The CIFF Proof Procedure for Abductive Logic Programming with Constraints: Definition, Implementation and a Web Application

Abduction has found broad application as a powerful tool for hypothetical reasoning with incomplete knowledge, which can be handled by labeling some pieces of information as abducibles, i.e. as possible hypotheses that can be assumed to hold, provided that they are consistent with the given knowledge base. Attempts to make the abductive reasoning an effective computational tool gave rise to Abductive Logic Programming (ALP) which combines abduction with standard logic programming. A number of so-called proof procedures for ALP have been proposed in the literature, e.g. the IFF procedure, the Kakas and Mancarella procedure and the SLDNFA procedure, which rely upon extensions of different semantics for logic programming. ALP has also been integrated with Constraint Logic Programming (CLP), in order to combine abductive reasoning with an arithmetic tool for constraint solving. In recent years, many proof procedures for abductive logic programming with constraints have been proposed, including ACLP and the A-System which have been applied to many fields, e.g. multi-agent systems, scheduling, integration of information. This dissertation describes the development of a new abductive proof procedure with constraints, namely the CIFF proof procedure. The description is both at the theoretical level, giving a formal definition and a soundness result with respect to the three-valued completion semantics, and at the implementative level with the implemented CIFF System 4.0 as a Prolog meta-interpreter. The main contributions of the CIFF proof procedure are the advances in the expressiveness of the framework with respect to other frameworks for abductive logic programming with constraints, and the overall computational performances of the implemented system. The second part of the dissertation presents a novel application of the CIFF proof procedure as the computational engine of a tool, the CIFFWEB system, for checking and (possibly) repairing faulty web sites. Indeed, the exponential growth of the WWW raises the question of maintaining and automatically repairing web sites, in particular when the designers of these sites require them to exhibit certain properties at both structural and data level. The capability of maintaining and repairing web sites is also important to ensure the success of the Semantic Web vision. As the Semantic Web relies upon the definition and the maintenance of consistent data schemas (XML/XMLSchema, RDF/RDFSchema, OWL and so on), tools for reasoning over such schemas (and possibly extending the reasoning to multiple web pages) show great promise. The CIFFWEB system is such a tool which allows to verify and to repair XML web sites instances, against sets of requirements which have to be fulfilled, through abductive reasoning. We define an expressive characterization of rules for checking and repairing web sites' errors and we do a formal mapping of a fragment of a well known XML query language, namely Xcerpt, to abductive logic programs suitable to fed as input to the CIFF proof procedure. Finally, the CIFF proof procedure detects the errors and possibly suggests modifications to the XML instances to repair them. The soundness of this process is directly inherited from the soundness of CIFF

