Quantum Theory and the Nature of Search
Quantum Theory and the Nature of Search Sachi Arafat and C.J.van Rijsbergen
Department of Computer Science
University of Glasgow,UK
Abstract
The conceptual model and mathematical formalism of quan-tum theory are employed in creating a novel framework for modeling the computational search process addressing problematic issues that restrict information retrieval research.
Mapping the mathematical formalism of search to that of quantum theory presents insightful perspectives about the na-ture of search.However,differences in operational semantics of quantum theory and search restrict the utility of the map-ping.An approach is suggested for resolving these semantic differences aiming toward a sound mathematical and concep-tual framework for search inspired by quantum theory.
Introduction
Information retrieval(IR)is the the?eld of research investi-gating the searching of information in documents,searching for documents themselves,searching for meta-data which describe documents,or searching within databases,whether stand-alone or datasets networked by hyper-links such as the Internet,for text,sound,video,images or other types of data. An IR system is commonly understood as that which deals with the relationship between objects and queries.Queries are formal statements of information needs addressed to an IR system by the user.The object is an entity which stores information in a database,known as a https://www.wendangku.net/doc/306562990.html,er queries are matched to documents stored in a database.Of-ten the documents themselves are not kept or stored directly in the IR system,but are instead represented in the system by their pointers.Automated information retrieval systems were originally used to manage information explosion in sci-enti?c literature in the last few decades.The value of infor-mation is directly related to its ability to be located and used effectively,search engines thereby form a crucial compo-nent in the research and understanding of modern times.For something so crucial,IR can be a confusing area of study. Firstly,there is an underlying dif?culty,with the very def-inition of IR,since there exists the adjacent?elds of doc-ument retrieval,text retrieval,information seeking,infor-mation science,information management and others each with their own bodies of literature,theory and technolo-gies which are deeply related to IR and each other to the Copyright c 2007,American Association for Arti?cial Intelli-gence(https://www.wendangku.net/doc/306562990.html,).All rights reserved.point where the boundaries are unclear.Secondly,IR is a broad interdisciplinary?eld,that draws upon secondary ?elds such as cognitive science,linguistics,computer sci-ence,library science and it does so in a loosely organized fashion.It is tempting to refer to this conjunction of di-verse areas as“search science”,however,due to the pres-ence of ad-hoc techniques used to perform experimentation in IR and the absence of a(general)formal language for de?nition of IR concepts,components and results,it can-not be called a science.Furthermore,there are no speci?c de?nitions of search.With the abundance of methods avail-able for?nding information,whether through computer ap-plications,libraries/librarians,a combination thereof or oth-erwise,a formal de?nition would need to accommodate a process far more complex than that of traditional web-based querying through systems like Google.The lack of a gen-eral formal speci?cation method for search processes,IR re-search,and the absence of strict a scienti?c method under-pinning it,has posed major barriers to future development and usefulness of research in the?eld(Arafat,van Rijsber-gen,&Jose2005).
Recent work in(van Rijsbergen2004)based on ideas bor-rowed from quantum theory(QT)has suggested methods of formalizing aspects of IR aiming toward a comprehensive theoretical basis in which a search process can be completely de?ned and reasoned about,and a scienti?c basis inspired by operational methods in QT.It was subsequently found that there is a potential for QT methods to play a wider role in resolving the above IR issues(of de?nition and lack of sci-enti?c method)than suggested.In addition,it was found that apart from the mathematical formalism of QT which of-fers analytical tools convenient for representing IR concepts, the scienti?c method and operational structure(the way QT employs states and state changes)is also very useful.In-spired by these peculiar connections and on attempting to apply these methods and map search to QT,it was found that search requires to be re-examined from a perspective quite different from how it is traditionally perceived(see (Arafat,van Rijsbergen,&Jose2005))in order to deduce the feasibility,utility and method of the mapping.Thinking about search in this new way also suggests approaches for re-de?ning the concept of search.The overall goal for our research can be equated to being able to formally refer to IR as“search science”by establishing a speci?c de?nition of
search and deducing scienti?c methods for the investigation of search,so it can be in all respects,a science.
This paper highlights the nature of the search process and the main problems responsible for IR research being in its current non-ideal state.An outline is given of current work on employing QT to address one of these problems proceed-ing with an approach to resolve the other causes.In the next section,with reference to the traditional laboratory per-spective of IR(Ingwersen&Jarvelin2005),the nature and scope of the the evaluation problem and user problem are discussed.Both these problems are dependent on the de?-nition problem,which therefore needs to be addressed?rst. The laboratory view of search is a hindrance to adequate conceptualizations of these problems,thus an alternate view is suggested.The stack model provides this view enabling the visualization of the interaction of different research ar-eas,with the advantage that the de?nition,evaluation,and user problems can be visualized in terms of the model.The section‘A New Perspective’concludes with details of all the key problems particularly elaborating the conceptual prob-lem of de?ning search and with that resolved the section ‘The Middle Form’outlines a scienti?c method for IR us-ing the stack model.Further bene?ts of adopting QT con-cepts for IR are also presented.Our approach to solving the research problems in IR with inspiration from QT raises several new and interesting questions,suggesting changes in the method of experimentation,and re-de?ning boundaries between related research areas.
