normal and strong expansion equivalence for argumentation frameworks given a semantics s two argumentation frameworks afs f and g are said to be standard equivalent if they possess the same extensions and strongly equivalent if for any af h f conjoined with h and g conjoined with h are standard equivalent argumentation is a dynamic process and in general new arguments occur in response to a former argument or more precisely attack a former argument for this reason rather than considering arbitrary expansions we focus here on expansions where new arguments and attacks may be added but the attacks among the old arguments remain unchanged we define and characterize two new notions of equivalence between afs which lie in between standard and strong equivalence namely normal and strong expansion equivalence furthermore using the characterization theorems proved in this paper we draw the connections between all mentioned notions of equivalence including further equivalence relations so called weak and local expansion equivalence

ergodic theory for markov fibred systems and parabolic rational maps a paraboiic rational map of the riemann sphere admits a non atomic h conformal measure on its julia set where h the hausdorff dimension of the julia set and satisfies 1 2 h 2 with respect to this measure the rational map is conservative exact and there is an equivalent a finite invariant measure finiteness of the measure is characterised central limit theorems are proved in the case of a finite invariant measure and return sequences are identified in the case of an infinite one a theory of markov fibred systems is developed and parabolic rational maps are considered within this framework

abstract argumentation systems in this paper we develop a theory of abstract argumentation systems an abstract argumentation system is a collection of defeasible proofs called arguments that is partially ordered by a relation expressing the difference in conclusive force the prefix abstract indicates that the theory is concerned neither with a specification of the underlying language nor with the development of a subtheory that explains the partial order an unstructured language without logical connectives such as negation makes arguments not pairwise inconsistent but groupwise incompatible incompatibility and difference in conclusive force cause defeat among arguments the aim of the theory is to find out which arguments eventually emerge undefeated these arguments are considered to be in force several results are established the main result is that arguments that are in force are precisely those that are in the limit of a so called complete argumentation sequence

collet eckmann and holder we prove that collet eckmann condition for rational functions which requires exponential expansion only along the critical orbits yields the holder regularity of fatou components this implies geometric regularity of julia sets with non hyperbolic and critically recurrent dynamics in particular polynomial collet eckmann julia sets are locally connected if connected and their hausdorff dimension is strictly less than 2 the same is true for rational collet eckmann julia sets with at least one non empty fully invariant fatou component

adaptation and parameter estimation in systems with unstable target dynamics and nonlinear parametrization in this paper we propose a solution to the problem of adaptive control and parameter estimation in systems with unstable target dynamics models of uncertainties are allowed to be nonlinearly parameterized and required to be smooth and monotonic functions of linear functionals of the parameters the mere assumption of existence of nonlinear operator gains for the target dynamics is sufficient to guarantee that system solutions are bounded reach a neighborhood of the target set and the mismatches between the modeled uncertainties and their compensator converge to zero with respect to parameter convergence a standard persistent excitation condition suffices to ensure that it is exponential when a weaker nonlinear version of persistent excitation is satisfied asymptotic convergence is guaranteed the spectrum of possible applications ranges from tyre road slip control to asynchronous message transmission in spiking neural oscillators

a general framework for sound assumption based argumentation dialogues we propose a formal model for argumentation based dialogues between agents using assumption based argumentation aba as the underlying argumentation framework thus the dialogues amount to conducting an argumentation process in aba the model is given in terms of aba specific utterances debate trees and forests implicitly built during and drawn from dialogues legal move functions amounting to protocols and outcome functions the model is generic in that it is not restricted to any specific dialogue types and can be used to support a wide range thereof we prove a formal connection between dialogues and three well known argumentation semantics i e grounded admissible and ideal extensions by giving soundness results for our dialogue models with respect to these semantics thus our dialogues can be seen as a distributed mechanism for successfully determining acceptability of claims with respect to the semantics considered while constructing argumentation frameworks and arguments for these claims

extending abstract argumentation systems theory abstract in this paper we extend the theory of abstract argumentation systems proposed by vreeswijk 1997 this framework stands at a high abstraction level and provides a general model for argumentation activity however the theory reveals an inherent limitation in that the premises of the argumentation process are assumed to be indefeasible and this introduces the need of an implicit constraint on the strength of the arguments in order to preserve correctness in many application contexts the information available to start reasoning is not guaranteed to be completely reliable therefore it is natural to assume that premises can be discarded during the argumentation process we extend the theory by admitting that premises can be defeated and relaxing the implicit assumption about their strength besides fixing the technical problems related to this hidden assumption e g ensuring that warranted arguments are compatible our proposal provides an integrated model for belief revision and defeasible reasoning confirming the suitability of argumentation as a general model for the activity of intelligent reasoning in presence of various kinds of uncertainty