Law, Politics and Paradox : Orientations in Legal Formalism

The aim of this dissertation is to analyze the significance of the logical phenomenon of paradox for law and its relation to politics. I examine a selection of formal legal and political theories that in different ways understand law as a totality of norms, communications or behaviors, how paradox emerges in these theories, and what implications their understanding of paradox has for the relationship between law and politics. I argue that these legal and political theories can be meaningfully and in a novel way grouped according to their orientation to legal totality and paradox. To my knowledge, there is no research systematically mapping orientations to paradox in legal theory. It is the objective of this dissertation to fill this lack. Paradox presents challenges for formal thought, i.e. thought that analyzes the logic of totalities. Law, considered as a totality or form, gathers a plurality of entities under a common denominator and into a legal order. It is in reflecting on such formalization that we encounter paradoxes. This work aims to contribute to a growing literature on the implications of formalism for contemporary social and political thought by providing a legal theoretical perspective hitherto missing in these discussions. I use as a heuristic device a grouping of formal thought presented by the philosopher Paul M. Livingston. According to this grouping, there are three main orientations in contemporary formal thought to totality: the constructivist-criteriological, the paradoxico-critical and the generic orientation. These orientations arise on grounds of the “metalogical choice”: they prefer to view totality (such as law as a system or order) either as complete but inconsistent (the paradoxico-criticism), or as consistent but incomplete (the constructivist-criteriological and the generic orientation). I will apply, and modify when necessary, this categorization in order to analyze the theories of Hans Kelsen, Niklas Luhmann, Giorgio Agamben, Alain Badiou and Hans Lindahl, and to provide a systematic mapping of how the nature of law as a totality is understood in contemporary formal legal-political thought. Accounts of modern law encounter a paradox, I argue, if they observe law as an autonomous, self-referential totality that claims for itself the right to draw a distinction between itself and non-law. The paradox of autonomous law is that it cannot consistently show that it is itself legal as a totality. The basic problem that this implies is that the legal system or collective is unable to legitimate its existence and identity in response to challenges in any other way than by drawing on its own resources – which precisely is what the challenge targets in the first place. If we think of law as offering a framework within which questions of justice and injustice can be answered, the paradox emerges when we question the justice of this framework itself. The dissertation defends the paradoxico-critical orientation. It argues that the legal system is a paradoxical totality, which implies that there is no neutral metalanguage, such as natural law, that could solve the problem of law’s self-reference for good. This challenges legal theory to show how the problem of nihilistic relativism, the mere perpetuation of the self-referential legal system, can be mitigated and law’s normative authority in society rethought. In Chapter 1, I define the notion of paradox, explicate its meaning and role in formal thought and motivate its application to legal theory. In Chapter 2, I show that in his theory of the basic norm, Kelsen can be understood as oscillating between the constructivist-criteriological position and the paradoxico-criticism, between an attempt at guaranteeing legal order’s consistency in a metalanguage, i.e. legal science, and an acknowledgement of law as an inconsistent totality. In Chapter 3, I interpret Luhmann as a paradoxico-evolutionary thinker: he observes the legal system as constitutively inconsistent but emphasizes the ways in which the system seeks to make this inconsistency unproblematic for functional reasons. In Chapter 4, I show that in systems theory, just like in Kelsen’s pure theory, the politics of the paradox remains unarticulated. I also show that, for Agamben, a paradoxico-critical thinker, the paradoxical articulation of law and politics is exposed in the state of exception, which, in his analysis, has become the new normal, requiring “messianic” politics to deactivate the whole nihilistic sovereign-legal apparatus. For Badiou, the representative of the generic orientation, which I discuss in Chapter 5, what can be said within a language, and by implication a legal system, is pre-determined by that language. Politics, the desire to say the unsayable, is thrown fully outside the language and the legal system to a position from which law’s incompleteness, its incapacity to offer space for justice and politics, can only be disclosed. Both Agamben and Badiou, thus, think about politics as “post-juridical.” In Chapter 6, I show that the very inconsistency and paradox at the heart of the legal order is, for Lindahl’s paradoxico-criticism, the site of the politics of its limits. This dissertation, then, concludes that the paradoxical limits of the legal totality can be understood as the site of politics in law. Taking law’s paradox into account allows for a non-nihilistic conception of politically contestable law and legal authority.Väitöskirja selvittää paradoksin käsitteen merkitystä oikeudelle ja oikeuden ja politiikan väliselle suhteelle. Analysoin oikeusfilosofian alaan kuuluvassa tutkimuksessani, miten valikoimani oikeus- ja politiikan teoreetikot ymmärtävät oikeuden normeista, kommunikaatioista tai toiminnasta koostuvana kokonaisuutena, miten paradoksi ilmenee heidän teorioissaan ja mitä seurauksia sillä on heidän käsitykselleen oikeuden ja politiikan suhteesta. Väitän, että oikeus- ja politiikan teorian kenttää voi uudella tavalla hahmottaa selvittämällä suhtautumistapoja oikeuden paradoksiin. Aiemmin oikeusteoriassa ei ole systemaattisesti selvitetty käsityksiä oikeuden paradoksista, ja väitöskirjan tavoitteena on täyttää tämä aukko. Se osallistuu kasvavaan filosofiseen keskusteluun formaalin ajattelun merkityksestä yhteiskunta- ja poliittiselle teorialle ja tarjoaa oikeusteoreettisen näkökulman, joka keskustelusta vielä puuttuu. Paradoksi hahmottuu oikeusteoreettisena ongelmana, kun oikeutta teoretisoidaan kokonaisuutena eli oikeusjärjestyksenä. Käytän tutkimuksessani heuristisena apuna filosofi ja loogikko Paul M. Livingstonin kehittämää formaalin ajattelun jaottelua kolmeen, konstruktivistis-kriteriologiseen, paradoksis-kriittiseen ja geneeriseen suuntaukseen. Nämä suuntaukset käsittävät kokonaisuuksien luonteen eri tavoin ja siten tekevät erilaisen “metaloogisen valinnan”: ne käsittävät kokonaisuudet, kuten oikeuden systeeminä tai normijärjestyksenä, joko täydellisinä mutta paradoksaalisina tai konsistentteinä mutta epätäydellisinä. Sovellan tutkimuksessani tätä jaottelua ja analysoin sen avulla Hans Kelsenin, Niklas Luhmannin, Giorgio Agambenin, Alain Badioun ja Hans Lindahlin oikeus-poliittista ajattelua. Tavoitteena on systemaattisesti selvittää, miten nykyaikaisessa formaalissa oikeus-poliittisessa ajattelussa ymmärretään oikeuden luonne kokonaisuutena. Väitöskirja puolustaa paradoksis-kriittistä suuntausta. Väitän, että moderni oikeus voidaan ymmärtää paradoksaalisena, jos se käsitetään autonomisena, itseensä viittaavana kokonaisuutena, joka pidättää itselleen oikeuden vetää raja oikeuden ja ei-oikeuden välille. Autonomisen oikeuden paradoksi on se, ettei oikeusjärjestys pysty itse ristiriidattomasti oikeuttamaan itseään. Oikeusjärjestys mahdollistaa riidanratkaisun sekä oikean ja väärän, laillisen ja laittoman erottamisen toisistaan, mutta oikeuden yritykset ratkaista tarjoamansa riidanratkaisun oma oikeutus ja laillisuus johtavat paradoksiin. Seurauksena on, että oikeusjärjestelmä ja -yhteisö kykenee vastamaan kohtaamaansa kritiikkiin vain omasta näkökulmastaan, mikä juuri on kritiikin kohteena. Väitöskirjassa esitetään, että oikeusjärjestelmän ymmärtäminen paradoksaalisena kokonaisuutena merkitsee sekä ”metakielen”, kuten itsenäisen luonnonoikeuden, hylkäämistä ratkaisuna oikeuden itseensä viittaavuuden ongelmaan että luopumista täydellisen ja konsistentin oikeusjärjestyksen ideasta. Tästä seuraa, että oikeusteoria joutuu kohtaamaan oikeuden poliittisuuden, nihilistisen relativismin ongelman sekä etsimään uusia tapoja käsittää oikeuden normatiivisuus ja auktoriteetti yhteiskunnassa

