748 research outputs found

    Control and Archaism

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    The presentation will delve into the relationship between control society and archaism. Deleuze’s conceptualization of control implies the reconfiguration of former spaces of discipline. While the Foucauldian model of discipline was characterized by enclosed spaces (such as prisons, armies, and churches), Deleuze’s notion of control highlights a continuous network where individuals are no longer molded but modulated. This prompts us to ponder the shift in the temporal structure that occurs during the transition from a disciplinary society to one governed by control. Specifically, this presentation aims to explore the disparities in our historical perspectives when viewed from disciplinary and control paradigms. In this context, I will explore Deleuze and Guattari's concept of ‘archaism’. According to Deleuze and Guattari, archaism is an inherent aspect of capitalism, its continual endeavor to reconstruct territoriality and replicate antiquated coding patterns. Capitalism necessitates archaism due to its lack of inherent belief structures. In essence, the system, which the duo name the ‘age of cynicism’, requires the revival of old codes to sustain its systems of subjugation and dominance. As my presentation will demonstrate, one can discern a transformation in the evolution of archaism as society shifts from discipline to control. By comparing the fascist archaism of the thirties in Germany and the archaism of contemporary alt-right movements, I will show that a disciplinary society presupposes a more centralized form of archaism, which is highly susceptible to state control and deeply ingrained in the institutional fabric of social life. Conversely, a control society implies a diversification and creativity in archaic attitudes, hinting at its potential for emancipation—a viewpoint emphasized by Deleuze and Guattari themselves in ’Anti-Oedipus’

    Belief Revision in Expressive Knowledge Representation Formalisms

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    We live in an era of data and information, where an immeasurable amount of discoveries, findings, events, news, and transactions are generated every second. Governments, companies, or individuals have to employ and process all that data for knowledge-based decision-making (i.e. a decision-making process that uses predetermined criteria to measure and ensure the optimal outcome for a specific topic), which then prompt them to view the knowledge as valuable resource. In this knowledge-based view, the capability to create and utilize knowledge is the key source of an organization or individual’s competitive advantage. This dynamic nature of knowledge leads us to the study of belief revision (or belief change), an area which emerged from work in philosophy and then impacted further developments in computer science and artificial intelligence. In belief revision area, the AGM postulates by Alchourrón, Gärdenfors, and Makinson continue to represent a cornerstone in research related to belief change. Katsuno and Mendelzon (K&M) adopted the AGM postulates for changing belief bases and characterized AGM belief base revision in propositional logic over finite signatures. In this thesis, two research directions are considered. In the first, by considering the semantic point of view, we generalize K&M’s approach to the setting of (multiple) base revision in arbitrary Tarskian logics, covering all logics with a classical model-theoretic semantics and hence a wide variety of logics used in knowledge representation and beyond. Our generic formulation applies to various notions of “base”, such as belief sets, arbitrary or finite sets of sentences, or single sentences. The core result is a representation theorem showing a two-way correspondence between AGM base revision operators and certain “assignments”: functions mapping belief bases to total — yet not transitive — “preference” relations between interpretations. Alongside, we present a companion result for the case when the AGM postulate of syntax-independence is abandoned. We also provide a characterization of all logics for which our result can be strengthened to assignments producing transitive preference relations (as in K&M’s original work), giving rise to two more representation theorems for such logics, according to syntax dependence vs. independence. The second research direction in this thesis explores two approaches for revising description logic knowledge bases under fixed-domain semantics, namely model-based approach and individual-based approach. In this logical setting, models of the knowledge bases can be enumerated and can be computed to produce the revision result, semantically. We show a characterization of the AGM revision operator for this logic and present a concrete model-based revision approach via distance between interpretations. In addition, by weakening the KB based on certain domain elements, a novel individual-based revision operator is provided as an alternative approach

    Deciding FO-rewritability of Regular Languages and Ontology-Mediated Queries in Linear Temporal Logic

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    Our concern is the problem of determining the data complexity of answering an ontology-mediated query (OMQ) formulated in linear temporal logic LTL over (Z,<) and deciding whether it is rewritable to an FO(<)-query, possibly with some extra predicates. First, we observe that, in line with the circuit complexity and FO-definability of regular languages, OMQ answering in AC0, ACC0 and NC1 coincides with FO(<,≡)-rewritability using unary predicates x ≡ 0 (mod n), FO(<,MOD)-rewritability, and FO(RPR)-rewritability using relational primitive recursion, respectively. We prove that, similarly to known PSᴘᴀᴄᴇ-completeness of recognising FO(<)-definability of regular languages, deciding FO(<,≡)- and FO(<,MOD)-definability is also PSᴘᴀᴄᴇ-complete (unless ACC0 = NC1). We then use this result to show that deciding FO(<)-, FO(<,≡)- and FO(<,MOD)-rewritability of LTL OMQs is ExᴘSᴘᴀᴄᴇ-complete, and that these problems become PSᴘᴀᴄᴇ-complete for OMQs with a linear Horn ontology and an atomic query, and also a positive query in the cases of FO(<)- and FO(<,≡)-rewritability. Further, we consider FO(<)-rewritability of OMQs with a binary-clause ontology and identify OMQ classes, for which deciding it is PSᴘᴀᴄᴇ-, Π2p- and coNP-complete

