthy nor unhealthy, and lead to a transitive diagnosis that indicates the pathways of movement open to a person rather than a fixed diagnostic category; this is followed by a plan for treatment tailored to the client’s construing; the personal construct formulation process is a collaborative affair; and the clinician has expertise in various tools that may aid the formulation and testing of hypotheses. Personal construct psychology provides an illustration of a constructivist approach that has accepted the empirical challenge.

In this paper we offer an analysis of the so-called causative SE construction exemplified by sentences like Juan se afeita en la barberia (‘Juan gets a shave at the barbershop’). Even though these sentences look like ordinary reflexive constructions, the subject is not interpreted as an agent, but as a causer who initiates an event whose agent is implicit. For instance, in the sentence above, the barber is the agent of the shaving event, not Juan. We propose that this unique interpretation arises only in certain transitive configurations that involve change of state semantics and intrinsic reflexivity. This syntactic configuration, coupled with extra-linguistic knowledge about causal chains, accounts for the syntactic and semantic properties of causative SE constructions.

This chapter investigates and examines a general criticism of the AHP method and 30 specific subjects, shortcomings and drawbacks. It establishes the procedure as follows

Complex activity recognition is challenging due to the inherent diversity and causality of performing a complex activity, with each of its instances having its own configuration of primitive events and their temporal causal dependencies. This leads us to define a primitive event-based approach that employs Granger causality to discover temporal causal dependencies. Our approach introduces a temporal causal network generated from an optimized network skeleton to explicitly characterize these unique temporal causal configurations of a particular complex activity as a variable number of nodes and links. It can be analytically shown that the resulting network satisfies causal transitivity property, and as a result, all local cause-effect dependencies can be retained and are globally consistent. Empirical evaluations on benchmark datasets suggest our approach significantly outperforms the state-of-the-art methods. In particular, it is shown that our approach is rather robust against errors caused by the low-level detection from raw signals.

The Object Migration Automata (OMA) has been used as a powerful tool to resolve real-life partitioning problems in random Environments. The virgin OMA has also been enhanced by incorporating the latest strategies in Learning Automata (LA), namely the Pursuit and Transitivity phenomena. However, the single major handicap that it possesses is the fact that the number of objects in each partition must be equal. Obviously, one does not always encounter problems with equally-sized groups (When the true underlying problem has non-equally-sized groups, the OMA reports the best equally-sized solution as the recommended partition.). This paper is the pioneering attempt to relax this constraint. It proposes a novel solution that tackles partitioning problems where the partition sizes can be both equal and/or unequal, but when the cardinalities of the true partitions have a Greatest Common Divisor (GCD). However, on attempting to resolve this less-constrained version, we encounter a few problems that deal with implementing the inter-partition migration of the objects. To mitigate these, we invoke a strategy that has been earlier used in the theory of automata, namely that of mapping the machine’s state space onto a larger space. This paper details how this strategy can be incorporated, and how such problems can be solved. In essence, it presents the design, implementation, and testing of a novel OMA-based method that can be implemented with the OMA itself, and also in all of its existing variants, including those incorporating the Pursuit and Transitivity phenomena. Numerical results demonstrate that the new approach can efficiently solve partitioning problems with partitions that have a common GCD.

The goal of entity matching in knowledge graphs is to identify sets of entities that refer to the same real-world object. Methods for entity matching in knowledge graphs, however, produce a collection of pairs of entities claimed to be duplicates. This collection that represents the sameAs relation may fail to satisfy some of its structural properties such as transitivity. We show that an ad-hoc enforcement of transitivity on the set of identified entity pairs may decrease precision. We therefore propose a methodology that starts with a given similarity measure, generates a set of entity pairs, and applies cluster editing to enforce transitivity, leading to overall improved performance.

The neutrosophic set theory allows us to model an imperfect, incomplete, and inconsistent data. In real-world problems the interval-valued neutrosophic sets are most popular and elegant model to deal with uncertainties. In this study, determinant and adjoint of interval-valued neutrosophic (IVN) matrices are defined based on the permanent function. Also, some results are obtained related to the determinant and adjoint of the interval-valued neutrosophic matrices. Furthermore, the concepts of complement, constant, reflexive, symmetric, transitive, and idempotent IVN-matrices are defined, and some properties of them related to determinant and adjoint are derived.