a model for belief revision abstract it is generally recognized that the possibility of detecting contradictions and identifying their sources is an important feature of an intelligent system systems that are able to detect contradictions identify their causes or readjust their knowledge bases to remove the contradiction called belief revision systems truth maintenance systems or reason maintenance systems have been studied by several researchers in artificial intelligence ai in this paper we present a logic suitable for supporting belief revision systems discuss the properties that a belief revision system based on this logic will exhibit and present a particular implementation of our model of a belief revision system the system we present differs from most of the systems developed so far in three respects first it is based on a logic that was developed to support belief revision systems second it uses the rules of inference of the logic to automatically compute the dependencies among propositions rather than having to force the user to do this as in many existing systems third it was the first belief revision system whose implementation relies on the manipulation of sets of assumptions not justifications

alternative foundations for reiter s default logic abstract we introduce an alternative conceptual basis for default reasoning in reiter s default logic in fact most formal or computational treatments of default logic suffer from the necessity of exhaustive consistency checks with respect to the finally resulting set of conclusions often this so called extension is just about being constructed on the theoretical side this exhaustive approach is reflected by the usual fixed point characterizations of extensions our goal is to reduce such global considerations to local and strictly necessary ones for this purpose we develop various techniques and instruments that draw on an analysis of interaction patterns between default rules embodied by their mutual blocking behavior these formal tools provide us with alternative means for addressing a variety of questions in default logic we demonstrate the utility of our approach by applying it to three traditional problems first we obtain a range of criteria guaranteeing the existence and non existence of extensions second we get alternative characterizations of extensions that avoid fixed point conditions finally we furnish a formal account of default proofs that was up to now neglected in the literature

dialectic proof procedures for assumption based admissible argumentation we present a family of dialectic proof procedures for the admissibility semantics of assumption based argumentation these proof procedures are defined for any conventional logic formulated as a collection of inference rules and show how any such logic can be extended to a dialectic argumentation system the proof procedures find a set of assumptions to defend a given belief by starting from an initial set of assumptions that supports an argument for the belief and adding defending assumptions incrementally to counter attack all attacks the proof procedures share the same notion of winning strategy for a dispute and differ only in the search strategy they use for finding it the novelty of our approach lies mainly in its use of backward reasoning to construct arguments and potential arguments and the fact that the proponent and opponent can attack one another before an argument is completed the definition of winning strategy can be implemented directly as a non deterministic program whose search strategy implements the search for defences

phase transitions for countable markov shifts we study the analyticity of the topological pressure for some one parameter families of potentials on countable markov shifts we relate the non analyticity of the pressure to changes in the recurrence properties of the system we give sufficient conditions for such changes to exist and not to exist we apply these results to the manneville pomeau map and use them to construct examples with different critical behavior

adaptive observers and parameter estimation for a class of systems nonlinear in the parameters we consider the problem of asymptotic reconstruction of the state and parameter values in systems of ordinary differential equations a solution to this problem is proposed for a class of systems of which the unknowns are allowed to be nonlinearly parameterized functions of state and time reconstruction of state and parameter values is based on the concepts of weakly attracting sets and non uniform convergence and is subjected to persistency of excitation conditions in the absence of nonlinear parametrization the resulting observers reduce to standard estimation schemes in this respect the proposed method constitutes a generalization of the conventional canonical adaptive observer design

on the evaluation of argumentation formalisms argumentation theory has become an important topic in the field of ai the basic idea is to construct arguments in favor and against a statement to select the acceptable ones and finally to determine whether the original statement can be accepted or not several argumentation systems have been proposed in the literature some of them the so called rule based systems use a particular logical language with strict and defeasible rules while these systems are useful in different domains e g legal reasoning they unfortunately lead to very unintuitive results as is discussed in this paper in order to avoid such anomalies in this paper we are interested in defining principles called rationality postulates that can be used to judge the quality of a rule based argumentation system in particular we define two important rationality postulates that should be satisfied the consistency and the closure of the results returned by that system we then provide a relatively easy way in which these rationality postulates can be warranted for a particular rule based argumentation system developed within a european project on argumentation

