An Argumentation-Theoretic Characterization of Defeasible Logic

英语论证作文范文英文回答：Introduction。

In the realm of discourse, the efficacy of human communication rests upon the ability to formulate and present a coherent and persuasive argument. The strength of an argument lies not merely in its content but also in the skillful deployment of rhetorical devices and logical reasoning.The Art of Argumentation。

Argumentation is the art of presenting a reasoned case in support of a specific claim or proposition. It involves the systematic arrangement of evidence, logical inferences, and rhetorical appeals to persuade the audience of the validity of one's stance. Effective arguments adhere to the principles of logical coherence, factual accuracy, andpersuasive appeal.Logical Reasoning。

The foundation of a strong argument rests upon sound logical reasoning. This encompasses employing inductive and deductive principles to derive conclusions from premises. Inductive arguments generalize from specific observations to broader conclusions, while deductive arguments infer conclusions from universally accepted premises.Rhetorical Devices。

The Beginning of Model Checking:A Personal PerspectiveE.Allen Emerson1,21.Department of Computer Sciencesputer Engineering Research CenterThe University of Texas at Austin,Austin TX78712,USAAbstract.Model checking provides an automated method for verify-ing concurrent systems.Correctness specifications are given in tempo-ral logic.The method hinges on an efficient andflexible graph-theoreticreachability algorithm.At the time of its introduction in the early1980’s,the prevailing paradigm for verification was a manual one of proof-theoretic reasoning using formal axioms and inference rules oriented to-wards sequential programs.The need to encompass concurrent programs,the desire to avoid the difficulties with manual deductive proofs,and thesmall model theorem for temporal logic motivated the development ofmodel checking.Keywords:model checking,model-theoretic,synthesis,history,origins1IntroductionIt has long been known that computer software programs,computer hardware designs,and computer systems in general exhibit errors.Working programmers may devote more than half of their time on testing and debugging in order to increase reliability.A great deal of research effort has been and is devoted to developing improved testing methods.Testing successfully identifies many significant errors.Yet,serious errors still afflict many computer systems including systems that are safety critical,mission critical,or economically vital.The US National Institute of Standards and Technology has estimated that programming errors cost the US economy$60B annually[Ni02].Given the incomplete coverage of testing,alternative approaches have been sought.The most promising approach depends on the fact that programs and more generally computer systems may be viewed as mathematical objects with behavior that is in principle well-determined.This makes it possible to specify using mathematical logic what constitutes the intended(correct)behavior.Then one can try to give a formal proof or otherwise establish that the program meets This work was supported in part by National Science Foundation grants CCR-009-8141&CCR-020-5483and funding from Fujitsu Labs of America. email:emerson@ URL:/∼emerson/its specification.This line of study has been active for about four decades now. It is often referred to as formal methods.The verification problem is:Given program M and specification h determine whether or not the behavior of M meets the specification h.Formulated in terms of Turing Machines,the verification problem was considered by Turing[Tu36]. Given a Turing Machine M and the specification h that it should eventually halt (say on blank input tape),one has the halting problem which is algorithmically unsolvable.In a later paper[Tu49]Turing argued for the need to give a(manual) proof of termination using ordinals,thereby presaging work by Floyd[Fl67]and others.The model checking problem is an instance of the verification problem.Model checking provides an automated method for verifying concurrent(nominally)finite state systems that uses an efficient andflexible graph search,to determine whether or not the ongoing behavior described by a temporal property holds of the system’s state graph.The method is algorithmic and often efficient because the system isfinite state,despite reasoning about infinite behavior.If the answer is yes then the system meets its specification.If the answer is no then the system violates its specification;in practice,the model checker can usually produce a counterexample for debugging purposes.At this point it should be emphasized that the verification problem and the model checking problem are mathematical problems.The specification is for-mulated in mathematical logic.The verification problem is distinct from the pleasantness problem[Di89]which concerns having a specification capturing a system that is truly needed and wanted.The pleasantness problem is inherently pre-formal.Nonetheless,it has been found that carefully writing a formal specifi-cation(which may be the conjunction of many sub-specifications)is an excellent way to illuminate the murk associated with the pleasantness problem.At the time of its introduction in the early1980’s,the prevailing paradigm for verification was a manual one of proof-theoretic reasoning using formal axioms and inference rules oriented towards sequential programs.The need to encom-pass concurrent programs,and the desire to avoid the difficulties with manual deductive proofs,motivated the development of model checking.In my experience,constructing proofs was sufficiently difficult that it did seem there ought to be an easier alternative.The alternative was suggested by temporal logic.Temporal logic possessed a nice combination of expressiveness and decidability.It could naturally capture a variety of correctness properties, yet was decidable on account of the“Small”Finite Model Theorem which en-sured that any satisfiable formula was true in somefinite model that was small. It should be stressed that the Small Finite Model Theorem concerns the satisfi-ability problem of propositional temporal logic,i.e.,truth in some state graph. This ultimately lead to model checking,i.e.,truth in a given state graph.The origin and development of model checking will be described below.De-spite being hampered by state explosion,over the past25years model checking has had a substantive impact on program verification efforts.Formal verification2has progressed from discussions of how to manually prove programs correct to the routine,algorithmic,model-theoretic verification of many programs.The remainder of the paper is organized as follows.Historical background is discussed in section2largely related to verification in the Floyd-Hoare paradigm; protocol verification is also considered.Section3describes temporal logic.A very general type of temporal logic,the mu-calculus,that defines correctness in terms offixpoint expressions is described in section4.The origin of model checking is described in section5along with some relevant personal influences on me.A discussion of model checking today is given in section6.Some concluding remarks are made in section7.2Background of Model CheckingAt the time of the introduction of model checking in the early1980’s,axiomatic verification was the prevailing verification paradigm.The orientation of this paradigm was manual proofs of correctness for(deterministic)sequential pro-grams,that nominally started with their input and terminated with their out-put.The work of Floyd[Fl67]established basic principles for proving partial correctness,a type of safety property,as well as termination and total correct-ness,forms of liveness properties.Hoare[Ho69]proposed an axiomatic basis for verification of partial correctness using axioms and inference rules in a formal deductive system.An important advantage of Hoare’s approach is that it was compositional so that the proof a program was obtained from the proofs of its constituent subprograms.The Floyd-Hoare framework was a tremendous success intellectually.It en-gendered great interest among researchers.Relevant notions from logic such as soundness and(relative)completeness as well as compositionality were in-vestigated.Proof systems were proposed for new programming languages and constructs.Examples of proofs of correctness were given for small programs.However,this framework turned out to be of limited use in practice.It did not scale up to“industrial strength”programs,despite its merits.Problems start with the approach being one of manual proof construction.These are formal proofs that can involve the manipulations of extremely long logical formulae. This can be inordinately tedious and error-prone work for a human.In practice, it may be wholly infeasible.Even if strict formal reasoning were used throughout, the plethora of technical detail could be overwhelming.By analogy,consider the task of a human adding100,000decimal numbers of1,000digits each.This is rudimentary in principle,but likely impossible in practice for any human to perform reliably.Similarly,the manual verification of100,000or10,000or even 1,000line programs by hand is not feasible.Transcription errors alone would be prohibitive.Furthermore,substantial ingenuity may also be required on the part of the human to devise suitable assertions for loop invariants.One can attempt to partially automate the process of proof construction using an interactive theorem prover.This can relieve much of the clerical burden.3However,human ingenuity is still required for invariants and various lemmas. Theorem provers may also require an expert operator to be used effectively.Moreover,the proof-theoretic framework is one-sided.It focuses on providing a way to(syntactically)prove correct programs that are genuinely(semantically) correct.If one falters or fails in the laborious process of constructing a proof of a program,what then?Perhaps the program is really correct but one has not been clever enough to prove it so.On the other hand,if the program is really incorrect,the proof systems do not cater for proving incorrectness.Since in practice programs contain bugs in the overwhelming majority of the cases,the inability to identify errors is a serious drawback of the proof-theoretic approach.It seemed there ought to be a better way.It would be suggested by temporal logic as discussed below.Remark.We mention that the term verification is sometimes used in a specific sense meaning to establish correctness,while the term refutation(or falsification) is used meaning to detect an error.More generally,verification refers to the two-sided process of determining whether the system is correct or erroneous.Lastly,we should also mention in this section the important and useful area of protocol work protocols are commonlyfinite state.This makes it possible to do simple graph reachability analysis to determine if a bad state is accessible(cf.