The multiplicative transitivity of intuitionistic fuzzy preference relations has been widely studied. Nevertheless, when the membership and non-membership degrees are 0, the multiplicative transitivity has a 2/3 probability to make errors. To address this issue, the exponent transformation functions of membership and non-membership degrees of intuitionistic fuzzy preference values are proposed. Based on these functions, the exponent-transformation-based multiplicative transitivity of an intuitionistic fuzzy preference relation is defined. To improve the inconsistency degree of an IFPR, a model is set up based on linear programming. A case study on green supplier selection is given to demonstrate the reliability of the proposed method in improving the inconsistency of an intuitionistic fuzzy preference relation.

This chapter examines how positivity and order play out in two important questions in mathematical economics, and in so doing, subjects the postulates of continuity, additivity and monotonicity to closer scrutiny. Two sets of results are offered: the first departs from Eilenberg’s necessary and sufficient conditions on the topology under which an anti-symmetric, complete, transitive and continuous binary relation exists on a topologically connected space; and the second, from DeGroot’s result concerning an additivity postulate that ensures a complete binary relation on a σ-algebra to be transitive. These results are framed in the registers of order, topology, algebra and measure-theory; and also beyond mathematics in economics: the exploitation of Villegas’ notion of monotonic continuity by Arrow-Chichilnisky in the context of Savage’s theorem in decision theory, and the extension of Diamond’s impossibility result in social choice theory by Basu-Mitra. As such, this chapter has also a synthetic and expository motivation, and can be read as a plea for inter-disciplinary conversations, connections and collaboration.

Most (if not all) nonmonotonic logics are assumed to be cumulative, which is often regarded as the minimum requirement for a logic. We argue that cumulativity, in particular, cumulative transitivity can be abandoned, in order to better characterize reasoning in uncertainty. But giving up cumulative transitivity makes it hard to obtain representation results for these logics. Borrowing the idea from strict-tolerant logics, we give some representation results for nonmonotonic logics that are not cumulatively transitive.

Among other possible criteria, verbs are classified according to their valency. This is recognized in traditional grammar, which refers to verbs as transitive, intransitive, copulative, and so on. But the complexity is much greater, if we consider the great number of different constructions in which each verb can occur. In this chapter several classification criteria of verbs are discussed and exemplified.

In this last chapter of Part I, the focus is on local relationships between elements of a line graph. Among these are discrete analogues of the geometric concepts of diameter, radius, and center. Some of the results involve connections for these quantities between graphs and their line graphs, and what happens to their values in iterated line graphs. The center of a graph is also defined in a natural way, and some intriguing results on the center of a line graph are described. The other topic is in response to a question about partially ordered sets: Which line graphs can their edges oriented so that the result is a transitive ordering? The answer can be given in terms of forbidden subgraphs.

We study the dichromatic number of a digraph, defined as the minimum number of parts in a partition of its vertex set into acyclic induced subdigraphs. We consider the class of oriented graphs such that the out-neighbourhood of any vertex induces a transitive tournament and prove for it a decomposition theorem. As a consequence, we obtain that oriented graphs in this class have dichromatic number at most 2, proving a conjecture of Naserasr and the first and third authors of this paper in Extension of the Gyarfas-Sumner conjecture to digraphs arXiv:2009.13319.

We construct all parallelisms of \(\mathrm{PG}(3,5)\) that are invariant under an automorphism group of order 25. Up to isomorphism their number is 14873. Using them we obtain 12 transitive deficiency one parallelisms, two of which belong to an infinite family constructed by Johnson.

Customers’ preferences related to the quality, the change, and the progress of their expectations have turned the quality in an indispensable competitive factor for hotel enterprises. The hotels have to evaluate the customer satisfaction and to assign to each factor a weight, expressing its importance for their customers. The aim of this paper is to evaluate the importance of hotel services. Our analysis involves more than 300 customers that answered to a survey and it takes into account five criteria: Food, Cleanliness, Staff, Price/benefit, and Comfort. To derive the ranking of preferences we used pairwise comparisons. The main issue linked to pairwise comparisons is the consistency of judgements. Transitivity thresholds recently proposed in literature give meaningful information about the reliability of the preferences. Our study shows how the use of ordinal threshold may provide a ranking of services different from that obtained by applying traditional consistency Saaty thresholds.

