Theory of Semi-Instantiation in Abstract Argumentation

We study instantiated abstract argumentation frames of the form (S, R, I), where (S, R) is an abstract argumentation frame and where the arguments x of S are instantiated by I(x) as well formed formulas of a well known logic, for example as Boolean formulas or as predicate logic formulas or as modal logic formulas. We use the method of conceptual analysis to derive the properties of our proposed system. We seek to define the notion of complete extensions for such systems and provide algorithms for finding such extensions. We further develop a theory of instantiation in the abstract, using the framework of Boolean attack formations and of conjunctive and disjunctive attacks. We discuss applications and compare critically with the existing related literature.     

Argumentation update in YALLA (Yet Another Logic Language for Argumentation)

This article proposes a complete framework for handling the dynamics of an abstract argumentation system. This frame can encompass several belief bases under the form of several argumentation systems, more precisely it is possible to express and study how an agent who has her own argumentation system can interact on a target argumentation system (that may represent a state of knowledge at a given stage of a debate). The two argumentation systems are defined inside a reference argumentation system called the universe which constitutes a kind of “common language”. This paper establishes three main results. First, we show that change in argumentation in such a framework can be seen as a particular case of belief update. Second, we have introduced a new logical language called YALLA in which the structure of an argumentation system can be encoded, enabling to express all the basic notions of argumentation theory (defense, conflict-freeness, extensions) by formulae of YALLA. Third, due to previous works about dynamics in argumentation we have been in position to provide a set of new properties that are specific for argumentation update.     

View-based explicit knowledge

In the information-based definition of knowledge, an agent is said to know α at a state s if α is true in all states that look the same as s to that agent. However, in systems where an agent's view of the system is partial, even if a state s′ may be logically indistinguishable from a state s, s′ may not be visible from s. For instance, in a distributed system, all global states in which the agent's local state does not change look the same to that agent but this set of global states may not be accessible because the agent may not even be aware of the existence of many agents in the network. We propose a logic of explicit knowledge built on agents' views and show it to be decidable.     

CTL AgentSpeak(L): A specification language for agent programs

This work introduces CTL AgentSpeak(L), a logic to specify and verify expected properties of rational agents implemented in the well-known agent oriented programming language AgentSpeak(L). Our approach is closely related to the BDICTL multi-modal logic, used to reason about agents in terms of their beliefs (B), desires (D), intentions (I), and the temporal logic CTL. A new interpretation for the temporal operators, grounded in the transition system induced by the operational semantics of AgentSpeak(L), is proposed. The main contribution of the approach is a better understanding of the relation between the programming language and its logical specification, enabling us to prove expected or desired properties for any agent programmed in the language, e.g., commitment strategies. The results, as well as the specification language proposed, are very useful to reconcile computational and philosophical aspects of practical reasoning, e.g., approaching single-minded commitment as a policy-based reconsideration case.     

Looking-ahead in backtracking algorithms for abstract argumentation

We refine implemented backtracking algorithms for a number of problems related to Dung's argumentation frameworks. Under admissible, preferred, complete, stable, semi stable, and ideal semantics we add enhancements, what are so-called global looking-ahead pruning strategies, to the-state-of-the-art implementations of two problems. First, we tackle the extension enumeration problem: constructing some/all set(s) of acceptable arguments of a given argumentation framework. Second, we address the acceptance decision problem: deciding whether an argument is in some/all set(s) of accepted arguments of a given argumentation framework. The experiments that we report show that the speedup gain of the new enhancements is quite significant.     

On desires and practical reasons

This paper challenges a common assumption about the relation between desires and practical reasons—namely, that if øing is an optimal way (or even just a way) for a person, P, to satisfy one of her desires, then P has a (normative) reason to ø. It challenges that assumption not by denying that desires are a source of practical reasons, but by showing that in some situations, rare though not impossible, P can lack a reason to ø despite having a desire that she could satisfy optimally by øing.     

AFRA: Argumentation framework with recursive attacks

The issue of representing attacks to attacks in argumentation is receiving an increasing attention as a useful conceptual modelling tool in several contexts. In this paper we present AFRA, a formalism encompassing unlimited recursive attacks within argumentation frameworks. AFRA satisfies the basic requirements of definition simplicity and rigorous compatibility with Dung’s theory of argumentation. This paper provides a complete development of the AFRA formalism complemented by illustrative examples and a detailed comparison with other recursive attack formalizations.     

