Resumen: El texto pretende un acercamiento al carácter amoroso de la escritura de Maria Gabriela Llansol. Explica cómo ésta, igual que la de María Zambrano, lleva la defensa amorosa del devenir de Nietzsche un paso más allá, en tanto nace de un interés por la otredad en sí misma y no de una voluntad de autoafirmación. La ruptura de las nociones convencionales de tiempo, espacio e identidad será una de las vías que utiliza. En ello puede apreciarse cierta similitud con (...) Muḥyī al-Dīn Ibn ʿArabī, de quien aprendió la necesidad de buscar un tiempo propio para el alma, diferente del cuantitativo y cuya doctrina del amor y de la santidad exige un genuino interés en la otredad en tanto otredad. -/- Abstract: The text is an attempt to approach the loving character of the writing of Maria Gabriela Llansol. It explains how her works, similarly to those of María Zambrano, go further than Nietzsche in the affirmation of the becoming: as long as there is not will of self-affirmation, but an authentic interest in alterity. One of the paths she explores is to break the conventional notions of time, space and identity. It is possible to appreciate two coincidences with Muḥyī al-Dīn Ibn ʿArabī. First, Llansol learned from him the need of an own time for the soul, different from quantitative time. Second, Ibn ʿArabī’s doctrine of love and sainthood also implies a genuine interest in otherness as otherness. (shrink)

This article explores the relationship between the philosophy of the limit of Eugenio Trías and the sufism of Ibn ʿArabī. Firstly, it explains the function of the philosophy of religion in the triasian system and why the andalusian master has a privileged position. Secondly, it presents some essential aspects of the akbarian doctrine obtured by the philosophy of limit, as the declaration of the unity of Being, the path of servanthood, the transit from the sudden passion of love to the (...) spiritual love, the spiritual knighthood and the station of no-station. All of them share a common element: the trascendence of the egoic and the interest on the other as other. Finally, the article defends that Trias obturates the andalusian master doctrine due to the influence of Henry Corbin and mainly to the own limitations of its own philosophical project. The absent Ibn ʿArabī will be its shadow. (shrink)

Political fact-checkers evaluate the truthfulness of politicians’ claims. This paper contributes to an emerging scholarly debate on whether fact-checkers treat political parties differently in a systematic manner depending on their ideology (bias). We first examine the available approaches to analyze bias and then present a new approach in two steps. First, we propose a logistic regression model to analyze the outcomes of fact-checks and calculate how likely each political party will obtain a truth score. We test our model with a (...) sample of fact-checks from Newtral, a major Spanish fact-checker. Our model would signal bias under two assumptions: a) all political parties are on average equally accurate in their statements; b) the verification method gives precise instructions and is implemented systematically. We investigate this second assumption with a series of interviews with Newtral fact-checkers. We show that standard verification protocols are so loosely implemented that fact-checks reflect a set of journalistic decisions, rather than a bias in the statistical sense. We call for a more rigorous definition of verification methods as a pre-requisite for an unbiased assessment of politician’s claims. (shrink)

El presente artículo es un estudio sobre las diferenciaciones (aqsām) del amor, uno de los puntos más importantes del principal escrito que Ibn ʿArabī dedicó a la cuestión amorosa, el capítulo 178 de Las Iluminaciones de La Meca (al-Futūḥāt al-Makkiyya). A través de un juego de oscilación y equilibrio entre perspectivas ontológicas y epistemológicas aparentemente enfrentadas –incomparabilidad/similaridad, oculto/manifiesto, unidad/multiplicidad, espíritu/cuerpo– y un recurrente manejo del lenguaje de las alusiones (išāra), el maestro andalusí distingue entre amor divino (ilāhī), espiritual (rūḥānī), natural (...) (ṭabī‘ī) y elemental (ʿunṣurī). Se ofrece un análisis y comentario del texto akbarí que pretende aclarar la especificidad de cada una de estas nociones, así como su íntima relación con el discurso amoroso del autor. (shrink)

