Ontology engineering is a hard and error-prone task, in which small changes may lead to errors, or even produce an inconsistent ontology. As ontologies grow in size, the need for automated methods for repairing inconsistencies while preserving as much of the original knowledge as possible increases. Most previous approaches to this task are based on removing a few axioms from the ontology to regain consistency. We propose a new method based on weakening these axioms to make them less restrictive, employing (...) the use of refinement operators. We introduce the theoretical framework for weakening DL ontologies, propose algorithms to repair ontologies based on the framework, and provide an analysis of the computational complexity. Through an empirical analysis made over real-life ontologies, we show that our approach preserves significantly more of the original knowledge of the ontology than removing axioms. (shrink)

We discuss the role of perceptron (or threshold) connectives in the context of Description Logic, and in particular their possible use as a bridge between statistical learning of models from data and logical reasoning over knowledge bases. We prove that such connectives can be added to the language of most forms of Description Logic without increasing the complexity of the corresponding inference problem. We show, with a practical example over the Gene Ontology, how even simple instances of perceptron connectives are (...) expressive enough to represent learned, complex concepts derived from real use cases. This opens up the possibility to import concepts learnt from data into existing ontologies. (shrink)

The properties of the ${\forall^{1}}$ quantifier defined by Kontinen and Väänänen in [13] are studied, and its definition is generalized to that of a family of quantifiers ${\forall^{n}}$ . Furthermore, some epistemic operators δ n for Dependence Logic are also introduced, and the relationship between these ${\forall^{n}}$ quantifiers and the δ n operators are investigated.The Game Theoretic Semantics for Dependence Logic and the corresponding Ehrenfeucht- Fraissé game are then adapted to these new connectives.Finally, it is proved that the ${\forall^{1}}$ quantifier (...) is not uniformly definable in Dependence Logic, thus answering a question posed by Kontinen and Väänänen in the above mentioned paper. (shrink)

We develop a semantics for independence logic with respect to what we will call general models. We then introduce a simpler entailment semantics for the same logic, and we reduce the validity problem in the former to the validity problem in the latter. Then we build a proof system for independence logic and prove its soundness and completeness with respect to entailment semantics.

We examine the transitions between sets of possible worlds described by the compositional semantics of Modal Dependence Logic, and we use them as the basis for a dynamic version of this logic. We give a game theoretic semantics, a (compositional) transition semantics and a power game semantics for this new variant of modal Dependence Logic, and we prove their equivalence; and furthermore, we examine a few of the properties of this formalism and show that Modal Dependence Logic can be recovered (...) from it by reasoning in terms of reachability. Then we show how we can generalize this approach to a very general formalism for reasoning about transformations between pointed Kripke models. (shrink)

We present a compositional semantics for first-order logic with imperfect information that is equivalent to Sevenster and Sandu’s equilibrium semantics (under which the truth value of a sentence in a finite model is equal to the minimax value of its semantic game). Our semantics is a generalization of an earlier semantics developed by the first author that was based on behavioral strategies, rather than mixed strategies.

In Team Semantics, a dependency notion is strongly first order if every sentence of the logic obtained by adding the corresponding atoms to First-Order Logic is equivalent to some first-order sentence. In this work it is shown that all nontrivial dependency atoms that are strongly first order, downwards closed, and relativizable are definable in terms of constancy atoms.Additionally, it is shown that any strongly first-order dependency is safe for any family of downwards closed dependencies, in the sense that every sentence (...) of the logic obtained by adding to First-Order Logic both the strongly first-order dependency and the downwards closed dependencies is equivalent to some sentence of the logic obtained by adding only the downwards closed dependencies. (shrink)

We introduce and discuss a knowledge-driven distillation approach to explaining black-box models by means of two kinds of interpretable models. The first is perceptron (or threshold) connectives, which enrich knowledge representation languages such as Description Logics with linear operators that serve as a bridge between statistical learning and logical reasoning. The second is Trepan Reloaded, an ap- proach that builds post-hoc explanations of black-box classifiers in the form of decision trees enhanced by domain knowledge. Our aim is, firstly, to target (...) a model-agnostic distillation approach exemplified with these two frameworks, secondly, to study how these two frameworks interact on a theoretical level, and, thirdly, to investigate use-cases in ML and AI in a comparative manner. Specifically, we envision that user-studies will help determine human understandability of explanations generated using these two frameworks. (shrink)