Financial credit-risk evaluation with neural and neurofuzzy systems

Credit-risk evaluation decisions are important for the financial institutions involved due to the high level of risk associated with wrong decisions. The process of making credit-risk evaluation decision is complex and unstructured. Neural networks are known to perform reasonably well compared to alternate methods for this problem. However, a drawback of using neural networks for credit-risk evaluation decision is that once a decision is made, it is extremely difficult to explain the rationale behind that decision. Researchers have developed methods using neural network to extract rules, which are then used to explain the reasoning behind a given neural network output. These rules do not capture the learned knowledge well enough. Neurofuzzy systems have been recently developed utilizing the desirable properties of both fuzzy systems as well as neural networks. These neurofuzzy systems can be used to develop fuzzy rules naturally. In this study, we analyze the beneficial aspects of using both neurofuzzy systems as well as neural networks for credit-risk evaluation decisions.     

Independence for partition regular equations

A matrix A is said to be partition regular (PR) over a subset S of the positive integers if whenever S is finitely coloured, there exists a vector x, with all elements in the same colour class in S, which satisfies Ax=0. We also say that S is PR for A. Many of the classical theorems of Ramsey Theory, such as van der Waerden's theorem and Schur's theorem, may naturally be interpreted as statements about partition regularity. Those matrices which are partition regular over the positive integers were completely characterised by Rado in 1933.Given matrices A and B, we say that A Rado-dominates B if any set which is PR for A is also PR for B. One trivial way for this to happen is if every solution to Ax=0 actually contains a solution to By=0. Bergelson, Hindman and Leader conjectured that this is the only way in which one matrix can Rado-dominate another. In this paper, we prove this conjecture for the first interesting case, namely for 1×3 matrices. We also show that, surprisingly, the conjecture is not true in general.     

Avoidance control

We consider dynamical systems subject to control by two agents, one of whom desires that no trajectory of the system, emanating from outside a given set, intersects the set, no matter what the admissible actions of the other agent. Conditions are given whose satisfaction assures that a given control results in avoidance. Furthermore, these conditions are constructive in that they yield an avoidance feedback control. Some examples are presented.     

Steiner pentagon systems

A Steiner pentagon system is a pair (K_n, P) where K_n isthe complete undirected graph on n vertices. P is a collection of edge-disjoint pentagons which partition K_n, and such that every part of distinct vertices of K_n is joined by a path of length two in exactly one pentagon of the collection P. The number n is called the order of the system. This paper gives a somplete solution of the existence problem of Steiner pentagon systems. In particular it is shown that the spectrum for Steiner pentagon systems (=the set of all orders for which a Steiner pentagon system exists) is precisely the set of all n ≡ 1 or 5 (mod 10), except 15, for which no such system exists.     

Rich preference-based argumentation frameworks

An argumentation framework is seen as a directed graph whose nodes are arguments and arcs are attacks between the arguments. Acceptable sets of arguments, called extensions, are computed using a semantics. Existing semantics are solely based on the attacks and do not take into account other important criteria like the intrinsic strengths of arguments.The contribution of this paper is three fold. First, we study how preferences issued from differences in strengths of arguments can help in argumentation frameworks. We show that they play two distinct and complementary roles: (i) to repair the attack relation between arguments, (ii) to refine the evaluation of arguments. Despite the importance of both roles, only the first one is tackled in existing literature. In a second part of this paper, we start by showing that existing models that repair the attack relation with preferences do not perform well in certain situations and may return counter-intuitive results. We then propose a new abstract and general framework which treats properly both roles of preferences. The third part of this work is devoted to defining a bridge between the argumentation-based and the coherence-based approaches for handling inconsistency in knowledge bases, in particular when priorities between formulae are available. We focus on two well-known models, namely the preferred sub-theories introduced by Brewka and the demo-preferred sets defined by Cayrol, Royer and Saurel. For each of these models, we provide an instantiation of our abstract framework which is in full correspondence with it.     

Dichotomies and moving singularities

We consider a linear differential system ε ^σ Φ (t,ε)Y′ =A(t, ε)Y, with ε a small parameter and Φ(t, ε) a function which may vanish in the domain of definition. Under some conditions imposed on the eigenvalues of the matrixA(t, ε), there exists an invertible matrixH(t, ε) which is continuous on ([0,a] × [0, ε₀]). The transformationY=H(t, ε)Z takes then dimensional linear system into two differential systems of orderk andn?k respectively, withk. Thus the investigaton ofn dimensional systems encountered in singular perturbation as well as in stability theory is considerably simplified.     

