A dialectical model of assessing conflicting arguments in legal reasoning

Inspired by legal reasoning, this paper presents a formal framework for assessing conflicting arguments. Its use is illustrated with applications to realistic legal examples, and the potential for implementation is discussed. The framework has the form of a logical system for defeasible argumentation. Its language, which is of a logic-programming-like nature, has both weak and explicit negation, and conflicts between arguments are decided with the help of priorities on the rules. An important feature of the system is that these priorities are not fixed, but are themselves defeasibly derived as conclusions within the system. Thus debates on the choice between conflicting arguments can also be modelled.The proof theory of the system is stated in dialectical style, where a proof takes the form of a dialogue between a proponent and an opponent of an argument. An argument is shown to be justified if the proponent can make the opponent run out of moves in whatever way the opponent attacks. Despite this dialectical form, the system reflects a declarative, or relational approach to modelling legal argument. A basic assumption of this paper is that this approach complements two other lines of research in AI and Law, investigations of precedent-based reasoning and the development of procedural, or dialectical models of legal argument.Supported by a research fellowship of the Royal Netherlands Academy of Arts and Sciences, and by Esprit WG 8319 Modelage.     

Choosing reference classes and building provisional models

A well-known problem in default logic is the ability of naive reasoners to explain bothg and ¬g from a set of observations. This problem is treated in at least two different ways within that camp.One approach is examination of the various explanations and choosing among them on the basis of various explanation comparators. A typical comparator is choosing the explanation that depends on the most specific observation, similar to the notion of narrowest reference class.Others examine default extensions of the observations and choose whatever is true in any extension, or what is true in all extensions or what is true in preferred extensions. Default extensions are sometimes thought of as acceptable models of the world that are discarded as more knowledge becomes available.We argue that the notions of specificity and extension lack clear semantics. Furthermore, we show that the problems these ideas were supposed to solve can be handled easily within a probabilistic framework.     

A Hyperbase for Binary Lattice Hyperidentities

We define an identity to be hypersatisfied by a variety V if, whenever the operation symbols of V, are replaced by arbitrary terms (of appropriate arity) in the operations of V, the resulting identity is satisfied by V in the usual sense. Whenever the identity is hypersatisfied by a variety V, we shall say that is a V hyperidentity. For example, the identity x + x y = x (x + y) is hypersatisfied by the variety L of all lattices. A proof of this consists of a case-by-case examination of { + , } {x, y, x y, x y}, the set of all binary lattice terms. In an earlier work, we exhibited a hyperbase ^L for the set of all binary lattice (or, equivalently, quasilattice) hyperidentities of type 2, 2. In this paper we provide a greatly refined hyperbase _L . The proof that _L is a hyperbase was obtained by using the automated reasoning program Otter 3.0.4.     

An Algebraic Approach to Propositional Fuzzy Logic

We investigate the variety corresponding to a logic (introduced in Esteva and Godo, 1998, and called there), which is the combination of ukasiewicz Logic and Product Logic, and in which Gödel Logic is interpretable. We present an alternative (and slightly simpler) axiomatization of such variety. We also investigate the variety, called the variety of algebras, corresponding to the logic obtained from by the adding of a constant and of a defining axiom for one half. We also connect algebras with structures, called f-semifields, arising from the theory of lattice-ordered rings, and prove that every algebra can be regarded as a structure whose domain is the interval [0, 1] of an f-semifield , and whose operations are the truncations of the operations of to [0, 1]. We prove that such a structure is uniquely determined by up to isomorphism, and we establish an equivalence between the category of algebras and that of f-semifields.     

Modular Control and Coordination of Discrete-Event Systems

In the supervisory control of discrete-event systems based on controllable languages, a standard way to handle state explosion in large systems is by modular supervision: either horizontal (decentralized) or vertical (hierarchical). However, unless all the relevant languages are prefix-closed, a well-known potential hazard with modularity is that of conflict. In decentralized control, modular supervisors that are individually nonblocking for the plant may nevertheless produce blocking, or even deadlock, when operating on-line concurrently. Similarly, a high-level hierarchical supervisor that predicts nonblocking at its aggregated level of abstraction may inadvertently admit blocking in a low-level implementation. In two previous papers, the authors showed that nonblocking hierarchical control can be guaranteed provided high-level aggregation is sufficiently fine; the appropriate conditions were formalized in terms of control structures and observers. In this paper we apply the same technique to decentralized control, when specifications are imposed on local models of the global process; in this way we remove the restriction in some earlier work that the plant and specification (marked) languages be prefix-closed. We then solve a more general problem of coordination: namely how to determine a high level coordinator that forestalls conflict in a decentralized architecture when it potentially arises, but is otherwise minimally intrusive on low-level control action. Coordination thus combines both vertical and horizontal modularity. The example of a simple production process is provided as a practical illustration. We conclude with an appraisal of the computational effort involved.     