a general account of argumentation with preferences this paper builds on the recent aspic formalism to develop a general framework for argumentation with preferences we motivate a revised definition of conflict free sets of arguments adapt aspic to accommodate a broader range of instantiating logics and show that under some assumptions the resulting framework satisfies key properties and rationality postulates we then show that the generalised framework accommodates tarskian logic instantiations extended with preferences and then study instantiations of the framework by classical logic approaches to argumentation we conclude by arguing that aspic s modelling of defeasible inference rules further testifies to the generality of the framework and then examine and counter recent critiques of dung s framework and its extensions to accommodate preferences

augmenting tractable fragments of abstract argumentation we present a new approach to the efficient solution of important computational problems that arise in the context of abstract argumentation our approach makes known algorithms defined for restricted fragments generally applicable at a computational cost that scales with the distance from the fragment thus in a certain sense we gradually augment tractable fragments surprisingly it turns out that some tractable fragments admit such an augmentation and that others do not more specifically we show that the problems of credulous and skeptical acceptance are fixed parameter tractable when parameterized by the distance from the fragment of acyclic argumentation frameworks for most semantics other tractable fragments such as the fragments of symmetrical and bipartite frameworks seem to prohibit an augmentation the acceptance problems are already intractable for frameworks at distance 1 from the fragments for our study we use a broad setting and consider several different semantics for the algorithmic results we utilize recent advances in fixed parameter tractability

statistical properties of dynamical systems with some hyperbolicity this paper is about the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts though not necessarily all of their phase spaces the main results are for discrete time systems to put this work into context recall that for axiom a attractors the picture has been fairly complete since the 1970 s see s1 b r2 since then much progress has been made on two fronts there is a general nonuniform theory that deals with properties common to all diffeomorphisms with nonzero lyapunov exponents o p1 ka ly and there are detailed analyses of specific kinds of dynamical systems including for example billiards 1 dimensional and henon type maps s2 bsc hk j bc2 by1 statistical properties such as exponential decay of correlations are not enjoyed by all diffeomorphisms with nonzero lyapunov exponents the goal of this paper is a systematic understanding of these and other properties for a class of dynamical systems larger than axiom a this class will not be defined explicitly but it includes some of the much studied examples by looking at regular returns to sets with good hyperbolic properties one could give systems in this class a simple dynamical representation conditions for the existence of natural invariant measures exponential mixing and central limit theorems are given in terms of the return times these conditions can be checked in concrete situations giving a unified way of proving a number of results some new and some old among the new results are the exponential decay of correlations for a class of scattering billiards and for a positive measure set of henon type maps

an assumption based tms abstract this paper presents a new view of problem solving motivated by a new kind of truth maintenance system unlike previous truth maintenance systems which were based on manipulating justifications this truth maintenance system is in addition based on manipulating assumption sets as a consequence it is possible to work effectively and efficiently with inconsistent information context switching is free and most backtracking and all retraction is avoided these capabilities motivate a different kind of problem solving architecture in which multiple potential solutions are explored simultaneously this architecture is particularly well suited for tasks where a reasonable fraction of the potential solutions must be explored

statistical properties of maps with indifferent periodic points in this note we present an axiomatic approach to the decay of correlations for maps of arbitrary dimension with indifferent periodic points as applications we apply our results to the well known manneville pomeau equation and the inhomogeneous diophantine approximation algorithm

conditional entailment bridging two approaches to default reasoning abstract in recent years two conceptually different interpretations of default expressions have been advanced extensional interpretations in which defaults are regarded as prescriptions for extending one s set of beliefs and conditional interpretations in which defaults are regarded as beliefs whose validity is bound to a particular context the two interpretations possess virtues and limitations that are practically orthogonal to each other the conditional interpretations successfully resolve arguments of different specificity e g penguins don t fly in spite of being birds but fail to capture arguments of irrelevance e g concluding red birds fly from birds fly the opposite is true for the extensional interpretations this paper develops a new account of defaults called conditional entailment which combines the benefits of the two interpretations like prioritized circumscriptions conditional entailment resolves arguments by enforcing priorities among defaults however instead of having to be specified by the user these priorities are extracted automatically from the knowledge base similarly conditional entailment possesses a sound and complete proof theory based on interacting arguments and amenable to implementation in conventional atmss