[vB78],[Su78]).What was lacking here was aflexible and expres-sive means to specify a richer class of properties.3Temporal LogicModal and temporal logics provided key inspiration for model checking.Origi-nally developed by philosophers,modal logic deals with different modalities of truth,distinguishing between P being true in the present circumstances,pos-sibly P holding under some circumstances,and necessarily P holding under all circumstances.When the circumstances are points in time,we have a modal tense logic or temporal logic.Basic temporal modalities include sometimes P and always P.Several writers including Prior[Pr67]and Burstall[Bu74]suggested that temporal logic might be useful in reasoning about computer programs.For in-stance,Prior suggested that it could be used to describe the“workings of a digital computer”.But it was the seminal paper of Pnueli[Pn77]that made the crit-ical suggestion of using temporal logic for reasoning about ongoing concurrent programs which are often characterized as reactive systems.Reactive systems typically exhibit ideally nonterminating behavior so that they do not conform to the Floyd-Hoare paradigm.They are also typically non-deterministic so that their non-repeatable behavior was not amenable to testing. Their semantics can be given as infinite sequences of computation states(paths) or as computation trees.Examples of reactive systems include microprocessors, operating systems,banking networks,communication protocols,on-board avion-ics systems,automotive electronics,and many modern medical devices.4Pnueli used a temporal logic with basic temporal operators F(sometimes) and G(always);augmented with X(next-time)and U(until)this is today known as LTL(Linear Time Logic).Besides the basic temporal operators applied to propositional arguments,LTL permitted formulae to be built up by forming nestings and boolean combinations of subformulae.For example,G¬(C1∧C2) expresses mutual exclusion of critical sections C1and C2;formula G(T1⇒(T1U C1)specifies that if process1is in its trying region it remains there until it eventually enters its critical section.The advantages of such a logic include a high degree of expressiveness permit-ting the ready capture of a wide range of correctness properties of concurrent programs,and a great deal offlexibility.Pnueli focussed on a proof-theoretic approach,giving a proof in a deductive system for temporal logic of a small example program.Pnueli does sketch a decision procedure for truth overfinite state graphs.However,the complexity would be nonelementary,growing faster than anyfixed composition of exponential functions,as it entails a reduction to S1S,the monadic Second order theory of1Successor,(or SOLLO;see be-low).In his second paper[Pn79]on temporal logic the focus is again on the proof-theoretic approach.I would claim that temporal logic has been a crucial factor in the success of model checking.We have one logical framework with a few basic temporal operators permitting the expression of limitless specifications.The connection with natural language is often significant as well.Temporal logic made it possible, by and large,to express the correctness properties that needed to be expressed. Without that ability,there would be no reason to use model checking.Alternative temporal formalisms in some cases may be used as they can be more expressive or succinct than temporal logic.But historically it was temporal logic that was the driving force.These alternative temporal formalisms include:(finite state)automata(on infinite strings)which accept infinite inputs by infinitely often entering a desig-nated set of automaton states[Bu62].An expressively equivalent but less succinct formalism is that ofω-regular expressions;for example,ab cωdenotes strings of the form:one a,0or more b s,and infinitely many copies of c;and a property not expressible in LTL(true P)ωensuring that at every even moment P holds. FOLLO(First Order Language of Linear Order)which allows quantification over individual times,for example,∀i≥0Q(i);and SOLLO(Second Order Language of Linear Order)which also allows quantification over sets of times corresponding to monadic predicates such as∃Q(Q(0)∧∀i≥0(Q(i)⇒Q(i+1)).1These alterna-tives are sometimes used for reasons of familiarity,expressiveness or succinctness. LTL is expressively equivalent to FOLLO,but FOLLO can be nonelementarily more succinct.This succinctness is generally found to offer no significant practi-cal advantage.Moreover,model checking is intractably(nonelementarily)hard for FOLLO.Similarly,SOLLO is expressively equivalent toω−regular expres-sions but nonelementarily more succinct.See[Em90]for further discussion.1Technically,the latter abbreviates∃Q(Q(0)∧∀i,j≥0(i<j∧¬∃k(i<k<j))⇒(Q(i)⇒Q(j)).5Temporal logic comes in two broad styles.A linear time LTL assertion h is interpreted with respect to a single path.When interpreted over a program there is an implicit universal quantifications over all paths of the program.An assertion of a branching time logic is interpreted over computation trees.The universal A (for all futures)and existential E(for some future)path quantifiers are important in this context.We can distinguish between AF P(along all futures,P eventually holds and is thus inevitable))and EF P(along some future,P eventually holds and is thus possible).One widely used branching time logic is CTL(Computation Tree Logic)(cf. [CE81]).Its basic temporal modalities are A(for all futures)or E(for some fu-ture)followed by one of F(sometime),G(always),X(next-time),and U(until); compound formulae are built up from nestings and propositional combinations of CTL subformulae.CTL derives from[EC80].There we defined the precursor branching time logic CTF which has path quantifiers∀fullpath and∃fullpath, and is very similar to CTL.In CTF we could write∀fullpath∃state P as well as ∃fullpath∃state P These would be rendered in CTL as AF P and EF P,respec-tively.The streamlined notation was derived from[BMP81].We also defined a modal mu-calculus FPF,and then showed how to translate CTF into FPF. The heart of the translation was characterizing the temporal modalities such as AF P and EF P asfixpoints.Once we had thefixpoint characterizations of these temporal operators,we were close to having model checking.CTL and LTL are of incomparable expressive power.CTL can assert the existence of behaviors,e.g.,AGEF start asserts that it is always possible to re-initialize a circuit.LTL can assert certain more complex behaviors along a computation,such as GF en⇒F ex relating to fairness.(It turns out this formula is not expressible in CTL,but it is in“FairCTL”[EL87])The branching time logic CTL*[EH86]provides a uniform framework that subsumes both LTL and CTL,but at the higher cost of deciding satisfiability.There has been an ongoing debate as to whether linear time logic or branching time logic is better for program reasoning(cf.[La80],[EH86],[Va01]).Remark.The formal semantics of temporal logic formulae are defined with respect to a(Kripke)structure M=(S,S0,R,L)where S is a set of states,S0 comprises the initial states,R⊆S×S is a total binary relation,and L is a labelling of states with atomic facts(propositions)true there.An LTL formula h such as F P is defined over path x=t0,t1,t2...through M by the rule M,x|= F P iff∃i≥0P∈L(t i).Similarly a CTL formula f such as EGP holds of a state t0,denoted M,t0|=EGP,iffthere exists a path x=t0,t1,t2,...in M such that∀i≥0P∈L(t i).For LTL h,we define M|=h ifffor all paths x starting in S0,M,x|=h.For CTL formula f we define M|=f ifffor each s∈S0,M,s|=f.A structure is also known as a state graph or state transition graph or transition system.See[Em90]for details.64The Mu-calculusThe mu-calculus may be viewed as a particular but very general temporal logic. Some formulations go back to the work of de Bakker and Scott[deBS69];we deal specifically with the(propositional or)modal mu-calculus(cf.[EC80],[Ko83]). The mu-calculus provides operators for defining correctness properties using re-cursive definitions plus leastfixpoint and greatestfixpoint operators.Leastfix-points correspond to well-founded or terminating recursion,and are used to capture liveness or progress properties asserting that something does happen. Greatestfixpoints permit infinite recursion.They can be used to capture safety or invariance properties.The mu-calculus is very expressive and veryflexible.It has been referred to as a“Theory of Everything”.The formulae of the mu-calculus are built up from atomic proposition con-stants P,Q,...,atomic proposition variables Y,Z,...,propositional connectives ∨,∧,¬,and the leastfixpoint operator,µas well as the greatestfixpoint opera-tor,ν.Eachfixpoint formula such asµZ.