En su gran texto dedicado al amor — el capítulo 178 de _Las Iluminaciones de La Meca_—, Ibn ʿArabī comenta siete cualidades (_ṣ__ifāt_) que, según el Corán, suscitan el amor de Dios hacia los seres humanos. A lo largo de nuestro trabajo analizaremos el comentario akbarí y mostraremos cómo la clave para actualizar dichas cualidades consiste en_ hacer del propio ser un regalo de __amor_. O lo que es lo mismo: realizar un movimiento análogo al de Dios en cuanto que (...) El Omni-Compasivo (_al-Ra__ḥ__mān_), Quien a cada instante, de modo incondicional y sin esperar nada a cambio, asiste amorosamente a todas y cada una de Sus criaturas. (shrink)

Dynamic topological logic combines topological and temporal modalities to express asymptotic properties of dynamic systems on topological spaces. A dynamic topological model is a triple 〈X ,f , V 〉, where X is a topological space, f : X → X a continuous function and V a truth valuation assigning subsets of X to propositional variables. Valid formulas are those that are true in every model, independently of X or f. A natural problem that arises is to identify the logics (...) obtained on familiar spaces, such as . It [9] it was shown that any satisfiable formula could be satisfied in some for n large enough, but the question of how the logic varies with n remained open.In this paper we prove that any fragment of DTL that is complete for locally finite Kripke frames is complete for . This includes DTL○; it also includes some larger fragments, such as DTL1, where “henceforth” may not appear in the scope of a topological operator. We show that satisfiability of any formula of our language in a locally finite Kripke frame implies satisfiability in by constructing continuous, open maps from the plane into arbitrary locally finite Kripke frames, which give us a type of bisimulation. We also show that the results cannot be extended to arbitrary formulas of DTL by exhibiting a formula which is valid in but not in arbitrary topological spaces. (shrink)

We show that given a finite, transitive and reflexive Kripke model 〈 W , ≼, ⟦ ⋅ ⟧ 〉 and $${w \in W}$$ , the property of being simulated by w (i.e., lying on the image of a literalpreserving relation satisfying the ‘forth’ condition of bisimulation) is modally undefinable within the class of S4 Kripke models. Note the contrast to the fact that lying in the image of w under a bi simulation is definable in the standard modal language even (...) over the class of K4 models, a fairly standard result for which we also provide a proof. We then propose a minor extension of the language adding a sequent operator $${\natural}$$ (‘tangle’) which can be interpreted over Kripke models as well as over topological spaces. Over finite Kripke models it indicates the existence of clusters satisfying a specified set of formulas, very similar to an operator introduced by Dawar and Otto. In the extended language $${{\sf L}^+ = {\sf L}^{\square\natural}}$$ , being simulated by a point on a finite transitive Kripke model becomes definable, both over the class of (arbitrary) Kripke models and over the class of topological S4 models. As a consequence of this we obtain the result that any class of finite, transitive models over finitely many propositional variables which is closed under simulability is also definable in L + , as well as Boolean combinations of these classes. From this it follows that the μ -calculus interpreted over any such class of models is decidable. (shrink)

A growing number of recreational races are being held in different locations, drawing many local and visiting runners. This study examined the relationships between quality, value, satisfaction, and loyalty among runners in a recreational race and examines potential differences in relationships between these constructs based on the runners’ experience. The participants were 985 runners with a mean age of 40.74±9.41years. Validated, reliable ad hoc instruments were used. A multi-group analysis was performed to ascertain the existence of relationships between the constructs (...) and differences in the relationships between the different study groups. The results show that quality is a direct antecedent of value and satisfaction. Value is directly related to satisfaction and indirectly related to loyalty. Satisfaction is related to the loyalty of participants in the race. Differences in the relationship between satisfaction and loyalty were dependent upon the runners’ experience. Loyalty to a race depends primarily on satisfaction and is modified by the runners’ experience. (shrink)

La necesidad de estudiar el lenguaje en su uso real y de comprender los efectos de los discursos en la realidad social ha generado un interés por observar discursos de alto impacto social tales como los discursos políticos, mediáticos y públicos. Un aspecto relevante por estudiar en estos discursos es lo denominado, por la teoría de enunciación, como modalización del discurso. Este fenómeno hace referencia a la postura del enunciador frente a lo que enuncia. Existen variadas categorías para observar la (...) modalización en el discurso; la menos estudiada ha sido la modalidad deóntica. Por esto, surge el interés de observar cómo este fenómeno de la modalización se presenta en un contexto discursivo de alto interés nacional como lo ha sido durante la pandemia de COVID-19. La presente investigación describe, a partir del estudio de la modalidad deóntica, la variación en el grado de obligatoriedad con que la autoridad sanitaria planteó las medidas para controlar la pandemia de COVID-19 en Chile. Para llevar a cabo este objetivo, se analizó un corpus seleccionado de 18 reportes sanitarios del MINSAL entregados en distintos momentos de la pandemia en Chile. Los resultados del estudio, desarrollado desde un paradigma interpretativo y con enfoque cualitativo, evidencian que existe variación en el grado de obligatoriedad con que se enunció el discurso sanitario y que dicha variación está directamente relacionada con los periodos de agudización de la crisis sanitaria (ej. olas de contagios). Así, también, se observó el uso de la variación en la modalización deóntica como una estrategia discursiva por parte del enunciatario. (shrink)