an axiomatic analysis of structured argumentation with priorities several systems of semantics have been proposed for structured argumentation with priorities as the proposed semantics often sanction contradictory conclusions even for skeptical reasoners there is a fundamental need for guidelines for understanding and evaluating them especially their conceptual foundation and relationship in this paper we present an axiomatic analysis of the semantics of structured defeasible argumentation both with and without preferences by introducing a class of ordinary attack relations satisfying a set of simple and intuitive properties we show that there exists a normal form for ordinary attack relations in the sense that stable extensions wrt any ordinary attack relation are stable extensions wrt the normal attack relations we relate the ordinary semantics to other approaches especially to the aspic framework and the prioritized approaches in logic programming

reasoning about preferences in argumentation frameworks the abstract nature of dung s seminal theory of argumentation accounts for its widespread application as a general framework for various species of non monotonic reasoning and more generally reasoning in the presence of conflict a dung argumentation framework is instantiated by arguments and a binary conflict based attack relation defined by some underlying logical theory the justified arguments under different extensional semantics are then evaluated and the claims of these arguments define the inferences of the underlying theory to determine a unique set of justified arguments often requires a preference relation on arguments to determine the success of attacks between arguments however preference information is often itself defeasible conflicting and so subject to argumentation hence in this paper we extend dung s theory to accommodate arguments that claim preferences between other arguments thus incorporating meta level argumentation based reasoning about preferences in the object level we then define and study application of the full range of dung s extensional semantics to the extended framework and study special classes of the extended framework the extended theory preserves the abstract nature of dung s approach thus aiming at a general framework for non monotonic formalisms that accommodate defeasible reasoning about as well as with preference information we illustrate by formalising argument based logic programming with defeasible priorities in the extended theory

weak gibbs measures for intermittent systems and weakly gibbsian states in statistical mechanics in this paper we associate weak gibbs measures for intermittent maps with non gibbsian weakly gibbsian states in statistical mechanics in the sense of dobrushin 4 5 we show a higher dimensional intermittent map of which the sinai bowen ruelle measure is a weak gibbs equilibrium state and a weakly gibbsian state in the sense of dobrushin admitting essential discontinuities in its conditional probabilities

parameter estimation and compensation in systems with nonlinearly parameterized perturbations we consider a class of systems influenced by perturbations that are nonlinearly parameterized by unknown constant parameters and develop a method for estimating the unknown parameters the method applies to systems where the states are available for measurement and perturbations with the property that an exponentially stable estimate of the unknown parameters can be obtained if the whole perturbation is known the main contribution is to introduce a conceptually simple modular design that gives freedom to the designer in accomplishing the main task which is to construct an update law to asymptotically invert a nonlinear equation compensation for the perturbations in the system equations is considered for a class of systems with uniformly globally bounded solutions for which the origin is uniformly globally asymptotically stable when no perturbations are present we also consider the case when the parameters can only be estimated when the controlled state is bounded away from the origin and show that we may still be able to achieve convergence of the controlled state we illustrate the method through examples and apply it to the problem of downhole pressure estimation during oil well drilling

argument graphs and assumption based argumentation abstract arguments in structured argumentation are usually defined as trees and extensions as sets of such tree based arguments with various properties depending on the particular argumentation semantics however these arguments and extensions may have redundancies as well as circularities which are conceptually and computationally undesirable focusing on the specific case of assumption based argumentation aba we propose novel notions of arguments and admissible grounded extensions both defined in terms of graphs we show that this avoids the redundancies and circularities of standard accounts and set out the relationship to standard tree based arguments and admissible grounded extensions as sets of arguments we also define new notions of graph based admissible grounded dispute derivations for aba for determining whether specific sentences hold under the admissible grounded semantics we show that these new derivations are superior with respect to standard dispute derivations in that they are complete in general rather than solely for restricted classes of aba frameworks finally we present several experiments comparing the implementation of graph based admissible grounded dispute derivations with implementations of standard dispute derivations suggesting that the graph based approach is computationally advantageous

semantical considerations on nonmonotonic logic abstract commonsense reasoning is nonmonotonic in the sense that we often draw on the basis of partial information conclusions that we later retract when we are given more complete information some of the most interesting products of recent attempts to formalize nonmonotonic reasoning are the nonmonotonic logics of mcdermott and doyle 1 2 these logics however all have peculiarities that suggest they do not quite succeed in capturing the intuitions that prompted their development in this paper we reconstruct nonmonotonic logic as a model of an ideally rational agent s reasoning about his own beliefs for the resulting system called autoepistemic logic we define an intuitively based semantics for which we can show autoepistemic logic to be both sound and complete we then compare autoepistemic logic with the approach of mcdermott and doyle showing how it avoids the peculiarities of their nonmonotonic logic

