Notion Of Equivalence Research Articles

A Unified View on Forgetting and Strong Equivalence Notions in Answer Set Programming

Answer Set Programming (ASP) is a prominent rule-based language for knowledge representation and reasoning with roots in logic programming and non-monotonic reasoning. The aim to capture the essence of removing (ir)relevant details in ASP programs led to the investigation of different notions, from strong persistence (SP) forgetting, to faithful abstractions, and, recently, strong simplifications, where the latter two can be seen as relaxed and strengthened notions of forgetting, respectively. Although it was observed that these notions are related, especially given that they have characterizations through the semantics for strong equivalence, it remained unclear whether they can be brought together. In this work, we bridge this gap by introducing a novel relativized equivalence notion, which is a relaxation of the recent simplification notion, that is able to capture all related notions from the literature. We provide the necessary and sufficient conditions for relativized simplifiability, which shows that the challenging part is for when the context programs do not contain all the atoms to remove. We then introduce an operator that combines projection and a relaxation of SP-forgetting to obtain the relativized simplifications. We furthermore provide complexity results that complete the overall picture.

Towards a geometrical equivalence of norms

Angular equivalence of norms, introduced by Kikianty and Sinnamon (2017), is a notion of norm equivalence that is more attuned to the geometry of the norms. For certain geometrical properties and two angularly equivalent norms, it is the case that if one of the norms has a property, then so does the other. In this paper, we show further results in this direction, namely angularly equivalent norms share the property of non-squareness; and that the exposed points of the unit balls are in the same direction, under the condition that these points are assumed to be smooth with respect to both norms. A discussion on (the angular equivalence of) the dual norms of angularly equivalent norms is also given, giving a partial answer to an open problem as stated in the paper by Kikianty and Sinnamon (2017).

Equivalence for flag codes

Given a finite field Fq and a positive integer n, a flag is a sequence of nested Fq-subspaces of a vector space Fqn and a flag code is a nonempty collection of flags. The projected codes of a flag code are the constant dimension codes containing all the subspaces of prescribed dimensions that form the flags in the flag code.In this paper we address the notion of equivalence for flag codes and explore in which situations such an equivalence can be reduced to the equivalence of the corresponding projected codes. In addition, this study leads to new results concerning the automorphism group of certain families of flag codes, some of them also introduced in this paper.

Stratification of the transverse momentum map

Given a Hamiltonian action of a proper symplectic groupoid (for instance, a Hamiltonian action of a compact Lie group), we show that the transverse momentum map admits a natural constant rank stratification. To this end, we construct a refinement of the canonical stratification associated to the Lie groupoid action (the orbit type stratification, in the case of a Hamiltonian Lie group action) that seems not to have appeared before, even in the literature on Hamiltonian Lie group actions. This refinement turns out to be compatible with the Poisson geometry of the Hamiltonian action: it is a Poisson stratification of the orbit space, each stratum of which is a regular Poisson manifold that admits a natural proper symplectic groupoid integrating it. The main tools in our proofs (which we believe could be of independent interest) are a version of the Marle–Guillemin–Sternberg normal form theorem for Hamiltonian actions of proper symplectic groupoids and a notion of equivalence between Hamiltonian actions of symplectic groupoids, closely related to Morita equivalence between symplectic groupoids.

Translation and Equivalence: An Argumentative Approach

Purpose: This article aims at establishing a dialogue between the Theory of Semantic Blocks (TSB), developed by Ducrot and Carel, and translation theories (the notions of equivalence, skopo, and translators’ role), seeking a possible strategy for solving difficult situations when translating humoristic texts that have polysemy or homonymy relations.
 Methodology: The research methodology involved a literature review, and in the end, a humorous statement containing polysemy was chosen to illustrate how the application of TSB would work in a translation. In this paper, we do not aim to choose the most correct approach but try to match the positive aspects of each one with TSB in order to find strategies that might help translators.
 Findings: We understood that establishing argumentative meaning for enunciates enables a more proper selection of linguistic entities because it is done based on an argumentative equivalence. This study is ongoing. Given its relatively lengthy nature, it may not be applicable in situations requiring simultaneous translation.
 Unique Contribution to Theory, Practice and Policy: However, further investigation could explore its use as a means of assessing the adequacy of written translations. A more comprehensive study is also essential to discover additional ways of streamlining the translator's tasks and to determine if TSB can address various translation challenges across different textual genres. In conclusion, studies like this play a crucial role in expanding the range of possibilities to enhance a translator's work. This enables them to navigate between languages and cultures more confidently, linguistically supported, without the need to remain invisible to be recognized as proficient professionals.