τ(Z)should be syntactically monotone meaning Z occurs under an even number of negations,and similarly forν.The mu-calculus is interpreted with respect to a structure M=(S,R,L). The power set of S,2S,may be viewed as the complete lattice(2S,S,∅,⊆,∪,∩).Intuitively,each(closed)formula may be identified with the set of states of S where it is true.Thus,false which corresponds to the empty set is the bottom element,true which corresponds to S is the top element,and implication (∀s∈S[P(s)⇒Q(s)])which corresponds to simple set-theoretic containment (P⊆Q)provides the partial ordering on the lattice.An open formulaτ(Z) defines a mapping from2S→2S whose value varies as Z varies.A givenτ: 2S→2S is monotone provided that P⊆Q impliesτ(P)⊆τ(Q).Tarski-Knaster Theorem.(cf.[Ta55],[Kn28])Letτ:2S→2S be a monotone functional.Then(a)µY.τ(Y)=∩{Y:τ(Y)=Y}=∩{Y:τ(Y)⊆Y},(b)νY.τ(Y)=∪{Y:τ(Y)=Y}=∪{Y:τ(Y)⊇Y},(c)µY.τ(Y)=∪iτi(false)where i ranges over all ordinals of cardinality at mostthat of the state space S,so that when S isfinite i ranges over[0:|S|],and (d)νY.τ(Y)=∩iτi(true)where i ranges over all ordinals of cardinality at mostthat of the state space S,so that when S isfinite i ranges over[0:|S|].Consider the CTL property AF P.Note that it is afixed point orfixpoint of the functionalτ(Z)=P∨AXZ.That is,as the value of the input Z varies,the value of the outputτ(Z)varies,and we have AF P=τ(AF P)=P∨AXAF P. It can be shown that AF P is the leastfixpoint ofτ(Z),meaning the set of states associated with AF P is a subset of the set of states associated with Z,for any fixpoint Z=τ(Z).This might be denotedµZ.Z=τ(Z).More succinctly,we normally write justµZ.τ(Z).In this case we have AF P=µZ.P∨AXZ.We can get some intuition for the the mu-calculus by noting the following fixpoint characterizations for CTL properties:7EF P=µZ.P∨EXZAGP=νZ.P∧AXZAF P=µZ.P∨AXZEGP=νZ.P∧EXZA(P U Q)=µZ.Q∨(P∧AXZ)E(P U Q)=µZ.Q∨(P∧EXZ)For all these properties,as we see,thefixpoint characterizations are simple and plausible.It is not too difficult to give rigorous proofs of their correctness (cf.[EC80],[EL86]).We emphasize that the mu-calculus is a rich and powerful formalism;its formulae are really representations of alternatingfinite state au-tomata on infinite trees[EJ91].Since even such basic automata as deterministic finite state automata onfinite strings can form quite complex“cans of worms”, we should not be so surprised that it is possible to write down highly inscrutable mu-calculus formulae for which there is no readily apparent intuition regard-ing their intended meaning.The mu-calculus has also been referred to as the “assembly language of program logics”reflecting both its comprehensiveness and potentially intricate syntax.On the other hand,many mu-calculus char-acterizations of correctness properties are elegant due to its simple underlying mathematical organization.In[EL86]we introduced the idea of model checking for the mu-calculus in-stead of testing satisfiability.We catered for efficient model checking in fragments of the the mu-calculus.This provides a basis for practical(symbolic)model checking algorithms.We gave an algorithm essentially of complexity n d,where d is the alternation depth reflecting the number of significantly nested least and greatestfixpoint operators.We showed that common logics such as CTL,LTL, and CTL*were of low alternation depth d=1or d=2.We also provided succinctfixpoint characterizations for various natural fair scheduling criteria.A symbolic fair cycle detection method,known as the“Emerson-Lei”algorithm, is comprised of a simplefixpoint characterization plus the Tarski-Knaster theo-rem.It is widely used in practice even though it has worst case quadratic cost. Empirically,it usually outperforms alternatives.5The Origin of Model CheckingThere were several influences in my personal background that facilitated the de-velopment of model checking.In1975Zohar Manna gave a talk at the University of Texas onfixpoints and the Tarski-Knaster Theorem.I was familiar with Di-jkstra’s book[Di76]extending the Floyd-Hoare framework with wlp the weakest liberal precondition for partial correctness and wp the weakest precondition for to-tal correctness.It turns out that wlp and wp may be viewed as modal operators, for which Dijkstra implicitly gavefixpoint characterizations,although Dijkstra did not favor this viewpoint.Basu and Yeh[BY75]at Texas gavefixpoint char-acterizations of weakest preconditions for while loops.Ed Clarke[Cl79]gave similarfixpoint characterizations for both wp and wlp for a variety of control structures.8I will now describe how model checking originated at Harvard University.In prior work[EC80]we gavefixpoint characterizations for the main modalities of a logic that was essentially CTL.These would ultimately provide thefirst key ingredient of model checking.Incidentally,[EC80]is a paper that could very well not have appeared.Some-how the courier service delivering the hard-copies of the submission to Amster-dam for the program chair at CWI(Dutch for“Center for Mathematics and Computer Science”)sent the package in bill-the-recipient mode.Fortunately, CWI was gracious and accepted the package.All that remained to undo this small misfortune was to get an overseas bank draft to reimburse them.The next work,entitled“Design and Synthesis of Synchronization Skeletons using Branching Time Logic”,was devoted to program synthesis and model checking.I suggested to Ed Clarke that we present the paper,which would be known as[CE81],at the IBM Logics of Programs workshop,since he had an invitation to participate.Both the idea and the term model checking were introduced by Clarke and Emerson in[CE81].Intuitively,this is a method to establish that a given program meets a given specification where:–The program defines afinite state graph M.–M is searched for elaborate patterns to determine if the specification f holds.–Pattern specification isflexible.–The method is efficient in the sizes of M and,ideally,f.–The method is algorithmic.–The method is practical.The conception of model checking was inspired by program synthesis.I was interested in verification,but struck by the difficulties associated with manual proof-theoretic verification as noted above.It seemed that it might be possible to avoid verification altogether and mechanically synthesize a correct program directly from its CTL specification.The idea was to exploit the small model property possessed by certain decidable temporal logics:any satisfiable formula must have a“small”finite model of size that is a function of the formula size. The synthesis method would be sound:if the input specification was satisfiable, it built afinite global state graph that was a model of the specification,from which individual processes could be extracted The synthesis method should also be complete:If the specification was unsatisfiable,it should say so.Initially,it seemed to me technically problematic to develop a sound and complete synthesis method for CTL.However,it could always be ensured that an alleged synthesis method was at least sound.This was clear because given anyfinite model M and CTL specification f one can algorithmically check that M is a genuine model of f by evaluating(verifying)the basic temporal modal-ities over M based on the Tarski-Knaster theorem.This was the second key ingredient of model posite temporal formulae comprised of nested subformulae and boolean combinations of subformulae could be verified by re-cursive descent.Thus,fixpoint characterizations,the Tarski-Knaster theorem, and recursion yielded model checking.9Thus,we obtained the model checking framework.A model checker could be quite useful in practice,given the prevalence offinite state concurrent systems. The temporal logic CTL had theflexibility and expressiveness to capture many important correctness properties.In addition the CTL model checking algorithm was of reasonable efficiency,polynomial in the structure and specification sizes. Incidentally,in later years we sometimes referred to temporal logic model check-ing.The crucial roles of abstraction,synchronization skeletons,andfinite state spaces were discussed in[CE81]:The synchronization skeleton is an abstraction where detail irrelevant to synchronization is suppressed.Most solutions to synchronization prob-lems are in fact given as synchronization skeletons.Because synchronization skeletons are in generalfinite state...proposi-tional temporal logic can be used to specify their properties.Thefinite model property ensures that any program whose synchroniza-tion properties can be expressed in propositional temporal logic can be realized by afinite state machine.Conclusions of[CE81]included the following prognostications,which seem to have been on target:[Program Synthesis]may in the long run be quite practical.Much addi-tional research will be needed,however,to make it feasible in practice....We believe that practical[model checking]tools could be developed in the near future.To sum up,[CE81]made several contributions.It introduced model check-ing,giving an algorithm of quadratic complexity O(|f||M|2).It introduced the logic CTL.It gave an algorithmic method for concurrent program synthesis(that was both sound and complete).It argued that most concurrent systems can be abstracted tofinite state synchronization skeletons.It described a method for efficiently model checking basic fairness using strongly connected components. An NP-hardness result was established for checking certain assertions in a richer logic than CTL.A prototype(and non-robust)model checking tool BMoC was developed,primarily by a Harvard undergraduate,to permit verification of syn-chronization protocols.A later paper[CES86]improved the complexity of CTL model checking to linear O(|f||M|).It showed how to efficiently model check relative to uncondi-tional and weak fairness.The EMC model checking tool was described,and a version of the alternating bit protocol verified.A general framework for efficiently model checking fairness properties was given in[EL87],along with a reduction showing that CTL*model checking could be done as efficiently as LTL model checking.Independently,a similar method was developed in France by Sifakis and his student[QS82].Programs were interpreted over transition systems.A branching10。