Behaviour Synthesis of the Erect Stance for a Biped Control

In this paper we use free fall approach to develop a high level control/command strategy for a bipedal robot called BIPMAN, based on a multi-chain mechanical model with a general control architecture. The strategy is composed of three levels: the Legs and arms level, the Coordinator level and the Supervisor level. The Coordinator level is devoted to controlling leg movements and to ensure the stability of the whole biped. Actually perturbation effects threaten the equilibrium of the human robot and can only be compensated using a dynamic control strategy. This one is based on dynamic stability studies with a center of mass acceleration control and a force distribution on each leg and arm. Free fall in the gravity field is assumed to be deeply involved in the human locomotor control. According to studies of this specific motion through a direct dynamic model,the notion of equilibrium classes is introduced. They allow one to define time intervals in which the biped is able to maintain its posture. This notion is used for the definition of a reconfigurable high level control of the robot.     

Mesh Selection for a Nearly Singular Boundary Value Problem

In this paper, we investigate the numerical solution of a model equation u _xx = exp(– ) (and several slightly more general problems) when 1 using the standard central difference scheme on nonuniform grids. In particular, we are interested in the error behaviour in two limiting cases: (i) the total mesh point number N is fixed when the regularization parameter 0, and (ii) is fixed when N. Using a formal analysis, we show that a generalized version of a special piecewise uniform mesh 12 and an adaptive grid based on the equidistribution principle share some common features. And the optimal meshes give rates of convergence bounded by |log()| as 0 and N is given, which are shown to be sharp by numerical tests.     

Higher-Order and Modal Logic as a Framework for Explanation-Based Generalization

Certain tasks, such as formal program development and theorem proving, fundamentally rely upon the manipulation of higher-order objects such as functions and predicates. Computing tools intended to assist in performing these tasks are at present inadequate in both the amount of knowledge they contain (i.e., the level of support they provide) and in their ability to learn (i.e., their capacity to enhance that support over time). The application of a relevant machine learning technique—explanation-based generalization (EBG)—has thus far been limited to first-order problem representations. We extend EBG to generalize higher-order values, thereby enabling its application to higher-order problem encodings.Logic programming provides a uniform framework in which all aspects of explanation-based generalization and learning may be defined and carried out. First-order Horn logics (e.g., Prolog) are not, however, well suited to higher-order applications. Instead, we employ Prolog, a higher-order logic programming language, as our basic framework for realizing higher-order EBG. In order to capture the distinction between domain theory and training instance upon which EBG relies, we extend Prolog with the necessity operator of modal logic. We develop a meta-interpreter realizing EBG for the extended language, Prolog, and provide examples of higher-order EBG.     

Query answering via cooperative data inference

This paper proposes the use of accessible information (data/knowledge) to infer inaccessible data in a distributed database system. Inference rules are extracted from databases by means of knowledge discovery techniques. These rules can derive inaccessible data due to a site failure or network partition in a distributed system. Such query answering requires combining incomplete and partial information from multiple sources. The derived answer may be exact or approximate. Our inference process involves two phases to reason with reconstructed information. One phase involves using local rules to infer inaccessible data. A second phase involves merging information from different sites. We shall call such reasoning processes cooperative data inference. Since the derived answer may be incomplete, new algebraic tools are developed for supporting operations on incomplete information. A weak criterion called toleration is introduced for evaluating the inferred results. The conditions that assure the correctness of combining partial results, known as sound inference paths, are developed. A solution is presented for terminating an iterative reasoning process on derived data from multiple knowledge sources. The proposed approach has been implemented on a cooperative distributed database testbed, CoBase, at UCLA. The experimental results validate the feasibility of this proposed concept and can significantly improve the availability of distributed knowledge base/database systems.List of notation Mapping - --< Logical implication - = Symbolic equality - ==< Inference path - Satisfaction - Toleration - Undefined (does not exist) - Variable-null (may or may not exist) - ^* Subtuple relationship - ^* s-membership - s-containment - Open subtuple - Open s-membership - Open s-containment - _P Open base - P Program - I Interpretation - DIP Data inference program - t Tuples - R Relations - Ø Empty interpretation - Open s-union - Open s-interpretation - Set of mapping from the set of objects to the set of closed objects - W Set of attributes - _W Set of sound inference paths on the set of attributes W - Set of relational schemas in a DB that satisfy MVD - ⁺ Range closure of W wrt      