stable adaptive control of a class of first order nonlinearly parameterized plants stable adaptive control algorithms are designed for a class of first order nonlinearly parameterized plants containing nonlinearities similar to those arising in fermentation process models when the plant nonlinearity is conveniently parameterized and when the controller parameters are adjusted adaptively the output error is shown to converge to zero stability of the overall system is proved using the lyapunov function with a suitably chosen cubic term

nonmonotonic logic ii nonmonotonic modal theories tradmonal logics suffer from the monotomclty problem new axioms never mvahdate old theorems one way to get nd of this problem ts to extend traditional modal logic in the following way the operator m usually read possible is extended so that mp is true whenever p is consistent with the theory then any theorem of this form may be mvahdated if p s added as an axiom this extension results m nonmonotomc versions of the systems t 4 and 5 these systems are complete in that a theorem is provable in a theory based on one of them just if it is true m all noncommittal models of that theory where a noncommittal model ts one m which as many thmgs are possible as possible nonmonotomc 4 is probably the most interesting of the three since it is stronger than ordinary 4 but has all the usual inferential machinery of 4 there is a straightforward proof procedure for the sententlal subset of nonmonotomc 4 this approach to nonmonotonlc logic may be applied to several problems in knowledge representation for aruficml mtelhgence its main advantages over competmg approaches are that tt factors out problems of resource hmltattons and allows the symbol m to appear m any context since m is a meaningful part of the language

subexponential decay of correlations we describe a method for proving subexponential lower bounds for correlations functions and apply it to study decay of correlations for maps with countable markov partitions one result is that ls young s upper estimates y2 are optimal in many situations our method is based on a general result concerning the asymptotics of renewal sequences of bounded operators acting on banach spaces which we apply to the iterates of the transfer operator

an argument based approach to reasoning with specificity we present a new priority based approach to reasoning with specificity which subsumes inheritance reasoning the new approach differs from other priority based approaches in the literature in the way priority between defaults is handled here it is conditional rather than unconditional as in other approaches we show that any unconditional handling of priorities between defaults as advocated in the literature until now is not sufficient to capture general defeasible inheritance reasoning we propose a simple and novel argumentation semantics for reasoning with specificity taking the conditionality of the priorities between defaults into account since the proposed argumentation semantics is a form of stable semantics of nonmonotonic reasoning it inherits a common problem of the latter where it is not always defined for every default theory we propose a class of stratified default theories for which the argumentation semantics is always defined we also show that acyclic and consistent inheritance networks are stratified we prove that the argumentation semantics satisfies the basic properties of a nonmonotonic consequence relation such as deduction reduction conditioning and cumulativity for well defined and stratified default theories we give a modular and polynomial transformation of default theories with specificity into semantically equivalent reiter default theories

the patterson measure for geometrically finite groups with parabolic elements new and old we study the patterson measure on the limit set of a geometrically finite kleinian group with parabolic elements using the conformality of the patterson measure in combination with basic hyperbolic geometry a global shadow lemma is obtained this macroscopic measure estimate is exploited to derive a khintchine type theorem which is then used for a finer analysis of the density of the limit set in terms of hausdorff measure

a logic for default reasoning the need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations it is this property which leads to the non monotonicity of any logic of defaults in this paper we propose a logic for default reasoning we then specialize our treatment to a very large class of commonly occuring defaults for this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover finally we provide criteria under which the revision of derived beliefs must be effected

equilibriums of some non holder potentials we consider one sided subshifts with some potential functions which satisfy the holder condition everywhere except at a fixed point and its preimages we prove that the systems have conformal measures and invariant measures absolutely continuous with respect to where may be finite or infinite we show that the systems are exact and are weak gibbs measures and equilibriums for we also discuss uniqueness of equilibriums and phase transition these results can be applied to some expanding dynamical systems with an indifferent fixed point

adaptive control of a class of nonlinearly parameterized plants a stable adaptive control method is developed for a class of first order nonlinearly parameterized plants the method is based on modified adaptive algorithms that yield a stable system in which the output errors are guaranteed to converge to zero the stability analysis is carried out using suitably constructed lyapunov functions