Contents摘要 (1)Abstract (1)Chapter 1 American Romanticism(1810--1865) (2)1.Background reasons (2)1.1 Politically this period was ripe (2)1.2 Economically American had never been wealthier (2)1.3 Culturally American own value emerged (2)2.Basic features and styles (2)2.1 Expressiveness (2)2.2 Imagination (2)2.3 Worship of nature (2)2.4 Simplicity (3)2.5 Cultural nationalism (3)2.6 Liberty,freedom,democracy and individualism (3)3.Influence (3)Chapter 2 American Realism(1865--1914) (3)1. Background changes (3)1.1 Politics (4)1.2 Economics (4)1.3 Cultural and social changes (4)2. Basic features and styles (4)2.1 Truthful description of the actualities of the real life andmaterial (4)2.2 Focus on ordinariness (4)3. Three dominant figures (4)4. Influence (5)Chapter 3 American Naturalism(1890--1914) (5)1. Background information (5)1.1 Cultural and Social Background (5)1.2 Religion and theoretical basis (5)2. Major ideas and features of Naturalism (5)2.1 Determinism (5)2.2 World: godless, indifferent, hostile (6)2.3 Style: scientific objectivity (6)2.4 Subjects and themes (6)3. A representative work that show the ideas and features above (6)3. Influence (6)Chapter 4 American Modernism(1914--1945) (6)1. Background information (6)1.1 Politics (6)1.2 Economy (7)1.3 Cultural and social background (7)2. Characteristics and features of Modernism (7)3. Major genres and a representative of each one (7)3.1 Modern poetry——Ezra Pound (7)3.2 Modern fiction——Ernest Hemingway (7)4. Influence (8)Chapter 5 American Postmodernism(1914--1945) (8)1. Background information (8)1.1 Politics (8)1.2 Economics (8)1.3 Social and international background (8)2. Characteristics and major features (8)2.1 Experimental writing techniques (8)2.3 Irony, playfulness and black humor (9)3.Influence (9)Bibliographies (9)摘要具有自身特点的新文学的出现，是一个国家真正形成的标志。