Background
The traditional model of a search process is depicted by Fig-ure1and still applies to most search systems,see(Ingw-ersen&Jarvelin2005).In order to search a data set,the documents in the set must?rst be indexed.The index is the same data set reduced to contain just the information (collection of words,media,and any metadata)about the set required to represent the collection of documents suf?-ciently according to a document model.Queries expressed by the user are interpreted according to a query model.A matching sub-process follows which takes the query and for each document assigns a value to the association between the interpretation of that query and the interpretation of the document according to their respective models.This asso-ciation is termed relevance and can be de?ned in a multi-tude of ways(Mizzaro1997).The results of the match-ing process are manipulated and shown to the user accord-ing to an interface model which is outside the scope of the laboratory model.For a simple list interface like that of Google,the results are ordered according to matching val-ues,so that documents deemed most relevant to the query appear higher than the less relevant ones.Unlike Google there are search engines which allow the user to in?uence the matching sub-process by feedback.The user feedback ex-pressed through the interface is known as relevance feedback and facilitates learning of user interests.A search system is evaluated according to its effectiveness and computational ef?ciency.The effectiveness of a search system is usually deduced on analysis of two features,its ability to correctly associate query&document(to judge relevance)and to ad-
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Figure1:Data?ow in the Laboratory model
equately present results on the interface.Effectiveness of a set of relevance judgments is traditionally deduced using
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measures(RET is the number of documents retrieved and RELRET is the number of previously judged relevant documents found in RET)to compare against prior human judgments on the same queries and in the same document collection,the majority of eval-uation experiments are performed this way.The method of evaluating result presentation,or interface models are equiv-alent to human-computer interaction evaluations employing questionnaires and usage log analysis.IR research tends to focus on improving the effectiveness of relevance judgments by the creation of novel models for individual components or methods for combining different models.To test a new measure for matching a query to documents,one would se-lect a test collection of previously collected user judgments and run precision/recall experiments for queries in the col-lection to deduce effectiveness.There are several problems to evaluation done this way,?rstly,conclusions to such an experiment are very subjective as they are limited to the scope of the test collection and to the context(factors in?u-encing human perception of information)dependent view-points of prior human judgments.Secondly,there are no de?nitive ways,in general,to deduce why one system per-forms better than another since prior user judgments assess the system view of relevance;and are informal opinions of the whole system not speci?c formal reasons attributed to particular components.The latter problem is inescapable when using human judgments.In order to further under-stand experimental results from test-collection based evalu-ation,one runs complementary live user-based experiments where users are given tasks to complete on a search sys-tem with effectiveness being judged using statistics on ques-tionnaires and usage logs.An inherent weakness is that an experiment cannot be duplicated even if the same users are retained since their context changes.Thus the experimental results are not de?nitive.Indeed such problems are inher-ently due to the human factor,and will be referred to as the evaluation problem.
Unlike relationships between components in a physical system such as in Figure2which are made apparent through a prior theoretical framework,IR research does not exhibit general frameworks to deduce such relationships between its components.In the physical system the effect of modi-fying one parameter on other parameters can be predicted, in an IR evaluation the user is a parameter but there are no ways to determine the effect of its modi?cation on the eval-
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Figure2:Simple physical model with underlying theory
uation.Since there are no formal methods to relate users, the potential effect on user judgments of modifying a com-ponent,is generally too unpredictable relative to the phys-ical case,prior to experimentation.An approach for creat-ing theoretical apparatus for IR with the ability to formally compare components would need to tackle the user issue, since concepts of effectiveness of a search system are in-evitably tied to user de?nitions.If instead there were a way to work with formally speci?ed abstract users which approx-imate real users then experiments can be duplicated and ver-i?ed.The problem would then be one related to the effec-tiveness of the approximation ability of abstract user mod-els.With an accepted user model,the abstract user would then be a controllable experimental factor.However,there are no general formal methods for abstracting user behav-iors for creation of abstract user speci?cations,and it is not common practice in IR research.Instead the research liter-ature uses brief and informal natural language descriptions for users,i.e.“the users are university students with moder-ate experience in searching”.A practical advantage of for-mal speci?cation is that it would allow relatively economical user simulation type experiments and provide(see(White et al.2005))de?nitive results for a speci?c user speci?cation which can then be veri?ed.With formal speci?cation the ef-fectiveness of a search engine can be identi?ed with speci?c user types and evaluation results can be reasoned about in terms of the user speci?cations.
A user cannot be de?ned out of context,and is strongly coupled to a set of user-system interactions,and an inter-face.Unfortunately the interface and the user-system inter-actions components are usually only speci?ed in informal natural language expressions.Overall,there is no way to formally specify an IR experiment in its entirety.As a result there is no way to formally reason about evaluation results with respect to the interface and interactions.Traditionally, only the document,query and matching models(Figure1) are formally speci?ed and admit several formal speci?ca-tions.For example,the association between a document and query termed relevance can be represented in terms of logical implications,conditional probabilities or inner prod-ucts in a vector space.Unfortunately there exists no uni-?ed framework for theoretically comparing between differ-ent representations in terms of effectiveness.These prob-lems with de?ning users,interface,user-system interaction, and the inability to compare different formal representations where they exist,hinders research as it severely limits the-oretical conceptualizations of search scenarios and deduc-tions therein.In comparison the simple physical system allows many degrees of freedom for devising hypothetical extensions to already speci?ed scenarios,such as extending Figure2with two balls and many walls.De?nition problems apply not only to specifying a search scenario but also to the
Figure3:Dependence of Research Problems
relationships between the IR research?eld and neighboring ?elds as stated in the introduction.