A polyhedral approach to the alldifferent system

This paper examines the facial structure of the convex hull of integer vectors satisfying a system of alldifferent predicates, also called an alldifferent system. The underlying analysis is based on a property, called inclusion, pertinent to such a system. For the alldifferent systems for which this property holds, we present two families of facet-defining inequalities, establish that they completely describe the convex hull and show that they can be separated in polynomial time. Consequently, the inclusion property characterises a group of alldifferent systems for which the linear optimization problem (i.e. the problem of optimizing a linear function over that system) can be solved in polynomial time. Furthermore, we establish that, for systems with three predicates, the inclusion property is also a necessary condition for the convex hull to be described by those two families of inequalities. For the alldifferent systems that do not possess that property, we establish another family of facet-defining inequalities and an accompanied polynomial-time separation algorithm. All the separation algorithms are incorporated within a cutting-plane scheme and computational experience on a set of randomly generated instances is reported. In concluding, we show that the pertinence of the inclusion property can be decided in polynomial time.     

Computation algorithms for disturbance rejection in multivariable systems

In this paper, one way of solving an important problem in linear time-invariant multivariable systems control for synthesizing feedback controllers to make the outputs of a physical system respond in a desirable manner to reference inputs and external disturbances is presented. The proposed algorithms can be regarded as a logical extension of the pole assignment problem in that, measurable or unmeasurable multiple disturbance acting on multivariable systems described by the 4-tuples (A,B,C,E) or the 6-tuples (A,B,C,D,E,F) can be rejected at the outputs in steady state. This is done by assignment of the `disturbance blocking zeros' at specified locations using the concept of pole assignment for computing the state feedback controllers. The performance of the algorithms is illustrated by a numerical example.     

Dynamical generalizations of the lagrange spectrum

We compute two invariants of topological conjugacy, the upper and lower limits of the inverse of Boshernitzan??s ne _n , where e _n is the smallest measure of a cylinder of length n, for three families of symbolic systems: the natural codings of rotations, three-interval exchanges, and Arnoux-Rauzy systems. The sets of values of these invariants for a given family of systems generalize the Lagrange spectrum, which is what we obtain for the family of rotations with the upper limit of 1/ne _n.     

Isomorphism and Embedding of Borel Systems on Full Sets

A Borel system consists of a measurable automorphism of a standard Borel space. We consider Borel embeddings and isomorphisms between such systems modulo null sets, i.e. sets which have measure zero for every invariant probability measure. For every t>0 we show that in this category, up to isomorphism, there exists a unique free Borel system (Y,S) which is strictly t-universal in the sense that all invariant measures on Y have entropy <t, and if (X,T) is another free system obeying the same entropy condition then X embeds into Y off a null set. One gets a strictly t-universal system from mixing shifts of finite type of entropy ≥t by removing the periodic points and “restricting” to the part of the system of entropy <t. As a consequence, after removing their periodic points the systems in the following classes are completely classified by entropy up to Borel isomorphism off null sets: mixing shifts of finite type, mixing positive-recurrent countable state Markov chains, mixing sofic shifts, beta shifts, synchronized subshifts, and axiom-A diffeomorphisms. In particular any two equal-entropy systems from these classes are entropy conjugate in the sense of Buzzi, answering a question of Boyle, Buzzi and Gomez.     

Dung’s Argumentation is Essentially Equivalent to Classical Propositional Logic with the Peirce–Quine Dagger

In this paper we show that some versions of Dung’s abstract argumentation frames are equivalent to classical propositional logic. In fact, Dung’s attack relation is none other than the generalised Peirce–Quine dagger connective of classical logic which can generate the other connectives ?, ù, ú, ?{\neg, \wedge, \vee, \to} of classical logic. After establishing the above correspondence we offer variations of the Dung argumentation frames in parallel to variations of classical logic, such as resource logics, predicate logic, etc., etc., and create resource argumentation frames, predicate argumentation frames, etc., etc. We also offer the notion of logic proof as a geometrical walk along the nodes of a Dung network and thus we are able to offer a geometrical abstraction of the notion of inference based argumentation. Thus our paper is also a contribution to the question:     

Algorithms for generating arguments and counterarguments in propositional logic

A common assumption for logic-based argumentation is that an argument is a pair 〈Φ,α〉 where Φ is minimal subset of the knowledgebase such that Φ is consistent and Φ entails the claim α. Different logics provide different definitions for consistency and entailment and hence give us different options for formalising arguments and counterarguments. The expressivity of classical propositional logic allows for complicated knowledge to be represented but its computational cost is an issue. In previous work we have proposed addressing this problem using connection graphs and resolution in order to generate arguments for claims that are literals. Here we propose a development of this work to generate arguments for claims that are disjunctive clauses of more than one disjunct, and also to generate counteraguments in the form of canonical undercuts (i.e. arguments that with a claim that is the negation of the conjunction of the support of the argument being undercut).