    Non-Rigid Designators in Epistemic and Temporal Free Description Logics (Extended Version)

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    Definite descriptions, such as 'the smallest planet in the Solar System', have been recently recognised as semantically transparent devices for object identification in knowledge representation formalisms. Along with individual names, they have been introduced also in the context of description logic languages, enriching the expressivity of standard nominal constructors. Moreover, in the first-order modal logic literature, definite descriptions have been widely investigated for their non-rigid behaviour, which allows them to denote different objects at different states. In this direction, we introduce epistemic and temporal extensions of standard description logics, with nominals and the universal role, additionally equipped with definite descriptions constructors. Regarding names and descriptions, in these languages we allow for: possible lack of denotation, ensured by partial models, coming from free logic semantics as a generalisation of the classical ones; and non-rigid designation features, obtained by assigning to terms distinct values across states, as opposed to the standard rigidity condition on individual expressions. In the absence of the rigid designator assumption, we show that the satisfiability problem for epistemic free description logics is NExpTime-complete, while satisfiability for temporal free description logics over linear time structures is undecidable

    Dual Forgetting Operators in the Context of Weakest Sufficient and Strongest Necessary Conditions

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    Forgetting is an important concept in knowledge representation and automated reasoning with widespread applications across a number of disciplines. A standard forgetting operator, characterized in [Lin and Reiter'94] in terms of model-theoretic semantics and primarily focusing on the propositional case, opened up a new research subarea. In this paper, a new operator called weak forgetting, dual to standard forgetting, is introduced and both together are shown to offer a new more uniform perspective on forgetting operators in general. Both the weak and standard forgetting operators are characterized in terms of entailment and inference, rather than a model theoretic semantics. This naturally leads to a useful algorithmic perspective based on quantifier elimination and the use of Ackermman's Lemma and its fixpoint generalization. The strong formal relationship between standard forgetting and strongest necessary conditions and weak forgetting and weakest sufficient conditions is also characterized quite naturally through the entailment-based, inferential perspective used. The framework used to characterize the dual forgetting operators is also generalized to the first-order case and includes useful algorithms for computing first-order forgetting operators in special cases. Practical examples are also included to show the importance of both weak and standard forgetting in modeling and representation

    Semiring Provenance for Lightweight Description Logics

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    We investigate semiring provenance--a successful framework originally defined in the relational database setting--for description logics. In this context, the ontology axioms are annotated with elements of a commutative semiring and these annotations are propagated to the ontology consequences in a way that reflects how they are derived. We define a provenance semantics for a language that encompasses several lightweight description logics and show its relationships with semantics that have been defined for ontologies annotated with a specific kind of annotation (such as fuzzy degrees). We show that under some restrictions on the semiring, the semantics satisfies desirable properties (such as extending the semiring provenance defined for databases). We then focus on the well-known why-provenance, which allows to compute the semiring provenance for every additively and multiplicatively idempotent commutative semiring, and for which we study the complexity of problems related to the provenance of an axiom or a conjunctive query answer. Finally, we consider two more restricted cases which correspond to the so-called positive Boolean provenance and lineage in the database setting. For these cases, we exhibit relationships with well-known notions related to explanations in description logics and complete our complexity analysis. As a side contribution, we provide conditions on an ELHI_bot ontology that guarantee tractable reasoning.Comment: Paper currently under review. 102 page

    From axioms over graphs to vectors, and back again: evaluating the properties of graph-based ontology embeddings

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    Several approaches have been developed that generate embeddings for Description Logic ontologies and use these embeddings in machine learning. One approach of generating ontologies embeddings is by first embedding the ontologies into a graph structure, i.e., introducing a set of nodes and edges for named entities and logical axioms, and then applying a graph embedding to embed the graph in Rn\mathbb{R}^n. Methods that embed ontologies in graphs (graph projections) have different formal properties related to the type of axioms they can utilize, whether the projections are invertible or not, and whether they can be applied to asserted axioms or their deductive closure. We analyze, qualitatively and quantitatively, several graph projection methods that have been used to embed ontologies, and we demonstrate the effect of the properties of graph projections on the performance of predicting axioms from ontology embeddings. We find that there are substantial differences between different projection methods, and both the projection of axioms into nodes and edges as well ontological choices in representing knowledge will impact the success of using ontology embeddings to predict axioms

    Ontologies as a Tool for Formalizing Data Validation Rules

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    Comparison of health data across national or even regional boundaries is a challenging task. Data sources, data collection methods, and data quality can vary widely and the quality of the indicators themselves is dependent upon the veracity of the underlying data. For any trans-regional or trans-national comparison of indicators, it is imperative to ensure data are appropriately validated. Ontologies provide a number of functionalities to help in this process. Data rules can be formalized using the ontology axioms, which are useful for removing the ambiguities of rules expressed in natural language. In addition, the axioms serve to identify the metadata and their corresponding semantic relationships, which can in turn be linked to standard data dictionaries or other ontologies. Moreover, ontologies provide the means for encapsulating the underlying data model of the domain allowing the rules and the data model to be maintained in a single application. Finally the expression of the axioms in description logic, as supported for example by the web ontology language, allows machine reasoning to validate data sets automatically against the formalized rules
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