Axiom weakening is a technique that allows for a fine-grained repair of inconsistent ontologies. Its main advantage is that it repairs on- tologies by making axioms less restrictive rather than by deleting them, employing the use of refinement operators. In this paper, we build on pre- viously introduced axiom weakening for ALC, and make it much more irresistible by extending its definitions to deal with SROIQ, the expressive and decidable description logic underlying OWL 2 DL. We extend the definitions of (...) refinement operator to deal with SROIQ constructs, in particular with role hierarchies, cardinality constraints and nominals, and illustrate its application. Finally, we discuss the problem of termi- nation of an iterated weakening procedure. (shrink)

When people combine concepts these are often characterised as “hybrid”, “impossible”, or “humorous”. However, when simply considering them in terms of extensional logic, the novel concepts understood as a conjunctive concept will often lack meaning having an empty extension (consider “a tooth that is a chair”, “a pet flower”, etc.). Still, people use different strategies to produce new non-empty concepts: additive or integrative combination of features, alignment of features, instantiation, etc. All these strategies involve the ability to deal with conflicting (...) attributes and the creation of new (combinations of) properties. We here consider in particular the case where a Head concept has superior ‘asymmetric’ control over steering the resulting concept combination (or hybridisation) with a Modifier concept. Specifically, we propose a dialogical approach to concept combination and discuss an implementation based on axiom weakening, which models the cognitive and logical mechanics of this asymmetric form of hybridisation. (shrink)

Axiom weakening is a novel technique that allows for fine-grained repair of inconsistent ontologies. In a multi-agent setting, integrating ontologies corresponding to multiple agents may lead to inconsistencies. Such inconsistencies can be resolved after the integrated ontology has been built, or their generation can be prevented during ontology generation. We implement and compare these two approaches. First, we study how to repair an inconsistent ontology resulting from a voting-based aggregation of views of heterogeneous agents. Second, we prevent the generation of (...) inconsistencies by letting the agents engage in a turn-based rational protocol about the axioms to be added to the integrated ontology. We instantiate the two approaches using real-world ontologies and compare them by measuring the levels of satisfaction of the agents w.r.t. the ontology obtained by the two procedures. (shrink)

Ontologies represent principled, formalised descriptions of agents’ conceptualisations of a domain. For a community of agents, these descriptions may differ among agents. We propose an aggregative view of the integration of ontologies based on Judgement Aggregation (JA). Agents may vote on statements of the ontologies, and we aim at constructing a collective, integrated ontology, that reflects the individual conceptualisations as much as possible. As several results in JA show, many attractive and widely used aggregation procedures are prone to return inconsistent (...) collective ontologies. We propose to solve the possible inconsistencies in the collective ontology by applying suitable weakenings of axioms that cause inconsistencies. (shrink)

We introduce a family of operators to combine Description Logic concepts. They aim to characterise complex concepts that apply to instances that satisfy \enough" of the concept descriptions given. For instance, an individual might not have any tusks, but still be considered an elephant. To formalise the meaning of "enough", the operators take a list of weighted concepts as arguments, and a certain threshold to be met. We commence a study of the formal properties of these operators, and study some (...) variations. The intended applications concern the representation of cognitive aspects of classi cation tasks: the interdependencies among the attributes that de ne a concept, the prototype of a concept, and the typicality of the instances. (shrink)