On Covariant and Canonical Hamiltonian Formalisms for Gauge Theories

The Hamiltonian description of classical gauge theories is a very well studied subject. The two best known approaches, namely the covariant and canonical Hamiltonian formalisms, have received a lot of attention in the literature. However, a full understanding of the relation between them is not available, especially when the gauge theories are defined over regions with boundaries. Here, we consider this issue, by first making it precise what we mean by equivalence between the two formalisms. Then, we explore several first-order gauge theories and assess whether their corresponding descriptions satisfy the notion of equivalence. We shall show that, even when in several cases the two formalisms are indeed equivalent, there are counterexamples that signal that this is not always the case. Thus, non-equivalence is a generic feature of gauge field theories. These results call for a deeper understanding of the subject.

Coarser Equivalences for Causal Concurrency

Trace theory (formulated by Mazurkiewicz in 1987) is a principled framework for defining equivalence relations for concurrent program runs based on a commutativity relation over the set of atomic steps taken by individual program threads. Its simplicity, elegance, and algorithmic efficiency makes it useful in many different contexts including program verification and testing. It is well-understood that the larger the equivalence classes are, the more benefits they would bring to the algorithms and applications that use them. In this paper, we study relaxations of trace equivalence with the goal of maintaining its algorithmic advantages. We first prove that the largest appropriate relaxation of trace equivalence, an equivalence relation that preserves the order of steps taken by each thread and what write operation each read operation observes, does not yield efficient algorithms. Specifically, we prove a linear space lower bound for the problem of checking, in a streaming setting, if two arbitrary steps of a concurrent program run are causally concurrent (i.e. they can be reordered in an equivalent run) or causally ordered (i.e. they always appear in the same order in all equivalent runs). The same problem can be decided in constant space for trace equivalence. Next, we propose a new commutativity-based notion of equivalence called grain equivalence that is strictly more relaxed than trace equivalence, and yet yields a constant space algorithm for the same problem. This notion of equivalence uses commutativity of grains , which are sequences of atomic steps, in addition to the standard commutativity from trace theory. We study the two distinct cases when the grains are contiguous subwords of the input program run and when they are not, formulate the precise definition of causal concurrency in each case, and show that they can be decided in constant space , despite being strict relaxations of the notion of causal concurrency based on trace equivalence.

Predictive Monitoring against Pattern Regular Languages

While current bug detection techniques for concurrent software focus on unearthing low-level issues such as data races or deadlocks, they often fall short of discovering more intricate temporal behaviours that can arise even in the absence of such low-level issues. In this paper, we focus on the problem of dynamically analysing concurrent software against high-level temporal specifications such as LTL. Existing techniques for runtime monitoring against such specifications are primarily designed for sequential software and remain inadequate in the presence of concurrency — violations may be observed only in intricate thread interleavings, requiring many re-runs of the underlying software in conjunction with the analysis. Towards this, we study the problem of predictive runtime monitoring , inspired by the analogous problem of predictive data race detection studied extensively recently. The predictive runtime monitoring question asks, given an execution σ, if it can be soundly reordered to expose violations of a specification. In general, this problem may become easily intractable when either the specifications or the notion of reorderings used is complex. In this paper, we focus on specifications that are given in regular languages. Our notion of reorderings is trace equivalence , where an execution is considered a reordering of another if it can be obtained from the latter by successively commuting adjacent independent actions. We first show that, even in this simplistic setting, the problem of predictive monitoring admits a super-linear lower bound of O ( n α ), where n is the number of events in the execution, and α is a parameter describing the degree of commutativity, and typically corresponds to the number of threads in the execution. As a result, predictive runtime monitoring even in this setting is unlikely to be efficiently solvable, unlike in the non-predictive setting where the problem can be checked using a deterministic finite automaton (and thus, a constant-space streaming linear-time algorithm). Towards this, we identify a sub-class of regular languages, called pattern languages (and their extension generalized pattern languages ). Pattern languages can naturally express specific ordering of some number of (labelled) events, and have been inspired by popular empirical hypotheses underlying many concurrency bug detection approaches such as the “small bug depth” hypothesis. More importantly, we show that for pattern (and generalized pattern) languages, the predictive monitoring problem can be solved using a constant-space streaming linear-time algorithm. We implement and evaluate our algorithm PatternTrack on benchmarks from the literature and show that it is effective in monitoring large-scale applications.