One of the main goals in education is to narrow the teaching according to students’ knowledge and skills; therefore, many topics may emerge and become important, and many research questions may be posed and studied. In this context and using a systemic approach, I present and discuss a methodology to analyze the visual reasoning processes given with the use of mathematical representations when learning differential calculus at a high school level. The interest is knowing how learners acquire and use some of the systems of mathematical representation and how they organize these systems to produce acceptable responses in the school environment. The representation systems used by the participants were modeled by digraphs, which turned out to be complete, entirely disconnected, and transitive; strong, weak, and idiosyncratic systems of representation were identified. Also, based on the conclusions, some teaching recommendations were created for making decisions in the classroom for students to acquire solid systems of representation by which acceptable answers may be given to solve differential calculus problems.

When members of an organization share communication codes, coordination across subunits is easier. But if groups interact separately, they will each develop a specialized code. This paper asks: Can organizations shape how people interact in order to create shared communication codes? What kinds of design interventions in communication structures and systems are useful? In laboratory experiments on triads composed of dyads that solve distributed coordination problems, we examine the effect of three factors: transparency of communication (versus privacy), role differentiation, and the subjects’ social history. We find that these factors impact the harmonization of dyadic codes into triadic codes, shaping the likelihood that groups develop group-level codes, converge on a single group-level code, and compress the group-level code into a single word. Groups with transparent communication develop more effective codes, while acyclic triads composed of strangers are more likely to use multiple dyadic codes, which are less efficient than group-level codes. Groups of strangers put into acyclic configurations appear to have more difficulty establishing “ground rules”—that is, the “behavioral common ground” necessary to navigate acyclic structures. These coordination problems are transient—groups of different structures end up with the same average communication performance if given sufficient time. However, lasting differences in the code that is generated remain.

In our days, problems relating to decision making support in the information and analytical systems are caused mainly by the need to handle a large volume of diverse information and the occurrence of a great number of alternatives of alternatives and multi-objective criteria when choosing them. Application of ontological descriptions in the decision making support chain ensures the dynamic formation of corresponding sets of alternatives and criteria based on the properties of concepts of the domain areas for which relevant decisions are made. Inclusion of ontological models in the information and analytical system environment allows effectively apply a method of hierarchy analysis as a systematic procedure for hierarchic representation and analysis of elements which establish the core of a problem. In this case, validity of a decision depends entirely on the correctness and relevance of ontological domain model, while the objectivity of a method is ensured by fixing the transitive consistency of expert judgment, which eliminates subjectivity and supports the principle of impartiality and justice.

In decision-making processes, preference relations are popular and powerful techniques for expert preference modeling (Urena et al. in Inf Sci 302:14–32, 2015). Consistency measures of preference relations are the vital basis of group decision-making (GDM) and have been studied extensively, which show that the supplied preferences satisfy some transitive properties (Wu and Xu in Omega 65(3):28–40, 2016). Consistency measures mainly consist of two parts: (1) judging whether each preference relation is of acceptable consistency; (2) improving the preference relation with unacceptable consistency. Based on double hierarchy hesitant fuzzy linguistic preference information, Gou et al. (Inf Sci 489:93–112 2019), Gou et al. (Int J Strateg Prop Manag 42(1):1–23, 2020) discussed the additive consistency measures and multiplicative consistency measures for DHHFLPRs, respectively. In this chapter, we will deeply discuss these two consistency measures for DHHFLPRs.

In this paper, we use the domain of object experiencer verbs in Greek to discuss the behavior of non-agentive causative construals of this verb class with clear implications for the syntax of causative predicates in general. We argue that eventive causative object experiencer verbs are best analyzed as instances of transitive internally caused change of state verbs. We then explore the consequences of this analysis for a group of verbs that have been labeled in the literature defeasible causative verbs. We substantiate the proposal that the layer introducing agents as external arguments is distinct from the layer introducing causers as external arguments. As a result, causers are conceived of as being part of the same event structural component that contains the resultant state, while agents are separated from it, being introduced in VoiceP.