The research problems discussed above can be grouped into three broad categories.Firstly there is an inability to verify experimental results in IR and other issues related to evaluation,these shall be collectively known as the evalu-ation problem.Secondly,the evaluation problem is related to inability in formally specifying users,which will be de-noted as the user problem.Finally,the de?nition problem denotes issues with formally de?ning all components,their inter-relationships,theoretically reasoning about them and the relationships of IR as a?eld with other?elds.Resolu-tion of the user and evaluation problems depend on the reso-lution of the de?nition problem.A fourth problem yet to be discussed is the conceptual problem which is addressed in the proceeding section completing the relationship between our research problems as illustrated in Figure3where the arrows denote dependence.The dependency between re-search problems is not formally provable on a general level, the?gure serves only to illustrate reasonable relationships as per common experience in IR research.It is at the same time interesting and unfortunate to note that due to the def-inition problem it is dif?cult to present without ambiguity these above research problems in a formal way,whether in a mathematical formalism or using formal natural lan-guage statements.The stack model of the proceeding sec-tion provides a new perspective of a search process that re-duces some of the ambiguity.The four categories of prob-lems appear to suf?ciently abstract the issues faced in our initial research,which in hindsight attempted to resolve the de?nition problem.Initially a part of the de?nition prob-lem was addressed to suggest a uni?ed theoretical basis for comparison between different types of document,query and matching models which had a variety of formal speci?ca-tions.Such was one of the goals of(van Rijsbergen2004) which showed that mapping of three types of these mod-els,the vector-space,probabilistic and logical models to the mathematical formalism of Hilbert spaces in the way em-ployed by quantum theory results in a single framework in which one is able to theoretically compare among models, providing greater opportunities for formal analysis than pre-viously available.One important aspect not elaborated in (van Rijsbergen2004)was that of modeling relevance feed-back in the QT formalism.In an attempt to model relevance feedback in the Hilbert Space formalism of quantum me-chanics a new set of problems were faced and interesting questions raised which collectively suggest novel inquiries about the nature of IR.
A New Perspective
Our approach to resolving the de?nition problem for docu-ment and matching models (as in (van Rijsbergen 2004))us-ing QT required an alternative conceptualization of a search process,in terms of states of the search engine and their transformation over the course of a search session.In terms of states and state changes,if the documents and their cor-responding relevance judgments (deduced from relevance feedback in the search session)are to be de?ned as the state of the search engine then relevance feedback corre-sponds to the evolution of the state.The simplest mapping of a document and matching model to the quantum theoretic Hilbert space is the trivial map of the vector space model in IR where documents d i are represented as vectors with co-ordinates d ij ∈R with values denoting the in?uence of the respective word in the document.In such a mapping each document vector |d i is a possible state of the search engine,and the document with only one term a pure state.The state of a search process can be represented as the mixture state ρ= i ∈|Doc |w i |d i d i |where the w i are relevance val-ues.It can also be represented as a superposition of docu-ment vectors,and in other forms.Therein lies a critical issue which will be alluded to in the proceeding section:What is the best way to represent the state of a search system?
The QT Hilbert space presents some new mathematical features which are useful for modeling details about the state of search.For example the in?uence of a word in a docu-ment is often denoted by the product of the word frequency within the document with its rarity among the collection of documents.In the Hilbert space these features of a word need not be amalgamated into a real-number product and can instead separately ‘stored’in complex number co-ordinates,which would increase the analytical power of the represen-tation of state.The reason for this is that keeping these term features separate would not decrease the analytical power of representation,as the traditional representation of terms can be established by multiplying the weights.Thus the ana-lytical power is at least the same.As the semantics behind the weights,frequency and rarity,are different concepts,it is useful to keep them separate for addressing research in-quiries about document models with respect to one param-eter and then comparing to inquiries pertaining to the other parameter.Also consider the way a real and complex num-ber are semantically related when used to represent concept pairs like amplitude and frequency of a wave.There is a striking similarity between these pairs and the pair word fre-quency and word rarity,for a term.The frequency of a term in a document is like amplitude (within that document),and its ‘rarity’or ‘inverse document frequency’is its frequency,like that of a wave.Whether there lies any bene?t in explor-ing these relationships between the representation of a term in a collection and an electric signal among a set of signals,is open to research.Finally,the argument of a complex num-ber r.e iθhas some simple mathematical structure pertaining to symmetry,which can be exploited to relate the rarity val-ues of terms (further elaboration is outside the scope of the paper).Thus,using complex numbers increases the analyt-ical power of term representation suggesting an area of in-
vestigation in itself.