Loewner functions for bilinear systems

This work brings together the moment matching approach based on Loewner functions and the classical Loewner framework based on the Loewner pencil in the case of bilinear systems. New Loewner functions are defined based on the bilinear Loewner framework, and a Loewner equivalent model is produced using these functions. This model is composed of infinite series that needs to be truncated in order to be implemented in practice. In this context, a new notion of approximate Loewner equivalence is introduced. In the end, it is shown that the moment matching procedure based on the proposed Loewner functions and the classical interpolatory bilinear Loewner framework both result in κ-Loewner equivalent models, the main difference being that the latter preserves bilinearity at the expense of a higher order.

Applying an Empirical Approach to the Search for Equivalents in Translating Administrative Terms Used in Civil Status Records

Equivalence is a central concept in translation theory, but it is also a controversial one. According to Catford 1965; Nida and Taber 1969; Toury 1980; Pym 1992, 1995, 2004; and Koller 1995, translation is defined in terms of equivalence relations. While some authors develop a theoretical notion of equivalence, others have an empirical approach. Indeed, Toury (1980) identified an empirical use of the term: equivalence could be a descriptive term, denoting concrete objects in two languages and subject to direct observation. This paper adopts Toury’s conception of equivalence. It aims to discuss how equivalence is achieved in translation. To this end, administrative terms found in civil status records are used as examples to show how the search for equivalence is carried out in a real-life situation. Even though administrative divisions’ names may appear normal on birth certificates, death certificates, marriage certificates, etc., searching for their equivalents in translation may pose problems. One of the difficulties is that administrative divisions differ from country to country. Examples cited in this paper consist of administrative terms used in Benin, Nigeria, Ghana, and Senegal. This research takes an empirical approach. Indeed, the search for equivalents in the target language (i.e. English or French) is based on real-life experience and observable data. The findings reveal that source language and target language items rarely have ‘the same meaning’ in the linguistic sense; but can function in the same situation. The contextual meaning of a term is more important in this discussion than the linguistic sense. Equivalence is not only a theoretical notion but also an empirical concept.

On von Neumann equivalence and group approximation properties

The notion of von Neumann equivalence (vNE), which encapsulates both measure equivalence and W^* -equivalence, was introduced recently by Ishan, Peterson, and Ruth (2019). They have shown that many analytic properties, such as amenability, property (T), the Haagerup property, and proper proximality are preserved under von Neumann equivalence. In this article, we expand on the list of properties that are stable under von Neumann equivalence, and prove that weak amenability, weak Haagerup property, and the approximation property (AP) are von Neumann equivalence invariants. In particular, we get that AP is stable under measure equivalence. Furthermore, our techniques give an alternate proof for vNE-invariance of the Haagerup property.

Knowledge Equivalence in Digital Twins of Intelligent Systems

A digital twin contains up-to-date data-driven models of the physical world being studied and can use simulation to optimise the physical world. However, the analysis made by the digital twin is valid and reliable only when the model is equivalent to the physical world. Maintaining such an equivalent model is challenging, especially when the physical systems being modelled are intelligent and autonomous. The paper focuses in particular on digital twin models of intelligent systems where the systems are knowledge-aware but with limited capability. The digital twin improves the acting of the physical system at a meta-level by accumulating more knowledge in the simulated environment. The modelling of such an intelligent physical system requires replicating the knowledge-awareness capability in the virtual space. Novel equivalence maintaining techniques are needed, especially in synchronising the knowledge between the model and the physical system. This paper proposes the notion of knowledge equivalence and an equivalence maintaining approach by knowledge comparison and updates. A quantitative analysis of the proposed approach confirms that compared to state equivalence, knowledge equivalence maintenance can tolerate deviation thus reducing unnecessary updates and achieve more Pareto efficient solutions for the trade-off between update overhead and simulation reliability.

