Automata for infinite argumentation structures

The theory of abstract argumentation frameworks (afs) has, in the main, focused on finite structures, though there are many significant contexts where argumentation can be regarded as a process involving infinite objects. To address this limitation, in this paper we propose a novel approach for describing infinite afs using tools from formal language theory. In particular, the possibly infinite set of arguments is specified through the language recognized by a deterministic finite automaton while a suitable formalism, called attack expression, is introduced to describe the relation of attack between arguments. The proposed approach is shown to satisfy some desirable properties which cannot be achieved through other “naive” uses of formal languages. In particular, the approach is shown to be expressive enough to capture (besides any arbitrary finite structure) a large variety of infinite afs including two major examples from previous literature and two sample cases from the domains of multi-agent negotiation and ambient intelligence. On the computational side, we show that several decision and construction problems which are known to be polynomial time solvable in finite afs are decidable in the context of the proposed formalism and we provide the relevant algorithms. Moreover we obtain additional results concerning the case of finitaryafs

Dimensions of Neural-symbolic Integration - A Structured Survey

Research on integrated neural-symbolic systems has made significant progress in the recent past. In particular the understanding of ways to deal with symbolic knowledge within connectionist systems (also called artificial neural networks) has reached a critical mass which enables the community to strive for applicable implementations and use cases. Recent work has covered a great variety of logics used in artificial intelligence and provides a multitude of techniques for dealing with them within the context of artificial neural networks. We present a comprehensive survey of the field of neural-symbolic integration, including a new classification of system according to their architectures and abilities.Comment: 28 page

Separation of Test-Free Propositional Dynamic Logics over Context-Free Languages

For a class L of languages let PDL[L] be an extension of Propositional Dynamic Logic which allows programs to be in a language of L rather than just to be regular. If L contains a non-regular language, PDL[L] can express non-regular properties, in contrast to pure PDL. For regular, visibly pushdown and deterministic context-free languages, the separation of the respective PDLs can be proven by automata-theoretic techniques. However, these techniques introduce non-determinism on the automata side. As non-determinism is also the difference between DCFL and CFL, these techniques seem to be inappropriate to separate PDL[DCFL] from PDL[CFL]. Nevertheless, this separation is shown but for programs without test operators.Comment: In Proceedings GandALF 2011, arXiv:1106.081

Bounds on the Automata Size for Presburger Arithmetic

Automata provide a decision procedure for Presburger arithmetic. However, until now only crude lower and upper bounds were known on the sizes of the automata produced by this approach. In this paper, we prove an upper bound on the the number of states of the minimal deterministic automaton for a Presburger arithmetic formula. This bound depends on the length of the formula and the quantifiers occurring in the formula. The upper bound is established by comparing the automata for Presburger arithmetic formulas with the formulas produced by a quantifier elimination method. We also show that our bound is tight, even for nondeterministic automata. Moreover, we provide optimal automata constructions for linear equations and inequations

The Origins of Computational Mechanics: A Brief Intellectual History and Several Clarifications

The principle goal of computational mechanics is to define pattern and structure so that the organization of complex systems can be detected and quantified. Computational mechanics developed from efforts in the 1970s and early 1980s to identify strange attractors as the mechanism driving weak fluid turbulence via the method of reconstructing attractor geometry from measurement time series and in the mid-1980s to estimate equations of motion directly from complex time series. In providing a mathematical and operational definition of structure it addressed weaknesses of these early approaches to discovering patterns in natural systems. Since then, computational mechanics has led to a range of results from theoretical physics and nonlinear mathematics to diverse applications---from closed-form analysis of Markov and non-Markov stochastic processes that are ergodic or nonergodic and their measures of information and intrinsic computation to complex materials and deterministic chaos and intelligence in Maxwellian demons to quantum compression of classical processes and the evolution of computation and language. This brief review clarifies several misunderstandings and addresses concerns recently raised regarding early works in the field (1980s). We show that misguided evaluations of the contributions of computational mechanics are groundless and stem from a lack of familiarity with its basic goals and from a failure to consider its historical context. For all practical purposes, its modern methods and results largely supersede the early works. This not only renders recent criticism moot and shows the solid ground on which computational mechanics stands but, most importantly, shows the significant progress achieved over three decades and points to the many intriguing and outstanding challenges in understanding the computational nature of complex dynamic systems.Comment: 11 pages, 123 citations; http://csc.ucdavis.edu/~cmg/compmech/pubs/cmr.ht

Exploiting Parallelism for Hard Problems in Abstract Argumentation

Abstract argumentation framework (AF) is a unifying framework able to encompass a variety of nonmonotonic reasoning approaches, logic programming and computational argumentation. Yet, efficient approaches for most of the decision and enumeration problems associated to AF s are missing, thus potentially limiting the efficacy of argumentation-based approaches in real domains. In this paper, we present an algorithm for enumerating the preferred extensions of abstract argumentation frameworks which exploits parallel computation. To this purpose, the SCC-recursive semantics definition schema is adopted, where extensions are defined at the level of specific sub-frameworks. The algorithm shows significant performance improvements in large frameworks, in terms of number of solutions found and speedup