小学上册英语第四单元真题试卷(有答案)英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.What do we call a young ostrich?A. ChickB. CalfC. KitD. Fawn答案:A.Chick2.We are going to a ________ (音乐会).3.The starfish can regenerate lost ______ (部分).4.The boy plays the ________.5.My _______ (兔子) is curious about everything.6.The __________ is a famous area known for its art.7.My uncle shares his __________ (知识) about fishing.8.The __________ (历史的轮回) reminds us of the cyclical nature of events.9.What is the term for the movement of the Earth around the sun?A. RotationB. RevolutionC. OrbitD. Spin答案: B10.Which planet is known as the Red Planet?A. EarthB. MarsC. JupiterD. Saturn答案:B11.The ______ is the path of the Earth around the sun.12.Asteroids are mostly found in the _______ belt.13.My favorite fruit is ________ (葡萄) in summer.14.The ancient city of Pompeii was buried by the eruption of ______ (维苏威火山).15.What shape has three sides?A. SquareB. TriangleC. CircleD. Rectangle答案: B16.My pet fish swims around its ______ (鱼缸).17.What do you call the process of learning and gaining knowledge?A. EducationB. RecreationC. VacationD. Celebration答案:A18.The country known for its ancient ruins and temples is ________ (以古代遗址和庙宇闻名的国家是________).19.根据图片把下列单词补充完整。