Constructions and equivalence of Sidon spaces

Sidon spaces have been introduced by Bachoc et al. (in: Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press, 2017) as the q-analogue of Sidon sets. The interest on Sidon spaces has increased quickly, especially after the work of Roth et al. (IEEE Trans Inform Theory 64(6):4412–4422, 2017), in which they highlighted the correspondence between Sidon spaces and cyclic subspace codes. Up to now, the known constructions of Sidon Spaces may be divided in three families: the ones contained in the sum of two multiplicative cosets of a fixed subfield of mathbb {F}_{q^n}, the ones contained in the sum of more than two multiplicative cosets of a fixed subfield of mathbb {F}_{q^n} and finally the ones obtained as the kernel of subspace polynomials. In this paper, we will mainly focus on the first class of examples, for which we provide characterization results and we will show some new examples, arising also from some well-known combinatorial objects. Moreover, we will give a quite natural definition of equivalence among Sidon spaces, which relies on the notion of equivalence of cyclic subspace codes and we will discuss about the equivalence of the known examples.

Program equivalence in a typed probabilistic call-by-need functional language

We extend a call-by-need variant of PCF with a binary probabilistic fair choice operator, which makes a lazy and typed variant of probabilistic functional programming. We define a contextual equivalence that respects the expected convergence of expressions and prove a corresponding context lemma. This enables us to show correctness of several program transformations with respect to contextual equivalence. Distribution-equivalence of expressions of numeric type is introduced. While the notion of contextual equivalence stems from program semantics, the notion of distribution equivalence is a direct description of the stochastic model. Our main result is that both notions are compatible: We show that for closed expressions of numeric type contextual equivalence and distribution-equivalence coincide. This provides a strong and often operationally feasible criterion for contextual equivalence of expressions and programs.

Equivalence in Argumentation Frameworks with a Claim-centric View: Classical Results with Novel Ingredients

A common feature of non-monotonic logics is that the classical notion of equivalence does not preserve the intended meaning in light of additional information. Consequently, the term strong equivalence was coined in the literature and thoroughly investigated. In the present paper, the knowledge representation formalism under consideration is claimaugmented argumentation frameworks (CAFs) which provide a formal basis to analyze conclusion-oriented problems in argumentation by adapting a claim-focused perspective. CAFs extend Dung AFs by associating a claim to each argument representing its conclusion. In this paper, we investigate both ordinary and strong equivalence in CAFs. Thereby, we take the fact into account that one might either be interested in the actual arguments or their claims only. The former point of view naturally yields an extension of strong equivalence for AFs to the claim-based setting while the latter gives rise to a novel equivalence notion which is genuine for CAFs. We tailor, examine and compare these notions and obtain a comprehensive study of this matter for CAFs. We conclude by investigating the computational complexity of naturally arising decision problems.

On the reduction of the topological classification of gradient-like flows problem to the classification of polar flows I. A. Saraev

In this paper we consider a class G(Mn) of gradient-like flows on connected closed manifolds of dimension n≥4 such that for any flow ft∈G(Mn) stable and unstable invariant manifolds of saddle equilibria do not intersect invariant manifolds of other saddle equilibria. It is known that the ambient manifold of any flow from the class G(Mn) can be splitted into connected summ of the sphere Sn , gft≥0 copies of direct products Sn−1×S1 , and a simply connected manifold which is not homeomorphic to the sphere. The number gft is determined only by the number of nodal equilibria and the number of saddle equilibria such that one of their invariant manifolds has the dimension (n−1) (we call such equilibria trivial saddles). A simply connected manifold which is not homeomorphic to the sphere presents in the splitting if and only if the set of saddle equilibria contains points with unstable manifolds of dimension i∈{2,…,n−2} (we call such equilibria non-trivial saddles). Moreover, the complete topological classification was obtained for flows from the class G(Mn) without non-trivial saddles. In this paper we prove that for any flow ft∈G(Mn) the carrier manifold can be splitted into a connected sum along pairwise disjoint smoothly embedded spheres (separating spheres) that do not contain equilibrium states of the flow ft and transversally intersect its trajectories. The restriction of the flow ft to the complements to these spheres uniquely (up to topological equivalence and numbering) defines a finite set of flows ft1,…,ftl defined on the components of a connected sum. Moreover, for any j∈1,…,l , the set of saddle equilibria of the flow ftj consists either only of trivial saddles or only of of non-trivial ones and then the flow ftj is polar. We introduce the notion of consistent topological equivalence for flows ft1,…ftj and show that flows ft,f′t∈G(Mn) are topologically equivalent if and only if for each of these flows the set of separating spheres exists that defines consistently topologically equivalent flows on the components of the connected sum.