Proximity relations are binary fuzzy relations that satisfy reflexivity and symmetry properties, but are not transitive. They induce the notion of distance between function symbols, which is further extended to terms. Given two terms, we aim at bringing them “sufficiently close” to each other, by finding an appropriate substitution. We impose no extra restrictions on proximity relations, allowing a term in unification to be close to two terms that themselves are not close to each other. Our unification algorithm works in two phases: first reducing the equation solving problem to constraints over sets of function symbols, and then solving the obtained constraints. Termination, soundness and completeness of both algorithms are shown. The unification problem has finite minimal complete set of unifiers.

Electronic health records (EHRs) contain important temporal information about disease progression and patients. However, mining temporal representations from discrete EHR data (e.g., diagnosis, medication, or procedure codes) for use in standard Machine Learning is challenging. We propose a transitive Sequential Pattern Mining approach (tSPM) to address the temporal irregularities involved in recording discrete records in EHRs. We perform experiments to compare the classification performance metrics for predicting “true” diagnosis between traditional sequential pattern mining (SPM) and the proposed tSPM algorithms across multiple diseases. We demonstrate that transitive approach is superior to the traditional SPM in mining temporal representations for diagnosis prediction.

Decision making processes are often based on (pairwise) preference relations. An important property of preference relations is transitivity. Many types of transitivity have been proposed in the literature, such as max–min and max–max transitivity, restricted max–min and max–max transitivity, additive and multiplicative transitivity, or Łukasiewicz transitivity. This paper focuses on weak transitivity. Weak transitivity has been defined for additive preference relations. We extend this definition to multiplicative preference relations and further introduce a generalized version called generalized weak transitivity. We show that for reciprocal additive and multiplicative preference relations weak transitivity is equivalent to generalized weak transitivity, and we also illustrate generalized weak transitivity for preference relations that are neither additive nor multiplicative. Finally, we show how a total order (ranking of the options) can be constructed for any generalized weak transitive preference relation.

Using mathematical modeling, we consider the phenomenon of singularity in the biological and social history. It is shown that hyperbolic trends in biological and social evolution can be explained by transitional processes that accompany the expansion of ecological niches due to periodically occurring revolutionary innovations. During these periods, strong positive feedbacks are actualized, leading to hyperbolic growth. However, this growth is then inhibited, and the system goes into a new qualitative state. Then, there is a relatively slow development of the updated system with a gradual accumulation of quantitative characteristics and a new innovative breakthrough. This cycle then repeats multiple times. In this regard, the system’s hyperbolic growth trends indicate the transitivity of its current state, while the time of singularity in this hyperbolic trend indicates the end of the transition process.

The issue of diagnosis is discussed, with Kelly’s approach to formulation involving transitive diagnosis being preferred. We look at personal construct approaches and research on psychological disorders, formulation in the relational extension of PCP, and construing in the wider culture. The chapter concludes with a consideration of the critiques of formulation.

We overview recent work on obtaining persistent homology based summaries of time-dependent data. Given a finite dynamic graph (DG), one first constructs a zigzag persistence module arising from linearizing the dynamic transitive graph naturally induced from the input DG. Based on standard results, it is possible to then obtain a persistence diagram or barcode from this zigzag persistence module. It turns out that these barcodes are stable under perturbations of the input DG under a certain suitable distance between DGs. We also overview how these results are also applicable in the setting of dynamic metric spaces, and describe a computational application to the analysis of flocking behavior.

In this chapter, we present a compositional analysis, in the framework of Montague grammar, of the meaning of transitive verbs and the declarative sentences to which they give rise. Pivotal to this result is the analysis of the characteristic function of the sets denoted by transitive verbs as functions of functions, that is, functions that are satisfied by two cyclic applications of an input value.

This chapter challenges several common assumptions regarding the assessment of outcome goodness. In Part I Larry Temkin challenges various Axioms of Transitivity, including the Axiom of Transitivity for All Things Considered Better Than, according to which for any three outcomes, A, B, and C, if, all things considered, A is better than B, and all things considered, B is better than C, then, all things considered, A is better than C. Whether or not the Axioms of Transitivity hold, he suggests, depends on the nature of the good; in particular, on whether an Internal Aspects View or an Essentially Comparative View of outcome goodness is correct. In Part II, Temkin considers whether we should be neutral between different possible locations of the good: space, time, and people. He suggests that from a normative perspective we should treat space differently than time, and people differently than space and time. Temkin shows that three intuitively plausible dominance principles regarding space, time, and people are incompatible. He also argues that in some cases we should give priority to people over space and time, and to time over space, but that, controversially, in some cases, we should give priority to time over people.