With the trivial map of the vector space model to the QT formalism there are many mathematical features that present interesting analytical possibilities for analysis of hypotheti-cal search processes.The dif?culty stems from representing any concept of dynamics.On the mathematical level a set of transformation matrices applied to the state represented by a density matrix ρ,would update it to a succeeding state UρU ?1.However what is the method for deducing trans-formation matrices?One can map the traditional method of relevance feedback in the vector space model which is a low-level approach,it involves keeping a ideal query vector and updating it on relevance feedback according to a sim-ple learning function.There are many interesting opportu-nities to do such mappings and corresponding mathematical manipulations in the Hilbert space which could upgrade the traditional low-level feedback within an elegant geometrical framework (see (van Rijsbergen 2004)).These opportuni-ties present initial advantages of mapping to a QT formal-ism,and are due only to the mathematics.How can one create transformation matrices at a higher level?Physical systems have underlying theory,or at least universal facts embedded in its design such as ideas about energy,which attach semantics to a state and allow characterization of its change according to the theory.The theory is used to deduce change operators which are used to for predicting physical events.For a search process state containing relevance judg-ments,state change would mean a change in the values of these judgments.General interests of the user can be de-duced through feedback,and while one can devise machine learning (or otherwise)models for predicting future interests on the low-level there are no general underlying higher-level principles.Any such underlying principles useful for pre-dicting change in user interests would need to model user behavior thereby requiring to address the user and de?nition problems.There are several questions raised in the pursuit of conceptualizing a search process in terms of states and state changes.In QT the evolution operators can have physical meaning and are rich in algebraic and geometric properties,for example a group structure for a set of unitary transforma-tions.What could be corresponding mathematical properties for relevance feedback operators,and what would,for exam-ple,a group structure for a set of feedbacks mean in terms of search concepts?These type of inquiries are inherent in the state based conceptualization of QT and its mathemati-cal formalism.There are no IR frameworks which inquire in this way.IR does not offer a general method to answer these inquiries,especially those about a higher-level approach to relevance feedback without ?rst resolving the user and de?-nition problems.
Stack Model
There are paradigmatic differences between QT and IR in their operational methods and semantics as discussed above.It is clear that the mapping to QT has mathematical bene-?ts,with features like complex numbers and algebraic struc-tures on the Hilbert space but it is unclear as to how one can use the QT formalism,what QT concepts cannot be used and most importantly what some QT concepts correspond-
ing to the formalism(such as algebraic structure)mean in IR terms.A bottom-up approach would be to assess the bene?ts of each feature of the QT framework individually,however it is dif?cult to deduce IR meanings for IR models created in a QT formalism.Instead a top-down approach is attempted
with the premise that the apparent paradigmatic differences between IR and QT can be reduced if one no longer thinks of a search process in the traditional sense,according to the laboratory model,but instead in the way QT would perceive a process,as a physical process.The search process can be abstracted as a physical process in which there are a set of interactions between two physical systems,the user and sys-tem.The stack model in Figure4is a visualization inspired by this perspective and is visually equivalent to a traditional network architecture diagram illustrating the design of the protocol of communication between two agents.It corre-sponds to a design method for visualizing arbitrary search scenario designs.Stack labels and slices are according to the purpose of a scenario design.For example in an inves-tigation focusing on document/matching models which is at the memory/reasoning level,one may not need to discern between the gestures and physical layers,combining them instead.The stacks method of design is unlike the laboratory model,since it freely includes(by design)other aspects of the user and system,including as in Figure4,the interface (gestures layer),hardware(physical layer),search strategy (session layer)and also details the user.According to Fig-ure4a user interacting with a system involves a reasoning sub-process instigated by the memory layer,which then in-?uences a search strategy(session layer)and activates corre-sponding gestures expressed by the physical layer represent-ing their physical expression tools.The system in Figure4 setup with the same design,observes the user’s physical ac-tion,interpreting a gesture in the context of other factors (such as prior user feedback)and updating its notion if user interests(memory)according to a user-interest update policy (reasoning).Memory and reasoning layers in the stack cor-respond respectively to the document and document model in the laboratory model.In the stack design a search pro-cess is a set of sub-processes either between agents which is of type observational or between components within an agent which are of two types expression and interpretation; these are common principles for any stack based model of a search process.The sub-process of type expression de-notes a general?ow of activity toward the memory level, it corresponds to one set of changes that are internal to an agent upon another agent interacting with it.The other set of changes internal to an agent are those that lead it to re-act to the prior interaction,these changes are of the expres-sion type and generally?ow from the memory layer toward the agent’s expressive faculty,the interface,denoted by the physical layer.By a‘?ow’of changes it is meant a set of effects which end at a destination(i.e.the memory layer for interpretation?ows)and are caused by entities in a preced-ing layer with the order corresponding to the type of?ow (see Figure4).
Stack design is a shift in the traditional conceptualization of IR toward the state-based conceptualization for physical systems in QT.It was inspired by the QT way of abstract-
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Figure4:A Stack Model
ing physical sub-systems and their relationships.In terms of the physical semantics of QT,each layer is a physical sub-system and can only directly in?uence adjacent sub-systems which preserve the order inherent in search systems.The stack model does not presume any speci?cation language for any layers.A clearer relationship between the user,de?-nition and evaluation problems can be observed when these problems are in terms of the stack visualization.First,as the research in(van Rijsbergen2004)shows,the mathemat-ical formalism of QT can be used as a language for mod-eling document and matching models,corresponding to the memory layer and reasoning layers;although a QT speci?-cation of the reasoning in a search engine is theoretically limited due to the relevance feedback issue(as discussed previously).Second,retrieval research provides no general frameworks for modeling interfaces and interactions,thus the gestures and session(containing search strategies)lay-ers have no general modeling language.Similarly on the user side there are no general modeling languages for any aspects.Instead the literature of IR and related disciplines provide several speci?c models for each layer often speci-?ed in natural language form,making it dif?cult to compare models theoretically.Hence the de?nition problem for IR on which the user problem depends is that of having sev-eral models speci?ed in different languages for each layer of each agent and no analytical way to compare between them.It is clear that there requires to be a methodology for modeling corresponding to the visual stack diagram.An ad-equate formalism for specifying each layer,inter-layer com-munication and between agent communication need to be deduced;this corresponds exactly to the de?nition problem and is addressed in the next section following a discussion of the conceptual problem on which it is dependent.