Elton's near unconditionality of bases as a threshold-free form of greediness

Elton's near unconditionality and quasi-greediness for largest coefficients are two properties of bases that made their appearance in functional analysis from very different areas of research. One of our aims in this note is to show that, oddly enough, they are connected to the extent that they are equivalent notions. We take advantage of this new description of the former property to further the study of the threshold function associated with near unconditionality. Finally, we make a contribution to the isometric theory of greedy bases by characterizing those bases that are 1-quasi-greedy for largest coefficients.

Equivalence in Bilingual Dictionaries: Types, Problems and Criticism

This article has set out some of the major issues related to the composition of bilingual dictionaries, namely their functional aspect which helps determining the nature of the intended book, either reception-oriented or production oriented, depending on the type of audience to whom this work is to be presented. After that, the notion of equivalence started taking its position as being the central point of this paper. This latter was gradually reflected. That is to say that the analysis began with word class equivalence, and then it developed to deal with those consisting of two or more words (collocations), to arrive after that to those with longer lexical combinations through relying on different ideas and points of view by theorists descending from different cultural and linguistic backgrounds with different ideas and points of view. Most of them went even further to discuss its subtypes, as called by Heming Yong and Jing Peng, or its degrees as proposed by Monia Bayar 2007. This has led to another level of discussion, i.e. the criticism of some ideas that seemed illogical, especially that carried on zero equivalence, categorical correspondence and others. As I proceed, the discussion has moved to another level. That is of enquiring multiple methods and techniques used to provide naturally sound equivalents with respect to the disparities between languages.

Observational Equivalence of Conditional Belief Bases

In nonmonotonic reasoning, a conditional of the form ‘If A then usually B’ is typically accepted if a situation where both A and B hold is deemed to be more plausible, more probable, or less surprising, etc., than a situation where A holds, but B does not hold. In a propositional setting, this leads to a relation on the propositional interpretations, also called worlds, by comparing worlds according to their plausibility. In this paper, we address the question of which kind of relations on the set of worlds can be obtained by completing a conditional belief base via an inductive inference operator. As a key concept for our investigations, we introduce and employ the notion of observational equivalence of belief bases that takes an inductive inference operator and a set of queries into account. This leads to the notion of the observational normal form (ONF) and, by focussing on so-called base conditionals, to the base conditional normal form (BCNF). The acceptance of base conditionals corresponds to the plausibility ordering on possible worlds induced by an inference method. Both normal forms ONF and BCNF are combined with renamings as an additional dimension. We establish the interrelationships among the normal forms and evaluate them empirically with respect to systematically generated belief bases.

Integrating museum studies into translation studies: towards a reconceptualization of the source text as sensory experience in museum audio description and the notion of experiential equivalence

ABSTRACT This article focuses on museum audio description (AD) as a modality of intersemiotic translation (IT) primarily addressed to people with visual impairments. Still at an early stage of development in terms of both academic research and professional practices, museum AD lies at the crossroads of a variety of disciplines, such as translation studies (TS) and museum studies (MS). The aim of this contribution is to suggest a reconceptualization of traditional notions in TS (source text and equivalence) in the context of museum AD and encompassing the translational phenomenon per se. Theoretical considerations from MS and specific guidelines for museum AD practices will offer cross-disciplinary insights to redefine such concepts and reflect upon translation as a semiosic process in which meanings are created, rather than transferred. This article suggests the coincidence in AD of source and target texts as sensory experience and puts forth the concept of experiential equivalence.