We have already observed (in Sect. 1.2) that, in the literature, the transitivity of the relation is a part of is often called into question. We cited there a number of works which take different and interesting views on the matter. In this chapter, we will introduce some general approaches which will hopefully delight both defenders and opponents of the assumed transitivity of the relation. We will introduce the concept of the local transitivity of a given relation which will be such that every transitive relation is also locally transitive.

A well-formed transitive resultative construction must show a relation of direct causation between its causing and caused subevents; that is, resultatives conform to the same well-formedness condition as lexical causatives. Yet the best formulation of this condition is the subject of continued discussion. This paper revisits this question in the context of transitive resultatives. They are ideal for this investigation as their verbs provide explicit information about the causing subevent, while lexical causatives are silent about this subevent. This paper investigates the relation between the causing and caused subevents through case studies of resultatives with the result phrases dry and awake. The case studies probe the complex interplay between the subject, the verb, the postverbal NP, and the result phrase using naturally occurring examples. The last case study investigates why resultatives with certain verb–AP combinations disallow a particular interpretation. Together these case studies support the prototypical understanding of direct causation in the literature.

We consider the decidability of the verification problem of programs modulo axioms — automatically verifying whether programs satisfy their assertions, when the function and relation symbols are interpreted as arbitrary functions and relations that satisfy a set of first-order axioms. Though verification of uninterpreted programs (with no axioms) is already undecidable, a recent work introduced a subclass of coherent uninterpreted programs, and showed that they admit decidable verification [26]. We undertake a systematic study of various natural axioms for relations and functions, and study the decidability of the coherent verification problem. Axioms include relations being reflexive, symmetric, transitive, or total order relations, functions restricted to being associative, idempotent or commutative, and combinations of such axioms as well. Our comprehensive results unearth a rich landscape that shows that though several axiom classes admit decidability for coherent programs, coherence is not a panacea as several others continue to be undecidable.

The ergative phenomenon in Chinese involves many hot-debated issues in the study of Chinese syntax and semantics, which was explored from various perspectives in previous researches. In this paper, a total number of 123 ergative verbs are sorted out in terms of their syntactic representation, semantic types and semantic features, and result in three findings. Firstly, the common semantic feature of ergative verbs is the meaning of change. Secondly, there are obvious internal differences in transitivity, causativity and volition of ergative verbs: unary ergative verbs indicate spontaneous and uncontrollable changes in events, with low transitivity and obvious non-volitional tendency; binary ergative verbs have higher transitivity and obvious causative tendency. Thirdly, the two relevant structures, ‘S+V+N’ and ‘N+V’, represent different stages before and after the change. The former structure represents the origin or motive force of the change, while the latter represents the state after the change. A temporal sequence and logical causality exist between them.

One objective of smart manufacturing is to resolve complex causalities of production processes, in order to minimize machine idle times. We introduce a methodology for mining from raw state time series of machines, possible causal relations between the machines of a given production environment. By applying the similarity measure cross-correlation on binary production state time series of two machines pairwise, we obtain a probability distribution, whose characteristic properties imply possible causal orderings of the two machines. In case of complex causalities, the measure may be applied to all possible machines pairwise, in order to extract a complete web of statistically significant causalities, without any prior context information of the environment. In this paper, we analyze the characteristic properties of such probability distributions and postulate four hypotheses, which constitute the steps of our methodology. Furthermore, we discuss the stochastic and temporal conditions that are necessary for the transitive propagation of causal states.