八年级英语议论文论证方法单选题40题1. In the essay, the author mentions a story about a famous scientist to support his idea. This is an example of _____.A.analogyB.exampleparisonD.metaphor答案：B。

本题主要考查论证方法的辨析。

选项A“analogy”是类比；选项B“example”是举例；选项C“comparison”是比较；选项D“metaphor”是隐喻。

文中提到一个关于著名科学家的故事来支持观点，这是举例论证。

2. The writer uses the experience of his own life to prove his point. This kind of method is called _____.A.personal storyB.example givingC.case studyD.reference答案：B。

选项A“personal story”个人故事范围较窄；选项B“example giving”举例；选项C“case study”案例分析；选项D“reference”参考。

作者用自己的生活经历来证明观点，这是举例论证。

3. The author cites several historical events to strengthen his argument. What is this method?A.citing factsB.giving examplesC.making comparisonsing analogies答案：B。

选项A“citing facts”引用事实，历史事件可以作为例子，所以是举例论证；选项B“giving examples”举例；选项C“making comparisons”比较；选项D“using analogies”使用类比。

a r X i v :c s /0207030v 2 [c s .A I ] 14 J u l 2002Alexander Bochman Computer Science Department,Holon Academic Institute of Technology,Israele-mail:bochmana@hait.ac.ilAbstractAn extension of an abstract argumentation framework,called collective argumentation,is introduced in which the attack relation is defined directly among sets of arguments.The extension turns out to be suitable,in particular,for representing semantics of dis-junctive logic programs.Two special kinds of collective argumentation are considered in which the opponents can share their argu-ments.IntroductionThe general argumentation theory [Bondarenko et al.,1997,Dung,1995b]has proved to be a powerful for nonmono-tonic formalisms in general,and semantics for normal logic programs,in particular.Thus,it has been shown that the main semantics for the latter,suggested in the literature,are naturally representable in this frame-work (see,e.g.,[Dung,1995a,Kakas and Toni,1999]).In this report we suggest a certain extension of the general argumentation theory in which the attack re-lation is defined directly among sets of arguments.In other words,we will permit situations in which a set of arguments ‘collectively’attacks another set of argu-ments in a way that is not reducible to attacks among particular arguments from these sets.It turns out that this extension is suitable for providing semantics for disjunctive logic programs in which the rules have multiple heads.In addition,it suggests a natural set-ting for studying kinds of argumentation in which the opponents could provisionally share their arguments.Moreover,the original argumentation theory can be ‘reconstructed’in this framework by requiring,in ad-dition,that the attack relation should be local in thesense that a set of arguments can attack another set of arguments only if it attacks a particular argument in this set.The plan of the paper is as follows.After a brief de-scription of the abstract argumentation theory,we sug-gest its generalization in which the attack relation is defined on sets of arguments.It is shown that the suggested collective argumentation theory is adequate for representing practically any semantics for disjunc-tive logic programs.As an application of the general theory,we consider two special cases of the general framework in which the opponents can share their ar-guments.The semantics obtained in this way will cor-respond to some familiar proposals,given in the liter-ature.1Abstract Argumentation TheoryWe give first a brief description of the argumentation theory from [Dung,1995b].Definition 1.1.An abstract argumentation theory is a pair A ,֒→ ,where A is a set of arguments ,while ֒→a binary relation of an attack on A .A general task of the argumentation theory consists in determining ‘good’sets of arguments that are safe in some sense with respect to the attack relation.To this end,we should extend first the attack relation to sets of arguments:if Γ,∆are sets of arguments,then Γ֒→∆is taken to hold iffα֒→β,for some α∈Γ,β∈∆.An argument αwill be called allowable for the set of arguments Γ,if Γdoes not attack α.For any set of arguments Γ,we will denote by [Γ]the set of all arguments allowable by Γ,that is[Γ]={α|Γ֒→α}An argument αwill be called acceptable for the set ofargumentsΓ,ifΓattacks any argument againstα.As can be easily checked,the set of arguments that are acceptable forΓcoincides with[[Γ]].Using the above notions,we can give a quite simple characterization of the basic objects of an abstract ar-gumentation theory.Definition1.2.A set of argumentsΓwill be called •conflict-free ifΓ⊆[Γ];•admissible if it is conflict-free andΓ⊆[[Γ]];•a complete extension if it is conflict-free andΓ= [[Γ]];•a preferred extension if it is a maximal complete extension;•a stable extension ifΓ=[Γ].A set of argumentsΓis conflict-free if it does not at-tack itself.A conflict-free setΓis admissible iffany argument fromΓis also acceptable forΓ,and it is a complete extension if it coincides with the set of ar-guments that are acceptable with respect to it.Fi-nally,a stable extension is a conflict-free set of argu-ments that attacks any argument outside it.Clearly, any stable extension is also a preferred extension,any preferred extension is a complete extension,and any complete extension is an admissible set.Moreover,as has been shown in[Dung,1995b],any admissible set is included in some complete extension.Consequently, preferred extensions coincide with maximal admissible sets.In addition,the set of complete extensions forms a complete lower semi-lattice:for any set of complete extensions,there exists a unique greatest complete ex-tension that is included in all of them.In particular, there always exists a least complete extension of an argumentation theory.As has been shown in[Dung,1995a],under a suit-able translation,the above objects correspond to well-known semantics suggested for normal logic programs. Thus,stable extensions correspond to stable models (answer sets),complete extensions correspond to par-tial stable models,preferred extensions correspond to regular models,while the least complete extension cor-responds in this sense to the well-founded semantics (WFS).These results have shown,in effect,that the abstract argumentation theory successfully captures the essence of logical reasoning behind normal logic programs.Unfortunately,the above argumentation theory can-not be extended directly to disjunctive logic programs. The reasons for this shortcoming,as well as a way of modifying the argumentation theory are discussed in the next section.2Collective ArgumentationWe begin with pointing out a peculiar discrepancy between the abstract argumentation theory,on the one hand,and the general abductive framework used for interpreting semantics for logic programs,on the other hand(see, e.g.,[Bondarenko et al.,1997, Dung,1995a,Kakas and Toni,1999]).The main ob-jects of the abductive argumentation theory are sets of assumptions(abducibles)of the form not p that play the role of arguments in the associated argumentation theory.In addition,the attack relation is defined in this framework as a relation between sets of abducibles and particular abducibles they attack.For example, the program rule r←not p,not q is interpreted as saying that the set of assumptions{not p,not q}at-tacks the assumption not r.The above attack relation is employed for defining the basic objects(such as extensions)of the source abduc-tive framework.The abstract argumentation theory defines its main objects,however,as sets of arguments. Consequently,they should correspond to sets of sets of assumptions in the abductive framework.The abduc-tive theory defines such objects,however,as certain plain sets of assumptions!In other words,we have a certain discrepancy between the levels of representa-tions of intended objects in these two theories.The above discrepancy will disappear once we notice that all the basic objects of the abstract argumentation theory are definable,in effect,in terms of the derived attack relationΓ֒→αbetween sets of arguments and particular arguments;only the latter was used in defin-ing the above operator[Γ].As a result,the abductive argumentation theory can be constructed in the same way as the abstract theory,with the only distinction that the attack relation between sets of arguments and particular arguments is not reducible to the attack re-lation among individual arguments.The above construction of abductive argumentation naturally suggests that assumptions,or abducibles, can be considered as full-fledged arguments,while the attack relation is best describable as a relation among sets of arguments.Indeed,once we allow for a possi-bility that a set of arguments can produce a nontrivial attack that is not reducible to attacks among partic-ular arguments,it is only natural to allow also for a possibility that a set of arguments could be attacked in such a way that we cannot single out a particular argument in the attacked set that could be blamedfor it.In a quite common case,for