Modeling of Diverse Scenarios
Unlike in traditional IR research,the stack design is used to model the evaluating agent,and hence the evaluation process itself as illustrated in Figure5.The practice of modeling the measurement device in QT inspired this way of using stacks. An information seeking process is one which considers the broader experience of the user in the search process which can involve more agents,and possibly human agents.An ex-ample would be the case of a user interacting with librarians, automated search systems and other agents in a library.The information seeking process is easily visualized by adding more stacks to the design of the typical information retrieval model of two stacks.A distributed search scenario such as
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Figure 5:Model of an Evaluation
in peer-to-peer searching or searching through multiple in-dexes representing an intranet,can also be visually depicted in the same way by a set of stacks.
In conclusion,our attempt at resolve the de?nition prob-lem for document and matching models (as initiated in (van Rijsbergen 2004))led to a different way of thinking about a search process,in terms of a stack design,which admits a visual description (Figure 4).It also created questions about high-level models of change based on relevance feedback,and about semantic mappings between QT and IR which are necessary for interpreting mathematical manipulations on the QT formalism.Inquiries about paradigmatic differ-ences between QT and IR are due to the conceptual prob-lem which is addressed in the next section.Addressing the de?nition problem (hence user and evaluation problems)is the same task as creating a formal framework corresponding to the stack visualization in which it is possible to deduce how and when one can use the QT formalism (or any other)for modeling components of a search process,i.e.relevance feedback.
The Conceptual Problem
The stack model depicts a search process as a physical pro-cess,a set of interactions between two or more physical sys-tems through subprocesses of the observation,interpretation and expression types.On a higher level the depiction is that of a communication process between agents.What then dif-ferentiates a search process from any other communication process?Is it that the system interface,as would be repre-sented by the gestures and physical layers is a search engine interface?What constitutes a search interface,is not the user always searching for something whether implicitly or other-wise?For example a user using any interface can be said to be searching for results of his interaction -instead of formal documents.This line of inquiry can be reformulated in the low-level language of interaction between physical systems:what is peculiar about the physical process in which search is done and any other physical process?What is search?This is the conceptual problem for IR on which the de?nition problem depends since to de?ne search,a search interface and other components,it is required to lay down principle interpretations about a search process.
Resolving the Conceptual Problem
The conceptual problem in Figure 5must be initially ad-dressed as all other problems depend on it.Initially we make some observations which illustrate the conceptual problem and then proceed to resolve it.First,it is important to realize
that relevance feedback can be implicit,any interaction with a search system is a relevance feedback.Second,a search interface is not necessarily explicit,and can be de?ned as an interface by which a user’s cognition is in?uenced,which thereby includes any interface that can be sensed assuming any sensory activity modi?es cognition in some way.As ex-empli?ed by information seeking,a user does not require a computerized search engine to search,any interaction with another human or agent is also search.Hence any commu-nication process is a search.Generalizing further in terms of the stack model,in any agent an internal sub-processes (of type expression or interpretation)which is an interaction between any two layers is a search process.Finally,any process in which change occurs is a search process.It is assumed that every physically existing process has change occurring in it,however insigni?cant,until it ceases to exist.It is also assumed that an abstract process,one not directly physically existing,exists indirectly,as it requires the ex-istence of physical processes to express it.For example,a mathematical description of a process is an abstract descrip-tion which can only exist when expressed,either in the mind of a mathematician by physical cognitive processes or in physical reality.Thus every process,physical or abstract is a search process.De?ning information as that which causes representations to change (see (Mackay 1969)),it is deduced from prior statements that every process can potentially ac-cept information.In terms of this de?nition and the stack model,the directed sub-processes in Figure 4denote infor-mation ?ow .
A common supposition of IR research is that the purpose of users interacting with a search engine is to ful?ll their in-formation need (IN).In light of current discussion,a user can never ful?ll the IN associated with him,as he is de?ned by a set of physical processes which exist as long he does,meaning that the user is always ready to accept information and therefore always has an IN.The concept of IN applies unambiguously to all agents,with information de?ned as in (Mackay 1969)since all agents change over time.Agents have a potential to change therefore have an IN meaning that the IR system has IN according to the generalized def-inition of IN and not in the traditional sense.All processes change over time,and are therefore search processes.De?n-ing information and search in this way directly addresses the conceptual problem.The de?nition problem now has a much larger scope,instead of referring to traditional com-puter based search it now refers to any process.This allows one to try any pre-existing formalisms for de?ning processes whether it be QT methods for de?ning physical processes or otherwise.Previously,aspects of IR were being mapped to QT for certain mathematical,and some operational bene?ts,now,since a physical process and a search process are de-?ned as the same thing,there are no conceptual problems to the mapping.The de?nition problem otherwise remains the same.