Cities have been compared to social reactors constrained by the communication and coordination possibilities offered by an urban environment that has only grown since the advent of the industrial age. We attempt to provide a first description of human interactions in the urban environment using Call Detailed Records (CDR) of the major mobile phone communication network operator in Chile. We build communication networks for 145 Chilean cities to describe and characterize the communication behavior of urban dwellers. We center our analysis in observed indicators of social activity, such as the number of contacts, number of calls and total communication time in each city and evaluate their scaling relationship with the number of mobile phones assigned to each city as an approximation of city size. Interestingly, the values of scaling exponents closely match recent explanations proposed in the literature. The topologies of voice-call networks among cities of increasing sizes are slightly assortative, albeit assortativeness decreases with size. Additionally, they show small average path length relative to their sizes, a typical feature of small-world networks. However, they decrease instead of growing when size is taken into account, unlike other complex networks. Different transitivity indices show mixed results. Average Watts-Strogatz clustering coefficient increases in larger cities much more than expected by pure chance as it has been shown in other social networks. On the other hand, the fact that classic transitivity index decreases seem to exhibit a regime change with a decreasing relation with size and an unexpected growth in larger cities. Both transitivity indices, as a whole, could describe among those who are making new interactions as the city grows. All these results indicate that while tightly knit human communities seem to lose cohesion as they grow, such community properties may progressively disappear among the three to four largest urban centers in Chile where the coordination of complex functions requires each city dweller to reach out to a larger network of people and speak for longer periods of time as compared to smaller cities. Finally, although these results are valid for all networks, there is a division into two regimes when networks reach a critical size of ~10,000 nodes, which raises the possibility of an empirical definition of city for Chile.

We formalize the theory of forcing in the set theory framework of Isabelle/ZF. Under the assumption of the existence of a countable transitive model of \( ZFC \), we construct a proper generic extension and show that the latter also satisfies \( ZFC \). In doing so, we remodularized Paulson’s ZF-Constructibility library.

This chapter reports on the rebranding of a British cancer charity as part of a wider internal culture change. During the cultural change process, management became aware that it was not reaching a particular socio-demographic group of cancer patients and sought to adjust the organisation’s brand identity. The first step of the brand-related consultancy involved identifying the brand personality projected in the charity’s existing materials. An analysis of lexis, transitivity and visuals showed that the organisation projected a classed and gendered brand personality that diverged from the group they were trying to reach. The second step involved developing a new brand personality through linguistic adaptation. The project concluded with a follow-up language audit some months after the new brand had been implemented. The chapter ends by discussing the wider impact of the project on the client and reflecting on the collaboration between linguists and third-sector organisations.

\(\rho \)Log-prox is a calculus for rule-based programming with strategies, which supports both exact and approximate computations. Rules are represented as conditional transformations of sequences of expressions, which are built from variadic function symbols and four kinds of variables: for terms, hedges, function symbols, and contexts. \(\rho \)Log-prox extends \(\rho \)Log by permitting in its programs fuzzy proximity relations, which are reflexive and symmetric, but not transitive. We introduce syntax and operational semantics of \(\rho \)Log-prox, illustrate its work by examples, and present a terminating, sound, and complete algorithm for the \(\rho \)Log-prox expression matching problem.

Nisan and Szegedy [16] conjectured that block sensitivity is at most polynomial in sensitivity for any Boolean function. Until a recent breakthrough of Huang [14], the conjecture had been wide open in the general case, and was proved only for a few special classes of Boolean functions. Huang’s result [14] implies that block sensitivity is at most the 4th power of sensitivity for any Boolean function. It remains open if a tighter relationship between sensitivity and block sensitivity holds for arbitrary Boolean functions; the largest known gap between these measures is quadratic [3, 8, 9, 11, 18, 21].