(English:) This contribution attempts a first non-normative approach to the problem of the classic, its definition and its meaning in an age of globalization. It reviews a series of common representations of the classic (and other analogous or contrary terms), stressing the programmatic-ideological aspect that generally characterizes them. Classic, actually, tends to be a foundational category, and therefore rests on delimitations that determine its exclusiveness as opposed to something else. This paper, in particular, criticizes the last boundary of the exclusivity (...) of the classic, that is, its normative opposition to fashion and actuality. On the contrary, it is argued that there is a substantial link between classic, actuality and fashion. On the basis of this connection, two deflationary definitions of the classic are proposed: the first regards it as part of the broader process of construction of historical identity by concrete individuals. The second, on the other hand, conceives it as a product of art, and, therefore, of a formative process of abilities, skills, taste, by which the classic becomes the object of technical, aesthetic and teleological judgments. -/- (Spanish:) En esta contribución se intenta una primera aproximación no normativa al problema del clásico, su definición y su significado en una era de globalización. Se revisa una serie de representaciones comunes sobre lo clásico (y otros términos análogos o contrarios), se destaca el aspecto programático-ideológico que por lo general las caracteriza. Clásico, en efecto, tiende a ser una categoría fundacional, por lo cual se apoya en delimitaciones que determinan su exclusividad por oposición a otra cosa. En este trabajo, en particular, se critica la última frontera de la exclusividad de lo clásico, es decir, su oposición normativa a la moda y la actualidad. Por el contrario, se argumenta que existe un vínculo sustancial entre el clásico, la actualidad y la moda. A partir de esta conexión, se proponen dos definiciones deflacionarias del clásico: la primera lo considera parte del proceso más amplio de construcción de la identidad histórica por parte de individuos concretos. El segundo, en cambio, lo concibe como un producto del arte, y, por tanto, de un proceso de formación de competencias, habilidades, gusto, por el cual el clásico se convierte en objeto de juicios técnicos, estéticos y teleológicos. (shrink)

Orthodox decision theory is fanatical in the way it treats small probabilities of enormous value, if unbounded utility functions are allowed. Some have suggested a fix, Nicolausian discounting, according to which outcomes with small enough probabilities should be ignored when making decisions. However, there are lotteries involving only small-probability outcomes, none of which should intuitively be ignored. So the Nicolausian discounter needs a procedure for distinguishing the problematic cases of small-probability outcomes from the unproblematic ones. In this paper, I present (...) a dilemma for Nicolausian discounting: the view must be coupled either with a procedure that delivers fanatical verdicts of its own, as bad as those of orthodox decision theory, or with one that entails intransitive cyclic preferences. (shrink)

The Handbook of Formal Argumentation is a community effort aimed at providing a comprehensive and up-to-date view of the state of the art and current trends in the lively research field of formal argumentation. The first volume of the Handbook is organised into five parts, containing nineteen chapters in all, each written by leading experts in the field. The first part provides a general and historical perspective on the field. The second part gives a comprehensive coverage of the argumentation formalisms (...) available in the literature at various levels of abstraction. The third part is devoted to cover some of the many dialogical aspects of argumentation, while the fourth one deals with algorithmic, computational and implementation issues. Finally, the fifth part provides some deeper analyses on the previously introduced topics. The Handbook of Formal Argumentation is an open-ended initiative of which the present volume is the first outcome. Further volumes are planned to cover topics not included in the present one and the initiative is conceived to grow by the support and feeding it receives from the community members. (shrink)

This paper presents a novel argumentation framework to support Issue-Based Information System style debates on design alternatives, by providing an automatic quantitative evaluation of the positions put forward. It also identifies several formal properties of the proposed quantitative argumentation framework and compares it with existing non-numerical abstract argumentation formalisms. Finally, the paper describes the integration of the proposed approach within the design Visual Understanding Environment software tool along with three case studies in engineering design. The case studies show the potential (...) for a competitive advantage of the proposed approach with respect to state-of-the-art engineering design methods. (shrink)

En la actualidad el pensamiento de Maquiavelo ha estado ligado a una praxis política que se juzga como mala desde el punto de vista ético. El secretario florentino, alejándose de la tradición estoica que marcó la filosofía política de la antigüedad y gran parte del medioevo, separa la política de la moral planteando un realismo político que evalúa los actos como eficientes o ineficientes, útiles o inútiles, fructíferos o infructíferos, tomando distancia de aquella calificación de bueno o malo. Sin embargo, (...) este simple acto, que no es más que la teorización y la explicitación de algo que se ha hecho desde siempre en la historia política, le valió ser tildado de hereje o que incluso su apellido se transformase en un término que hasta el día de hoy tiene una carga negativa en términos morales. Este artículo se adentra en aquellas interpretaciones, elementos históricos, teológicos y filosóficos del pensamiento de Maquiavelo, que con o sin intención, llevaron a que el secretario florentino fuera entendido como un pensador que hace apología de las malas praxis, acercándolo incluso a ideas heréticas. Palabras clave_: _Maquiavelo– Antimaquiavelismo - Realismo político – Herejía. (shrink)

Creating an integrated design space can be successful only if researchers agree on how to define and measure a certain phenomenon of interest. Adversarial collaborations and mathematical modeling can aid in reaching the necessary level of agreement when researchers depart from different theoretical perspectives.