example,we can disprove some conclusion jointly supported by the dis-puted set of arguments.The following generalization of the abstract argumentation framework reflects this idea.Definition2.1.A collective argumentation theory is a pair A,֒→ ,where A is a set of arguments,and֒→is an attack relation onfinite subsets of A satisfying the following monotonicity condition:(Monotonicity)IfΓ֒→∆,thenΓ∪Γ′֒→∆∪∆′.Though the attack relation is defined above only on finite sets of arguments,it can be naturally extended to arbitrary such sets by imposing the following com-pactness property:(Compactness)Γ֒→∆only ifΓ′֒→∆′,for somefiniteΓ′⊆Γ,∆′⊆∆.As the reader may notice,the suggested argumenta-tion framework has many properties in common with ordinary sequent calculus,or consequence relations. Moreover,we will use in what follows the same agree-ments for the attack relation as that commonly ac-cepted for consequence relations.Thus,Γ,Γ1֒→∆,∆1 will have the same meaning asΓ∪Γ1֒→∆∪∆1.Sim-ilarly,α,Γ֒→∆,βwill be an alternative notation for {α}∪Γ֒→{β}∪∆,etc.The argumentation theory from[Dung,1995a]sat-isfies all the above properties.Moreover,the above modification of the abstract argumentation theory has already been suggested,in effect,in [Kakas and Toni,1999].However,the attack relation defined in the latter paper satisfied also a couple of fur-ther properties described in the following definition. Definition2.2.A collective argumentation theory will be called•affirmative if no set of arguments attacks the empty set∅;•local if it satisfies the following condition:(Locality)IfΓ֒→∆,∆′,then eitherΓ֒→∆orΓ֒→∆′.•normal if it is both affirmative and local.If a collective argumentation theory is normal,then it can be easily shown thatΓ֒→∆will hold if and only ifΓ֒→α,for someα∈∆.Consequently,the attack relation in such argumentation theories is reducible to the relationΓ֒→αbetween sets of arguments and sin-gle arguments,and the resulting argumentation the-ory will coincide,in effect,with that given already in [Dung,1995a].It turns out,however,that the general,non-local framework of collective argumentation is precisely what is needed in order to represent semantics of dis-junctive logic programs.2.1Collective Argumentation andDisjunctive ProgramsDespite an obvious success,the abstract argumenta-tion theory is still not abundant with intuitions and principles that could guide its development indepen-dently of applications.In this respect,logic program-ming and its semantics constitute one of the crucial sources and driving forces behind development of ar-gumentation theories.Consequently,as afirst step in studying collective argumentation,we consider its representation capabilities in describing semantics for disjunctive logic programs.In what follows,given a set of propositional atoms C, we will denote bymantics suggested for disjunctive logic programs.Ac-cording to this principle,semantics of such programs should be completely determined by rules C←not D without positive atoms in bodies that are derivable from the source program.See also[Bochman,1998] for the role of this principle in determining semantics of logic programs of a most general kind.The above considerations indicate that practically all‘respectable’semantics for disjunctive programs should be expressible in terms of collective argumen-tation theories associated with such programs.It turns out,however,that the actual semantics sug-gested for disjunctive programs do notfit easily into the general constructions of Dung’s argumentation theory.A most immediate reason for this is that the operator[Γ]of the abstract argumentation theory is no longer suitable for capturing the main content of the collective attack relation,since the latter is defined as holding between sets of arguments.Accordingly,it seems reasonable to generalize it to an operator that outputs a set of sets of arguments:Γ ={∆|Γ֒→∆}As in the abstract argumentation theory, Γ will col-lect argument sets that are allowable with respect to Γ.Notice that,due to monotonicity of the attack re-lation, Γ will be closed with respect to subsets,that is,if∆∈ Γ andΦ⊆∆,thenΦ∈ Γ .Conse-quently,any set Γ will be completely determined by maximal argument sets belonging to it.As can be eas-ily verified,such maximal sets will always exist due to compactness of the attack relation.2.2Stable and Partial Stable Argument Sets Using the above generalized operator of allowa-bility,we can give a rather simple description of stable and partial stable models for disjunc-tive programs(see,e.g.,[Gelfond and Lifschitz,1991, Przymusinski,1991])in terms of collective argumen-tation.Definition2.3.•A set of argumentsΓwill be said to be stable with respect to a collective argumen-tation theory if it is a maximal set in Γ .•A pair of sets(Γ,∆)will be called p-stable ifΓ⊆∆,Γis a maximal set in ∆ ,and∆is a maximal set in Γ .The following lemmas give more direct,and often more convenient,descriptions of the above objects.The proofs are immediate,so we omit them.Lemma2.1.Γis a stable set iffΓ={α|Γ֒→Γ,α}. The above equation says that a stable set is a setΓconsisting of all argumentsαsuch thatΓdoes not attackΓ∪{α}.A similar description can be given for partial stable sets:Lemma2.2.(Γ,∆)is p-stable iffΓ⊆∆,∆={α|Γ֒→∆,α},andΓ={α|∆֒→Γ,α}.Recall that normal collective argumentation theories could be identified with abstract Dung’s argumenta-tion theories.Moreover,the above descriptions can be used to show that if a collective argumentation theory is normal,then stable argument sets will coincide with stable extensions,while p-stable pairs will correspond exactly to complete extensions of the abstract argu-mentation theory.These facts could also be obtained as a by-product of the correspondence between such objects and relevant semantics of disjunctive programs stated below.The correspondence between the above descriptions and(partial)stable models of disjunctive logic pro-grams is established in the following theorem. Theorem2.3.If A P is a collective argumentation theory corresponding to a disjunctive program P,then •C is a stable model of P iffnotC,not2.3Argument sharingIn ordinary disputation and argumentation the par-ties can provisionally accept some of the arguments defended by their adversaries in order to disprove the latter.Two basic cases of such an‘argument sharing’in attacking the opponents are described in the follow-ing definition(see also[Bondarenko et al.,1997]).Definition2.4.•Γpositively attacks∆(notation Γ֒→+∆)ifΓ,∆֒→∆;•Γnegatively attacks∆(notationΓ֒→−∆)if Γ֒→Γ,∆.In a positive attack,the proponent temporarily ac-cepts opponent’s arguments in order to disprove the latter,while in a negative attack she shows that her arguments are sufficient for challenging an addition of opponent’s arguments.Clearly,ifΓattacks∆directly, then it attacks the latter both positively and nega-tively.The reverse implications do not hold,however. Note that the above defined notion of a stable argu-ment set was formulated,in effect,in terms of negative attacks.Indeed,it is easy to see that a setΓis stable iffit negatively attacks any argument outside it:Γ={α|Γ֒→−α}As can be seen,the above definition is equivalent to the definition of stable extensions in the abstract ar-gumentation theory,given earlier,so stable extensions and stable sets of collective argumentation are indeed close relatives.Recall now that admissible argument sets in Dung’s ar-gumentation theory are definable as conflict-free sets that counterattack any argument against them.Given the above proliferation of the notion of an attack in col-lective argumentation,however,we can obtain a num-ber of possible definitions of admissibility by allowing different kinds of attack and/or counterattack among sets of arguments.Three such notions turns out to be of special interest.Definition2.5.A conflict-free set of argumentsΓwill be called•admissible ifΓ֒→∆whenever∆֒→Γ;•positively admissible ifΓ֒→+∆whenever ∆֒→+Γ;•negatively admissible ifΓ֒→−∆whenever ∆֒→−Γ.Plain admissibility is a direct counterpart of the corre-sponding notion from the abstract argumentation the-ory.Unfortunately,in the context of collective argu-mentation it lacks practically all the properties it has in the latter.Notice,in particular,that stable sets as defined above need not be admissible in this sense. As can be seen,positive and negative admissibility coincide with plain admissibility for respective‘ex-tended’attack relations.The latter have some specific features that make the overall structure simpler and more regular.They will be described in the following sections.3Negative ArgumentationThe definition below provides a general description of collective argumentation based on a negative attack. Such argumentation theories will be shown to be es-pecially suitable for studying stable argument sets. Definition3.1.A collective argumentation theory will be called negative