The Concept of Relevance
Relevance is a label and a reason attached to a particular set of changes.In a traditional search process a user is ex-pected to interact with some items,the semantic of these in-
teractions can be embedded in the interface,i.e.the Google ranked list where higher rank indicates increased likeliness of relation to the given query.The reason a user interacts with a particular item,such as a document link in the search results which are presented as a ranked list is complicated and uncertain as it pertains to user cognition.It is usually assumed that the user interacted with an element as they thought it was‘relevant’,or at least that they thought their interaction was‘relevant’.Thus,the word‘relevant’can be taken as a primitive,replacing otherwise complex descrip-tions of reasons for user interaction.In our approach where the user is modeled as an agent,one can state the reason for an interaction,in terms of the stack entities,changes within them,and in?uences between them.Upon a set of user inter-actions,the user interest as a general concept,is to be deter-mined from the‘relevant items’which have been involved in interaction.The word‘relevance’is assigned as a label for the general concept of user interest.Thus the words‘rele-vant’and‘relevance’are labels referring to complex reasons and concepts(respectively)pertaining to user cognition.The labels can be formally de?ned in terms of particular user models.However,these labels are not particularly impor-tant,as we have a formally de?ned arti?cial user agent,so those complex reasons/concepts referred to by these labels are well de?ned in our https://www.wendangku.net/doc/306562990.html,er interest is used in the de?nition of the user agent and is inscribed in the de?ni-tions of individual entities and their inter-relationships.One can still refer to arti?cial agents interacting with relevant data or make statements like“an arti?cial agent’s concept of relevance has changed”except now these statements can be re?ned in terms of the stack https://www.wendangku.net/doc/306562990.html,rmation need with respect to the user agent,retains its traditional meaning in our framework,changes of IN are not described in terms of concepts of relevance but in terms of the stack model,which in turn can be translated(see next section)into statements using the terms‘relevance’or‘relevant’.
Role of Quantum Theory
In the new conceptual model,every process is a search pro-cess,what is then the role of QT?Firstly,the operational methods of QT inspired the stack design to allow thinking about search in terms of states and state changes.Second, the QT formalism can be used to specify the memory and reasoning layers for the system,and the user in a simple user model as in(Aerts&Gabora2002).The main problem with the mapping of change in document/matching models was that while QT is associated to physical theories which it can use to create evolution matrices and give meaning to them, IR has no such high-level theory-and in order to have such a theory,one would need to?rst resolve the user and de?-nition problems.A speci?cation language is then required in which a user can be de?ned with respect to other compo-nents.It must be a single language for describing all layers of the stack in Figure4and their inter-relationships.We deduced a language of?ows/changes(information?ows) general enough to completely specify components during search.However for such a general language to be of use it must admit translations into other languages.A complete speci?cation of the language of?ows is outside the scope of this paper,a brief account proceeds the current section.A third role of QT is its semantics or physical theory,as our general speci?cation language uses the physics semantic of energy for assigning general meanings to changes.Recalling from the introduction,the aim is to create a search science. Search is now de?ned and the science is the topic of the next section.
The Middle Form
The language of?ows is a typed language corresponding to the stack,it is a‘middle form’borrowing ideas from QT to model IR.A search process is speci?ed by a number of agents,who are in turn speci?ed by their component stack. To each process belongs a set of?ows(changes)and a set of states,which are de?ned in formal natural language in terms of other components as necessary.The challenge is then to translate each?ow and state description to a language which admits the desired theoretical framework.With a fur-ther abuse of terminology,the following terms are equated:a ?ow,‘?ow of energy’,potential to change,information?ow (in that there is an IN of a component within an agent or a separate agent).IN admits properties which make it con-ceptually similar to physical energy.First there is the notion of IN conversion,each entity in a stack has a different type of IN(and‘?ow’)associated with it,the?ow to an entity from an adjacent entity is a conversion of some IN from the source entity to that of the destination entity or qualitatively it is a type conversion.It simply denotes cause and effect of changes.The type structure is then used to describe seman-tics at each layer of the stack.Secondly there is a concept of IN conservation.In the case of a human user,this supports the idea in the prior section that one is always searching and their IN is never ful?lled only changing,hence any quantita-tive conceptualization of IN must re?ect the constancy of IN. For an arti?cial user modelled on a human user with‘user in-terests’,its IN is translated as its‘potential to change’.In the arti?cial case,‘user interest’as inscribed in its stack model can be?xed to test hypothesis about that interest,however user interest is only part of the IN.During the lifetime of a simulated search process involving arti?cial user agents, the user agent always has the potential to change state un-til its pre-de?ned stopping condition prevents it.Therefore its‘internal activity’which forms its IN ensures the IN is always changing and that the agent is always‘searching’ac-cording to the de?nition of search in above sections.The constancy in the arti?cial agent refers to the fact that its po-tential to change always exists until its terminating condi-tion is reached,therefore its overall IN is always conserved. The intention of de?ning IN as‘energy’is to have a simple and universal underlying theoretical principle for all search processes on which further theory can be built eventually al-lowing an analytical scenario like that of the physical case (Figure2).Further elaboration on IN and reasons for relat-ing it to energy are outside the scope of this paper.
Translation
With a general speci?cation language in place what requires to follow are translations of a search scenario speci?cation
Figure6:Relationship between languages
in?ow language to a destination language which offers the desired analytical capability.A translation can be trivial,for example,the representation of the memory layer as anoma-lous state of knowledge in(Belkin,Oddy,&Brooks1982) has many similarities to the‘potentiality of concepts’rep-resentation in(Aerts&Gabora2002).Overall in order to unify the multitude of IR models for each layer both in their syntax and semantics(termed as representation and method space in(Arafat,van Rijsbergen,&Jose2005)substantial further research is necessary.A map of this research in Fig-ure6shows some of the goals.Note that a translation of that part of a description language referred to as‘syntax’will ex-hibit both a resultant syntax and a semantics.For example a relevance feedback algorithm translates to a matrix on the Hilbert space,a syntax,but this also carries QT semantics. Thus the de?nition problem,along with its dependents still exist but there is now a framework to systematically resolve them.The problem of creating a‘search science’is now transformed into the problem of de?ning appropriate trans-lations of the scenario to a formal language where there is a ‘science’to be used,if any.