Types with intersection: An introduction

This paper is an informal introduction to the theory of types which use a connective for the intersection of two types and a constant for a universal type, besides the usual connective for function-types. This theory was first devised in about 1977 by Coppo, Dezani and Sallé in the context of-calculus and its main development has been by Coppo and Dezani and their collaborators in Turin. With suitable axioms and rules to assign types to-calculus terms, they obtained a system in which (i) the set of types given to a term does not change under-conversion, (ii) some interesting sets of terms, for example the solvable terms and the terms with normal form, can be characterised exactly by the types of their members, and (iii) the type-apparatus is not so complex as polymorphic systems with quantifier-containing types and therefore probably not so expensive to implement mechanically as these systems.There are in fact several variant systems with different detailed properties. This paper defines and motivates the simplest one from which the others are derived, and describes its most basic properties. No proofs are given but the motivation is shown by examples. A comprehensive bibliography is included.     

Least Squares Policy Evaluation Algorithms with Linear Function Approximation

We consider policy evaluation algorithms within the context of infinite-horizon dynamic programming problems with discounted cost. We focus on discrete-time dynamic systems with a large number of states, and we discuss two methods, which use simulation, temporal differences, and linear cost function approximation. The first method is a new gradient-like algorithm involving least-squares subproblems and a diminishing stepsize, which is based on the -policy iteration method of Bertsekas and Ioffe. The second method is the LSTD() algorithm recently proposed by Boyan, which for =0 coincides with the linear least-squares temporal-difference algorithm of Bradtke and Barto. At present, there is only a convergence result by Bradtke and Barto for the LSTD(0) algorithm. Here, we strengthen this result by showing the convergence of LSTD(), with probability 1, for every [0, 1].     

More Church–Rosser Proofs

The proofs of the Church–Rosser theorems for , , and reduction in untyped -calculus are formalized in Isabelle/HOL, an implementation of Higher Order Logic in the generic theorem prover Isabelle. For -reduction, both the standard proof and Takahashi's are given and compared. All proofs are based on a general theory of commutating relations that supports an almost geometric style of reasoning about confluence diagrams.     

Hierarchies of polynomially solvable satisfiability problems

In this paper, we introduce general techniques for extending classes of polynomially solvable SAT instances. We generalize the approach of Gallo and Scutellà, who defined the hierarchy { _i }, where _l corresponds to the Generalized Horn class. We propose a family of polynomial hierarchies, where a polynomial hierarchy { _i } is a sequence of polynomially solvable classes that cover the whole set of CNF formulas, and such that _{i i+1} fori0. Following a different approach, based on a new decomposition technique, we define the class of Split-Horn formulas, which is an extension of _l. We discuss and compare the basic properties of the proposed classes; polynomial time algorithms for recognition and solution are provided.     

Modelling default and likelihood reasoning as probabilistic reasoning

This paper presents a probabilistic analysis of plausible reasoning about defaults and about likelihood. Likely and by default are in fact treated as duals in the same sense as possibility and necessity. To model these four forms probabilistically, a logicQDP and its quantitative counterpartDP are derived that allow qualitative and corresponding quantitative reasoning. Consistency and consequence results for subsets of the logics are given that require at most a quadratic number of satisfiability tests in the underlying prepositional logic. The quantitative logic shows how to track the propagation error inherent in these reasoning forms. The methodology and sound framework of the system highlights their approximate nature, the dualities, and the need for complementary reasoning about relevance.Much of this research was done while at the University of Technology, Sydney, Broadway, NSW, Australia, and some at the Turing Institute, 36 Nth. Hanover Str., Glasgow, Scotland.     