ifΓ֒→Γ,∆always implies Γ֒→∆.As can be easily verified,any collective argumentation theory will be negative with respect to the negative attack relation֒→−.Moreover,the latter determines a least negative‘closure’of the source attack relation. The following result gives an important alternative characterization of negative argumentation;it estab-lishes a correspondence between negative argumenta-tion and shift operations studied in a number of papers on disjunctive logic programming[Dix et al.,1994, Schaerf,1995,You et al.,2000].Lemma3.1.An argumentation theory is negative iffit satisfies:(Importation)IfΓ֒→∆,Φ,thenΓ,∆֒→Φ.Proof.If the argumentation theory is negative and Γ֒→∆,Φ,thenΓ,∆֒→Γ,∆,Φby monotonicity,and henceΓ,∆֒→Φ.The reverse implication is immedi-ate.As an important special case of Importation,we have that ifΓ֒→∆,thenΓ,∆֒→∅.Thus,any nontriv-ial negative argumentation theory is bound to be non-affirmative.Furthermore,this implies that self-contradictory arguments attack any argument:If∆֒→∆,then∆֒→ΓThese‘classical’properties indicate that negative at-tack is similar to a rule A⊢¬B holding in a supra-classical consequence relation.Though the latter doesnot admit contraposition,we nevertheless have that if A⊢¬(B∧C),then A,B⊢¬C.The connection between negative argumentation and stable argument sets is based on the following facts about general collective argumentation.Theorem3.2. 1.IfΓis negatively admissible,and ∆is a conflict-free set that includesΓ,then∆is also negatively admissible.2.Stable sets coincide with maximal negatively ad-missible sets.Proof.(1)Assume thatΓis negatively admissible,Γ⊆∆andΦ֒→−∆.ThenΦ֒→−∆,Γ,and hence Φ,∆֒→−Γby Importation.SinceΓis negatively ad-missible,we obtainΓ֒→−Φ,∆,and henceΓ,∆֒→−Φby Importation.But the latter amounts to∆֒→−Φ, which shows that∆is also negatively admissible. (2)It is easy to check that any stable set is negatively admissible.Moreover,any superset of a stable set will not already be conflict-free.Consequently stable sets will be maximal negatively admissible sets.In the other direction,ifΓis a maximal negatively admissible set andα/∈Γ,thenΓ∪{α}will not be conflict-free by the previous claim,and henceΓ,α֒→Γ,α.Conse-quentlyΓ,α֒→−Γ,and thereforeΓ֒→−Γ,α(sinceΓis negatively admissible).But the latter impliesΓ֒→−α, which shows thatΓis actually a stable set.Recall now that negatively admissible sets are precisely admissible sets with respect to the negative attack ֒→−.Moreover,in negative argumentation theories admissible sets will coincide with negatively admissi-ble ones,while any conflict-free set will already be pos-itively admissible.Accordingly,all nontrivial kinds of admissibility in such theories will boil down to(neg-ative)admissibility;furthermore,maximal admissible sets in such argumentation theories will coincide with stable sets.It can also be easily verified that any collective argu-mentation theory has the same stable sets as its neg-ative closure.So,Importation is an admissible rule for argumentation systems based on stable sets.As a result,negative argumentation theories suggest them-selves as a natural framework for describing stable sets. Though the above results demonstrate that negatively admissible sets behave much like logically consistent sets,there is a crucial difference:the empty set∅is not,in general,negatively admissible.Moreover, an argumentation theory may be‘negatively inconsis-tent’,that is,it may have no negatively admissible sets at all;this happens precisely when it has no stable sets.Unfortunately,the above considerations indicate also that negative argumentation is inappropriate for studying argument sets beyond stable ones.Recall that one of the main incentives for introducing par-tial stable and well-founded models for normal pro-grams was the desire to avoid taking stance on each and every literal and argument.However,negativity implies that self-contradictory arguments attack any argument whatsoever,so any admissible set is forced now to counter-attack any such argument.In partic-ular,if∆֒→Φ,then any admissible set should attack ∆∪Φ.This means that complete extensions(and par-tial stable models)are no longer a viable alternative for such argumentation systems.This means as well that Importation(and corresponding shift operations in logic programming)is an appropriate operation only for describing stable models1.4Positive ArgumentationThe following definition provides a description of ar-gumentation based on a positive attack.Definition4.1.A collective argumentation theory will be called positive ifΓ,∆֒→∆always implies Γ֒→∆.Any collective argumentation theory will be positive with respect to the positive attack relation֒→+.More-over,the latter determines a least positive extension of the source attack relation.Example.Consider an argumentation theory contain-ing only two argumentsαandβsuch thatα֒→αand α֒→β.As can be seen,this argumentation theory has no extensions,while the corresponding positive theory has a unique extension{β}.Similarly to negative argumentation,positive argu-mentation can be characterized by the‘exportation’property described in the lemma below:Lemma4.1.An argumentation theory is positive iffit satisfies:(Exportation)IfΓ,∆֒→Φ,thenΓ֒→∆,Φ.The above characterization implies,in particular,that self-conflicting arguments are attacked by any argu-ment:If∆֒→∆,thenΓ֒→∆So,in positive argumentation we are relieved,in effect, from the obligation to refute self-contradictory argu-ments.In particular,no allowable argument will be self-contradictory.It is interesting to note that positive and negative ar-gumentation are,in a sense,incompatible on pain of ly,if we combine positive and neg-ative argumentation,we obtain a symmetric attack re-lation:Lemma4.2.If an argumentation theory is both pos-itive an negative,thenα֒→βalways impliesβ֒→α.Proof.Ifα֒→β,thenα,β֒→α,βby monotonicity. Consequently,α,β֒→αby negativity and henceβ֒→αby positivity.In this case we can consider the attack relationα֒→βas expressing plain incompatibility of the arguments αandβin a classical logical sense.In other words, we could treat arguments as propositions and define α֒→βasα ¬β.4.1Local Positive ArgumentationAs a matter of fact,positively admissible sets were introduced for normal programs in[Kakas and Mankarella,1991](see also [Kakas and Toni,1999])under the name weakly stable sets;maximal such sets were termed stable theories.Accordingly,a study of such objects will amount to a study of admissible sets in collective argumentation theories that are positive closures of normal argumentation theories.Notefirst that a positive closure of a local argumen-tation theory need not,in general,be local.Still,the following property provides a characterization of posi-tive theories arising from local argumentation theories. Definition4.2.A collective argumentation theory will be called l-positive if it is positive and satisfies (Semi-locality)IfΓ֒→∆,Φ,then eitherΓ,∆֒→ΦorΓ,Φ֒→∆The following basic result shows that l-positive argu-mentation theories are precisely positive closures of lo-cal theories.Though the proof is not trivial,we omit it due to the lack of space.Theorem4.3.An argumentation theory is l-positive iffit is a positive closure of some local argumentation theory.Due to the above result,stable theories from [Kakas and Mankarella,1991]are exactly repre-sentable as maximal admissible sets in l-positive argumentation theories.It turns out that many properties of stable theories can be obtained in this abstract setting;the corresponding descriptions will be given in an extended version of this report.Still,we should mention that,since l-positive argumentation theories are not local,the corresponding structure of admissible sets is more complex than in the local case.For example,the set of admissible sets no longer forms a lower semi-lattice.5Preliminary ConclusionsCollective argumentation suggests itself as a natural extension of the abstract argumentation theory.It al-lows,in particular,to represent and study semantics for disjunctive logic programs.Speaking generally,it constitutes an argumentation framework in which the attack relation has structural properties allowing to represent cooperation and sharing of arguments among the parties.The present report is very preliminary,however;it only barely scratches the surface of the vast number of problems and issues that arise in this setting.One of such issues consists in extending the approach to other, weaker semantics suggested for disjunctive programs.A more general task amounts,however,to determining general argumentation principles underlying collective argumentation.This is a subject of an ongoing re-search.References[Bochman,1998]A.Bochman.A logical foundation for logic programming,I and II.Journal of Logic Programming,35:151–194,1998.[Bondarenko et al.,1997]A.Bondarenko,P.M. 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