New Problems
The language of?ows is a formal speci?cation method,and therefore a particular search scenario can itself be analyzed using concepts from computability/complexity theory.An important issue about recursion needs to be addressed here. As if every process is a search process,then indeed the re-searcher modeling a search process is also doing search. Are there any theoretical gains or problems due to this self-referential issue?Further questions of a de?nitive type are also within the scope of the formal speci?cation,some elab-orate ones can be formulated:“Is the effectiveness of a par-ticular IR system for some speci?ed set of abstract users al-ways limited in some way unless the user learns to effec-tively use some interface feature?”These types of questions are new inquiries for IR.
Conclusions
In this paper we have detailed the key research problems in IR explaining how thinking of IR as a physical process us-ing the operational setup of QT offered a new perspective on these problems and resulted in the stack model.The con-ceptual problem in IR was resolved by re-de?ning the con-cept of search and IN.With the conceptual problem resolved a framework for addressing the de?nition problem was in-troduced.The problem of creating a science for search is equivalent to translating from the?ow language representa-tion to a formalism with the desired analytic tools.A sub-stantial research effort is now required to formalize a?eld as interdisciplinary as information retrieval,but it is hoped that the framework presented will form a foundation to that effort.There are new interesting issues concerned with self-reference,which may need to be addressed?rst.The im-mediate research concern is to show the practical bene?t of the?ow-language based speci?cation by illustrating how its analytic ability can be used to in?uence design decisions in a particular IR system speci?cation with speci?c user de?-nitions.
A crucial practical implication of our work is formal user simulations which could reduce experimentation costs.A related implication is that if researchers can use pre-de?ned user models for their experiments then the need for live user studies is reduced.Other sub-parts of the research commu-nity,the more user orientated,would then concentrate on creating realistic user models.In any case,due to formal speci?cation there are likely to be clearer boundaries be-tween related research areas and some standardization of the research practices therein.
Acknowledgements
We gratefully acknowledge Peter Bruza,Matt Leifer and Alex Wilce for comments on our work and EPSRC for par-tial funding.
References
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A.s.k for information retrieval part two:Results of a de-sign study.Journal of Documentation38(3). Ingwersen,P.,and Jarvelin,K.2005.The Turn:Integration of Information Seeking and Retrieval in Context.Springer. Mackay,https://www.wendangku.net/doc/306562990.html,rmation,Mechanism and Mean-ing.The M.I.T Press.