an abstract argumentation theoretic approach to default reasoning abstract we present an abstract framework for default reasoning which includes theorist default logic logic programming autoepistemic logic non monotonic modal logics and certain instances of circumscription as special cases the framework can be understood as a generalisation of theorist the generalisation allows any theory formulated in a monotonic logic to be extended by a defeasible set of assumptions an assumption can be defeated or attacked if its contrary can be proved possibly with the aid of other conflicting assumptions we show that given such a framework the standard semantics of most logics for default reasoning can be understood as sanctioning a set of assumptions as an extension of a given theory if and only if the set of assumptions is conflict free in the sense that it does not attack itself and it attacks every assumption not in the set we propose a more liberal argumentation theoretic semantics based upon the notion of admissible extension in logic programming we regard a set of assumptions in general as admissible if and only if it is conflict free and defends itself by attacking every set of assumptions which attacks it we identify conditions for the existence of extensions and for the equivalence of different semantics

instantiating abstract argumentation with classical logic arguments postulates and properties in this paper we investigate the use of classical logic as a basis for instantiating abstract argumentation frameworks in the first part we propose desirable properties of attack relations in the form of postulates and classify several well known attack relations from the literature with regards to the satisfaction of these postulates furthermore we provide additional postulates that help us prove characterisation results for these attack relations in the second part of the paper we present postulates regarding the logical content of extensions of argument graphs that may be constructed with classical logic we then conduct a comprehensive study of the status of these postulates in the context of the various combinations of attack relations and extension semantics

the semantics and proof theory of linear logic linear logic is a new logic which was recently developed by girard in order to provide a logical basis for the study of parallelism it is described and investigated in 9 girard s presentation of his logic is not so standard in this paper we shall provide more standard proof systems and semantics we shall also extend part of girard s results by investigating the consequence relations associated with linear logic and by proving corresponding strong completeness theorems finally we shall investigate the relation between linear logic and previously known systems especially relevance logics

a logic based theory of deductive arguments abstract we explore a framework for argumentation based on classical logic in which an argument is a pair where the first item in the pair is a minimal consistent set of formulae that proves the second item which is a formula we provide some basic definitions for arguments and various kinds of counter arguments defeaters this leads us to the definition of canonical undercuts which we argue are the only defeaters that we need to take into account we then motivate and formalise the notion of argument trees and argument structures which provide a way of exhaustively collating arguments and counter arguments we use argument structures as the basis of our general proposal for argument aggregation there are a number of frameworks for modelling argumentation in logic they incorporate formal representation of individual arguments and techniques for comparing conflicting arguments in these frameworks if there are a number of arguments for and against a particular conclusion an aggregation function determines whether the conclusion is taken to hold we propose a generalisation of these frameworks in particular our new framework makes it possible to define aggregation functions that are sensitive to the number of arguments for or against we compare our framework with a number of other types of argument systems and finally discuss an application in reasoning with structured news reports

technical communique a direct adaptive controller for dynamic systems with a class of nonlinear parameterizations in this note the adaptive control problem is considered for a class of nonlinearly parametrized systems by introducing a novel kind of lyapunov functions a direct adaptive controller is developed for achieving asymptotic tracking control the transient performance of the resulting closed loop system can be guaranteed by suitably choosing the lyapunov function to construct the controller the effectiveness of the proposed scheme is illustrated with two examples

adaptive repetitive control for a class of nonlinearly parametrized systems in this note lyapunov based adaptive repetitive control is presented for a class of nonlinearly parametrized systems through the use of an integral lyapunov function the controller singularity problem is elegantly solved as it avoids the nonlinear parametrization from entering into the adaptive control and repetitive control global stability of the adaptive system and asymptotic convergence of the tracking error are established and tracking error bounds are provided to quantify the control performance both partially and fully saturated learning laws are analyzed in detail and compared analytically

encoding deductive argumentation in quantified boolean formulae there are a number of frameworks for modelling argumentation in logic they incorporate a formal representation of individual arguments and techniques for comparing conflicting arguments a common assumption for logic based argumentation is that an argument is a pair where f is minimal subset of the knowledge base such that f is consistent and f entails the claim a different logics provide different definitions for consistency and entailment and hence give us different options for argumentation classical propositional logic is an appealing option for argumentation but the computational viability of generating an argument is an issue to better explore this issue we use quantified boolean formulae to characterise an approach to argumentation based on classical logic