Efficient Decision Support Systems

This series is directed to diverse managerial professionals who are leading the transformation of individual domains by using expert information and domain knowledge to drive decision support systems (DSSs). The series offers a broad range of subjects addressed in specific areas such as health care, business management, banking, agriculture, environmental improvement, natural resource and spatial management, aviation administration, and hybrid applications of information technology aimed to interdisciplinary issues. This book series is composed of three volumes: Volume 1 consists of general concepts and methodology of DSSs; Volume 2 consists of applications of DSSs in the biomedical domain; Volume 3 consists of hybrid applications of DSSs in multidisciplinary domains. The book is shaped upon decision support strategies in the new infrastructure that assists the readers in full use of the creative technology to manipulate input data and to transform information into useful decisions for decision makers

The Role of Inversion in the Genesis, Development and the Structure of Scientific Knowledge

The main thrust of the argument of this thesis is to show the possibility of articulating a method of construction or of synthesis--as against the most common method of analysis or division--which has always been (so we shall argue) a necessary component of scientific theorization. This method will be shown to be based on a fundamental synthetic logical relation of thought, that we shall call inversion--to be understood as a species of logical opposition, and as one of the basic monadic logical operators. Thus the major objective of this thesis is to This thesis can be viewed as a response to Larry Laudan's challenge, which is based on the claim that ``the case has yet to be made that the rules governing the techniques whereby theories are invented (if any such rules there be) are the sorts of things that philosophers should claim any interest in or competence at.'' The challenge itself would be to show that the logic of discovery (if at all formulatable) performs the epistemological role of the justification of scientific theories. We propose to meet this challenge head on: a) by suggesting precisely how such a logic would be formulated; b) by demonstrating its epistemological relevance (in the context of justification) and c) by showing that a) and b) can be carried out without sacrificing the fallibilist view of scientific knowledge. OBJECTIVES: We have set three successive objectives: one general, one specific, and one sub-specific, each one related to the other in that very order. (A) The general objective is to indicate the clear possibility of renovating the traditional analytico-synthetic epistemology. By realizing this objective, we attempt to widen the scope of scientific reason or rationality, which for some time now has perniciously been dominated by pure analytic reason alone. In order to achieve this end we need to show specifically that there exists the possibility of articulating a synthetic (constructive) logic/reason, which has been considered by most mainstream thinkers either as not articulatable, or simply non-existent. (B) The second (specific) task is to respond to the challenge of Larry Laudan by demonstrating the possibility of an epistemologically significant generativism. In this context we will argue that this generativism, which is our suggested alternative, and the simplified structuralist and semantic view of scientific theories, mutually reinforce each other to form a single coherent foundation for the renovated analytico-synthetic methodological framework. (C) The third (sub-specific) objective, accordingly, is to show the possibility of articulating a synthetic logic that could guide us in understanding the process of theorization. This is realized by proposing the foundations for developing a logic of inversion, which represents the pattern of synthetic reason in the process of constructing scientific definitions

Proceedings of the 7th Sound and Music Computing Conference

Proceedings of the SMC2010 - 7th Sound and Music Computing Conference, July 21st - July 24th 2010

Music in Evolution and Evolution in Music

Music in Evolution and Evolution in Music by Steven Jan is a comprehensive account of the relationships between evolutionary theory and music. Examining the ‘evolutionary algorithm’ that drives biological and musical-cultural evolution, the book provides a distinctive commentary on how musicality and music can shed light on our understanding of Darwin’s famous theory, and vice-versa. Comprised of seven chapters, with several musical examples, figures and definitions of terms, this original and accessible book is a valuable resource for anyone interested in the relationships between music and evolutionary thought. Jan guides the reader through key evolutionary ideas and the development of human musicality, before exploring cultural evolution, evolutionary ideas in musical scholarship, animal vocalisations, music generated through technology, and the nature of consciousness as an evolutionary phenomenon. A unique examination of how evolutionary thought intersects with music, Music in Evolution and Evolution in Music is essential to our understanding of how and why music arose in our species and why it is such a significant presence in our lives