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黄自艺术歌曲钢琴伴奏及艺术成就
【摘要】黄自先生是我国杰出的音乐家，他以艺术歌曲的创作最为代表。而黄自先生特别强调了钢琴伴奏对于艺术歌曲组成的重要性。本文是以黄自先生创作的具有爱国主义和人道主义的艺术歌曲《天伦歌》为研究对象，通过对作品分析，归纳钢琴伴奏的弹奏方法与特点，并总结黄自先生的艺术成就与贡献。 【关键词】艺术歌曲；和声；伴奏织体；弹奏技巧 一、黄自艺术歌曲《天伦歌》的分析 （一）《天伦歌》的人文及创作背景。黄自的艺术歌曲《天伦歌》是一首具有教育意义和人道主义精神的作品。同时，它也具有民族性的特点。这首作品是根据联华公司的影片《天伦》而创作的主题曲，也是我国近代音乐史上第一首为电影谱写的艺术歌曲。作品创作于我国政治动荡、经济不稳定的30年代，这个时期，这种文化思潮冲击着我国各个领域，连音乐艺术领域也未幸免――以《毛毛雨》为代表的黄色歌曲流传广泛，对人民大众，尤其是青少年的不良影响极其深刻，黄自为此担忧，创作了大量艺术修养和文化水平较高的艺术歌曲。《天伦歌》就是在这样的历史背景下创作的，作品以孤儿失去亲人的苦痛为起点，发展到人民的发愤图强，最后升华到博爱、奋起的民族志向，对青少年的爱国主义教育有着重要的影响。 （二）《天伦歌》曲式与和声。《天伦歌》是并列三部曲式，为a+b+c，最后扩充并达到全曲的高潮。作品中引子和coda所使用的音乐材料相同，前后呼应，合头合尾。这首艺术歌曲结构规整，乐句进行的较为清晰，所使用的节拍韵律符合歌词的特点，如三连音紧密连接，为突出歌词中号召的力量等。 和声上，充分体现了中西方作曲技法融合的创作特性。使用了很多七和弦。其中，一部分是西方的和声，一部分是将我国传统的五声调式中的五个音纵向的结合，构成五声性和弦。与前两首作品相比，《天伦歌》的民族性因素增强，这也与它本身的歌词内容和要弘扬的爱国主义精神相对应。 （三）《天伦歌》的伴奏织体分析。《天伦歌》的前奏使用了a段进唱的旋律发展而来的，具有五声调性特点，增添了民族性的色彩。在作品的第10小节转调入近关系调，调性的转换使歌曲增添抒情的情绪。这时的伴奏加强和弦力度，采用切分节奏，节拍重音突出，与a段形成强弱的明显对比，突出悲壮情绪。 c段的伴奏采用进行曲的风格，右手以和弦为主，表现铿锵有力的进行。右手为上行进行，把全曲推向最高潮。左手仍以柱式和弦为主，保持节奏稳定。在作品的扩展乐段，左手的节拍低音上行与右手的八度和弦与音程对应，推动音乐朝向宏伟、壮丽的方向进行。coda 处，与引子材料相同，首尾呼应。 二、《天伦歌》实践研究 《天伦歌》是具有很强民族性因素的作品。所谓民族性，体现在所使用的五声性和声、传统歌词韵律以及歌曲段落发展等方面上。 作品的整个发展过程可以用伤感――悲壮――兴奋――宏达四个过程来表述。在钢琴伴奏弹奏的时候，要以演唱者的歌唱状态为中心，选择合适的伴奏音量、音色和音质来配合，做到对演唱者的演唱同步，并起到连接、补充、修饰等辅助作用。 作品分为三段，即a+b+c+扩充段落。第一段以五声音阶的进行为主，表现儿童失去父母的悲伤和痛苦，前奏进入时要弹奏的使用稍凄楚的音色，左手低音重复进行，在弹奏完第一个低音后，要迅速的找到下一个跨音区的音符；右手弹奏的要有棱角，在前奏结束的时候第四小节的t方向的延音处，要给演唱者留有准备。演唱者进入后，左手整体的踏板使用的要连贯。随着作品发展，伴奏与旋律声部出现轮唱的形式，要弹奏的流动性强，稍突出一些。后以mf力度出现的具有转调性质的琶音奏法，要弹奏的如流水般连贯。在重复段落，即“小
我国艺术歌曲钢琴伴奏-精
我国艺术歌曲钢琴伴奏-精 2020-12-12 【关键字】传统、作风、整体、现代、快速、统一、发展、建立、了解、研究、特点、突出、关键、内涵、情绪、力量、地位、需要、氛围、重点、需求、特色、作用、结构、关系、增强、塑造、借鉴、把握、形成、丰富、满足、帮助、发挥、提高、内心 【摘要】艺术歌曲中，伴奏、旋律、诗歌三者是不可分割的重 要因素，它们三个共同构成一个统一体，伴奏声部与声乐演唱处于 同样的重要地位。形成了人声与器乐的巧妙的结合，即钢琴和歌唱 的二重奏。钢琴部分的音乐使歌曲紧密的联系起来，组成形象变化 丰富而且不中断的套曲，把音乐表达的淋漓尽致。 【关键词】艺术歌曲；钢琴伴奏；中国艺术歌曲 艺术歌曲中，钢琴伴奏不是简单、辅助的衬托，而是根据音乐 作品的内容为表现音乐形象的需要来进行创作的重要部分。准确了 解钢琴伴奏与艺术歌曲之间的关系,深层次地了解其钢琴伴奏的风 格特点,能帮助我们更为准确地把握钢琴伴奏在艺术歌曲中的作用 和地位，从而在演奏实践中为歌曲的演唱起到更好的烘托作用。 一、中国艺术歌曲与钢琴伴奏 “中西结合”是中国艺术歌曲中钢琴伴奏的主要特征之一，作 曲家们将西洋作曲技法同中国的传统文化相结合，从开始的借鉴古 典乐派和浪漫主义时期的创作风格，到尝试接近民族乐派及印象主 义乐派的风格，在融入中国风格的钢琴伴奏写作，都是对中国艺术 歌曲中钢琴写作技法的进一步尝试和提高。也为后来的艺术歌曲写 作提供了更多宝贵的经验，在长期发展中，我国艺术歌曲的钢琴伴 奏也逐渐呈现出多姿多彩的音乐风格和特色。中国艺术歌曲的钢琴
写作中，不可忽略的是钢琴伴奏织体的作用，因此作曲家们通常都以丰富的伴奏织体来烘托歌曲的意境，铺垫音乐背景，增强音乐感染力。和声织体，复调织体都在许多作品中使用，较为常见的是综合织体。这些不同的伴奏织体的歌曲，极大限度的发挥了钢琴的艺术表现力，起到了渲染歌曲氛围，揭示内心情感，塑造歌曲背景的重要作用。钢琴伴奏成为整体乐思不可缺少的部分。优秀的钢琴伴奏织体，对发掘歌曲内涵，表现音乐形象，构架诗词与音乐之间的桥梁等方面具有很大的意义。在不断发展和探索中，也将许多伴奏织体使用得非常娴熟精确。 二、青主艺术歌曲《我住长江头》中钢琴伴奏的特点 《我住长江头》原词模仿民歌风格，抒写一个女子怀念其爱人的深情。青主以清新悠远的音乐体现了原词的意境，而又别有寄寓。歌调悠长，但有别于民间的山歌小曲；句尾经常出现下行或向上的拖腔，听起来更接近于吟哦古诗的意味，却又比吟诗更具激情。钢琴伴奏以江水般流动的音型贯穿全曲，衬托着气息宽广的歌唱，象征着绵绵不断的情思。由于运用了自然调式的旋律与和声，显得自由舒畅，富于浪漫气息，并具有民族风味。最有新意的是，歌曲突破了“卜算子”词牌双调上、下两阕一般应取平行反复结构的惯例，而把下阕单独反复了三次，并且一次比一次激动，最后在全曲的高音区以ff结束。这样的处理突出了思念之情的真切和执著，并具有单纯的情歌所没有的昂奋力量。这是因为作者当年是大革命的参加者，正被反动派通缉，才不得不以破格的音乐处理，假借古代的