The study of Self-organizing lists deals with the problem of lowering the average-case asymptotic cost of a list data structure receiving query accesses in Non-stationary Environments (NSEs) with the so-called “locality of reference” property. The de facto schemes for Adaptive lists in such Environments are the Move To Front (MTF) and Transposition (TR) rules. However, significant drawbacks exist in the asymptotic accuracy and speed of list re-organization for the MTF and TR rules. This paper improves on these schemes using the design of an Adaptive list data structure as a hierarchical data “sub”-structure. In this framework, we employ a hierarchical Singly-Linked-Lists on Singly-Linked-Lists (SLLs-on-SLLs) design, which divides the list data structure into an outer and inner list context. The inner-list context is itself a SLLs containing sub-elements of the list, while the outer-list context contains these sublist partitions as its primitive elements. The elements belonging to a particular sublist partition are determined using reinforcement learning schemes from the theory of Learning Automata. In this paper, we show that the Transitivity Pursuit-Enhanced Object Migration Automata (TPEOMA) can be used in conjunction with the hierarchical SLLs-on-SLLs as the dependence capturing mechanism to learn the probabilistic distribution of the elements in the Environment. The idea of Transitivity builds on the Pursuit concept that injects a noise filter into the EOMA to filter divergent queries from the Environment, thereby increasing the likelihood of training the Automaton to approximate the “true” distribution of the Environment. By taking advantage of the Transitivity phenomenon based on the statistical distribution of the queried elements, we can infer “dependent” query pairs from non-accessed elements in the transitivity relation. The TPEOMA-enhanced hierarchical SLLs-on-SLLs schemes results in superior performances to the MTF and TR schemes as well as to the EOMA-enhanced hierarchical SLLs-on-SLLs schemes in NSEs. However, the results are observed to have superior performances to the PEOMA-enhanced hierarchical schemes in Environments with a Periodic non-stationary distribution but were inferior in Markovian Switching Environments.

We extend the graceful higher-order basic Knuth-Bendix order (KBO) of Becker et al. to an ordering that orients combinator equations left-to-right. The resultant ordering is highly suited to parameterising the first-order superposition calculus when dealing with the theory of higher-order logic, as it prevents inferences between the combinator axioms. We prove a number of desirable properties about the ordering including it having the subterm property for ground terms, being transitive and being well-founded. The ordering fails to be a reduction ordering as it lacks compatibility with certain contexts. We provide an intuition of why this need not be an obstacle when using it to parameterise superposition.

We present a pairwise learning to rank approach based on a neural net, called DirectRanker, that generalizes the RankNet architecture. We show mathematically that our model is reflexive, antisymmetric, and transitive allowing for simplified training and improved performance. Experimental results on the LETOR MSLR-WEB10K, MQ2007 and MQ2008 datasets show that our model outperforms numerous state-of-the-art methods, while being inherently simpler in structure and using a pairwise approach only.

Natural Language Query Interfaces (NLQIs) have once again captured the public imagination, but developing them for the Semantic Web has proven to be non-trivial. This is unfortunate, because the Semantic Web offers many opportunities for interacting with smart devices, including those connected to the Internet of Things. In this paper, we present an NLQI to the Semantic Web based on a Compositional Semantics (CS) that can accommodate many particularly tricky aspects of the English language, including nested n-ary transitive verbs, superlatives, and chained prepositional phrases, and even ambiguity. Key to our approach is a new data structure which has proven to be useful in answering NL queries. As a consequence of this, our system is able to handle NL features that are often considered to be non-compositional. We also present a novel method to memoize sub-expressions of a query formed from CS, drastically improving query execution times with respect to large triplestores. Our approach is agnostic to any particular database query language. A live demonstration of our NLQI is available online.

Direct trust links among users may be unreliable due to noise. Simple use of these direct trust links may lead to inferior recommend effects, and most of the existed methods don’t consider the difference in trust strength. We propose a novel model called TrustE which combines the trust relationships and users similarity. Specifically, we design a new method called Trust Circuit in TrustE to model trust relationships which calculates trust values by taking into account the asymmetry, transitivity, attenuation, and multiplicity-paths of trusts. Then we calculate user similarity through meta-paths guided embedded representation learning in the heterogeneous information network. Finally, we combine trust value and users similarity to get the personalized numbers of reliable potential friends for each user and make recommendation for target user according to his friends’ preferences. The experimental results on Epinions and Douban datasets verify that TrustE is superior to other existing recommendation methods and it also has high accuracy for cold-start users’ recommendation.

Existing work has shown how an agent’s desire to defer choice may reveal the contingencies she considers relevant to her decision. We explore if this conclusion remains true when preferences are incomplete, that is, when the agent is unable to express a clear ranking among all alternatives. Remarkably we show that the incompleteness of preference does not preclude the existence of a subjective state space; rather it reflects an agent who cannot aggregate the various states she considers possible. An application to social choice and some general results concerning the representation of incomplete but transitive relations are also provided.