This paper aims at comparing and relating belief revision and argumentation as approaches to model reasoning processes. Referring to some prominent literature references in both fields, we will discuss their (implicit or explicit) assumptions on the modeled processes and hence commonalities and differences in the forms of reasoning they are suitable to deal with. The intended contribution is on one hand assessing the (not fully explored yet) relationships between two lively research fields in the broad area of defeasible reasoning and (...) on the other hand pointing out open issues and potential directions for future research. (shrink)

This paper focuses on sections of Nietzsche's Twilight of the Idols that deal with Goethe, with the aim of reflecting on the anthropological ideal that Nietzsche outlines in his late period. I give particular attention to the way in which Nietzsche deals with concepts such as "German", "(good) European", and "free spirit", connecting them in a coherent picture. Finally, I argue that the Renaissance plays an important role in Nietzsche's anthropological project, for it helps to define the spiritual strength that (...) characterizes the healthy type of man whom Nietzsche thought destined to realize his late philosophy. (shrink)

Wilfrid Sellars’ denunciation of the Myth of the Given was meant to clarify, against empiricism, that perceptual episodes alone are insufficient to ground and justify perceptual knowledge. Sellars showed that in order to accomplish such epistemic tasks, more resources and capacities, such as those involved in using concepts, are needed. Perceptual knowledge belongs to the space of reasons and not to an independent realm of experience. Dan Hutto and Eric Myin have recently presented the Hard Problem of Content as an (...) ensemble of reasons against naturalistic accounts of content. In a nutshell, it states that covariance relations—even though they are naturalistically acceptable explanatory resources—do not constitute content. The authors exploit this move in order to promote their preferred radical enactivist and anti-representationalist option, according to which, basic minds—the lower stratum of cognition—do not involve content. Although it is controversial to argue that the Hard Problem of Content effectively dismisses naturalistic theories of representation, a central aspect of it—the idea that information as covariance does not suffice to explain content—finds support among the defenders of classical cognitive representationalism, such as Marcin Miłkowski. This support—together with the acknowledgment this remark about covariance is a point already made by Sellars in his criticism of the Myth of the Given—has a number of interesting implications. Not only is it of interest for the debates about representationalism in cognitive science, where it can be understood as an anticipatory move, but it also offers some clues and insights for reconsidering some issues along Sellarsian lines—a conflation between two concepts of representation that is often assumed in cognitive science, a distinction between two types of relevant normativities, and a reconsideration of the naturalism involved in such explanations. (shrink)

Reciprocal libertarianism is a version of left-wing libertarianism that combines self-ownership with an egalitarian distribution of resources according to reciprocity. In this paper, I show that reciprocal libertarianism is a coherent and appealing view. I discuss how reciprocal libertarians can handle conflicts between self-ownership and reciprocity, and I show that reciprocal libertarianism can be realised in a framework of individual ownership of external resources or in a socialist scheme of common ownership (libertarian socialism). I also compare reciprocal libertarianism with left-libertarian (...) approaches: I argue that a reciprocity-sensitive version of left-libertarianism (reciprocal left-libertarianism) is coherent and morally superior to traditional left-libertarianism, on grounds of incorporating a distinctively solidaristic and recognition-oriented aspect of equality. The policy implications of reciprocal libertarianism will differ depending on which rights people can have over external resources, but all reciprocal libertarian views acknowledge the existence of social rights that people have as co-operators. (shrink)

Léon Brunschvicg's contribution to philosophical thought in fin-de-siècle France receives full explication in the first English-language study on his work. Arguing that Brunschvicg is crucial to understanding the philosophical schools which took root in 20th-century France, Pietro Terzi locates Brunschvicg alongside his contemporary Henri Bergson, as well as the range of thinkers he taught and influenced, including Lévinas, Merleau-Ponty, de Beauvoir, and Sartre. Brunschvicg's deep engagement with debates concerning spiritualism and rationalism, neo-Kantian philosophy, and the role of mathematics in (...) philosophy made him the perfect supervisor for a whole host of nascent philosophical ideas which were forming in the work of his students. Terzi outlines Brunchvicg's defence of neo-Kantian judgement, historical analysis and the inextricability of the natural and humanist sciences to any rigorous system of philosophy, with wide-ranging implications for contemporary scholarship. (shrink)