On characterizations of recursively enumerable languages

Summary Geffert has shown that earch recursively enumerable languageL over can be expressed in the formL{h(x) ^–1 g(x)x in ⁺} ^* where is an alphabet andg, h is a pair of morphisms. Our purpose is to give a simple proof for Geffert's result and then sharpen it into the form where both of the morphisms are nonerasing. In our method we modify constructions used in a representation of recursively enumerable languages in terms of equality sets and in a characterization of simple transducers in terms of morphisms. As direct consequences, we get the undecidability of the Post correspondence problem and various representations ofL. For instance,L =(L ₀) ^* whereL ₀ is a minimal linear language and is the Dyck reductiona, A.     

An investigation of the maintenance and support characteristics of commercial software

This study demonstrates an objective method used to evaluate the enhanceability of commercial software. It examines the relationship between enhancement and repair, and suggests that enhancement be considered when developing formal models of defect cause. Another definition of defect-prone software is presented that concentrates attention on software that requires unusually high repair considering the magnitude of planned enhancement.     

Viscous Lattices

Let E be an arbitrary space, and an extensive dilation of P(E) into itself, with an adjoint erosion . Then, the image [P(E)] of P(E) by is a complete lattice P where the sup is the union and the inf the opening of the intersection according to . The lattice L, named viscous, is not distributive, nor complemented. Any dilation on P(E) admits the same expression in L. However, the erosion in L is the opening according to of the erosion in P(E). Given a connection C on P(E) the image of C under turns out to be a connection C on L as soon as (C)eq C. Moreover, the elementary connected openings _x of C and _(x) are linked by the relation _(x) = _x. A comprehensive class of connection preverving closings is constructed. Two examples, binary and numerical (the latter comes from the heart imaging), prove the relevance of viscous lattices in interpolation and in segmentation problems.Jean Serra obtained the degree of Mining Engineer, in 1962 in Nancy, France, and in 1967 his Ph.D. for a work dealing with the estimation of the iron ore body of Lorraine by geostatistics. In cooperation with Georges Matheron, he laid the foundations of a new method, that he called Mathematical Morphology (1964). Its purpose was to describe quantitatively shapes and textures of natural phenomena, at micro and macro scales. In 1967, he founded with G. Matheron, the Centre de Morphologie Mathematique, at School of Mines of Paris, on the campus of Fontainebleau. Since this time, he has been working in this framework as a Directeur de Recherches. His main book is a two-volume treatise entitled Image Analysis and Mathematical Morphology (Ac. Press, 1982, 1988). He has been Vice President for Europe of the International Society for Stereology from 1979 to 1983. He founded the International Society for Mathematical Morphology in 1993, and was elected his first president. His achievements include several patents of devices for image processing, various awards and titles, such as the first AFCET award, in 1988, or Doctor Honoris Causa of the University of Barcelona (Spain) in 1993. He recently developed a new theory of segmentation, which is based on set connections (2001–2004), and currently works on colour image processing.     

Implementing the ‘Fool's model’ of combinatory logic

This paper studies Fool's models of combinatory logic, and relates them to Hindley's D-completeness problem. A fool's model is a family of sets of formulas, closed under condensed detachment. Alternatively, it is a model ofCL in naive set theory. We examine Resolution; and the P-W problem. A sequel shows T is D-complete; also, its extensions. We close with an implementation FMO of these ideas.     

Low-Rank Approximation of Integral Operators by Interpolation

A central component of the analysis of panel clustering techniques for the approximation of integral operators is the so-called -admissibility condition min {diam(),diam()} 2dist(,) that ensures that the kernel function is approximated only on those parts of the domain that are far from the singularity. Typical techniques based on a Taylor expansion of the kernel function require a subdomain to be far enough from the singularity such that the parameter has to be smaller than a given constant depending on properties of the kernel function. In this paper, we demonstrate that any is sufficient if interpolation instead of Taylor expansionisused for the kernel approximation, which paves the way for grey-box panel clustering algorithms.     

Automatic Extraction of Collocations From Korean Text

In this paper, we propose a statistical method to automaticallyextract collocations from Korean POS-tagged corpus. Since a large portion of language is represented by collocation patterns, the collocational knowledge provides a valuable resource for NLP applications. One difficulty of collocation extraction is that Korean has a partially free word order, which also appears in collocations. In this work, we exploit four statistics, frequency,randomness, convergence, and correlation' in order to take into account the flexible word order of Korean collocations. We separate meaningful bigrams using an evaluation function based on the four statistics and extend the bigrams to n-gram collocations using a fuzzy relation. Experiments show that this method works well for Korean collocations.