In this work, we shall study structural abduction and how ways of searching for solutions to the corresponding abductive problems could be modeled. Specifically, we shall define modal semantic tableaux for normal modal systems and study its applications to structural abduction. This method even makes structural abduction clearer and, as it shall be seen, when a radical change of logic is epistemologically required, the corresponding tableau will have pertinent information to suggest it.

One might expect that, in pure coordination games, coordination would become less frequent as the number of options increases. Contrary to this expectation, we report an experiment which found more frequent coordination when the option set was unrestricted than when it was restricted. To try to explain this result, we develop a method for eliciting the general rules that subjects use to identify salient options in restricted and unrestricted sets. We find that each such rule, if used by all subjects, (...) would generate greater coordination in restricted sets. However, subjects tend to apply different rules to restricted and unrestricted sets. (shrink)

Este artículo explora la relación entre la filosofía del límite de Eugenio Trías y el sufismo de Ibn ʿArabī. En primer lugar, pretende explicar la función de la filosofía de la religión en el sistema triasiano y por qué el maestro andalusí ocupa un lugar privilegiado en ella. Segundo, se ocupa de algunos aspectos esenciales de la doctrina akbarí que la filosofía del límite obtura, como la declaración de la unidad del Ser (tawḥīd), la conjugación de lo exotérico y lo (...) esotérico, la superación de la propia creencia, el camino de la servidumbre (ʿubūdiyya), el tránsito de la pasión súbita de amor (hawā) al amor espiritual (ḥubb), la caballería espiritual (futuwwa) y la morada de la no-morada (maqām lā maqām), los cuales comparten un nexo común: el trascendimiento de lo egoico y el interés en el otro en tanto otro. Finalmente, se defenderá que la obturación triasiana se debe tanto al influjo de Henry Corbin, como sobre todo, a las propias limitaciones de su proyecto filosófico, para el que el Ibn ʿArabī ausente constituye una suerte de sombra. (shrink)

Given the pervasiveness of AI systems and their potential negative effects on people’s lives (especially among already marginalised groups), it becomes imperative to comprehend what goes on when an AI system generates a result, and based on what reasons, it is achieved. There are consistent technical efforts for making systems more “explainable” by reducing their opaqueness and increasing their interpretability and explainability. In this paper, we explore an alternative non-technical approach towards explainability that complement existing ones. Leaving aside technical, statistical, (...) or data-related issues, we focus on the very conceptual underpinnings of the design decisions made by developers and other stakeholders during the lifecycle of a machine learning project. For instance, the design and development of an app to track snoring to detect possible health risks presuppose some picture or another of “health”, which is a key notion that conceptually underpins the project. We take it as a premise that these key concepts are necessarily present during design and development, albeit perhaps tacitly. We argue that by providing “justificatory explanations” about how the team understands the relevant key concepts behind its design decisions, interested parties could gain valuable insights and make better sense of the workings and outcomes of systems. Using the concept of “health”, we illustrate how a particular understanding of it might influence decisions during the design and development stages of a machine learning project, and how making this explicit by incorporating it into ex-post explanations might increase the explanatory and justificatory power of these explanations. We posit that a greater conceptual awareness of the key concepts that underpin design and development decisions may be beneficial to any attempt to develop explainability methods. We recommend that “justificatory explanations” are provided as technical documentation. These are declarative statements that contain at its simplest: (1) a high-level account of the understanding of the relevant key concepts a team possess related to a project’s main domain, (2) how these understandings drive decision-making during the life-cycle stages, and (3) it gives reasons (which could be implicit in the account) that the person or persons doing the explanation consider to have plausible justificatory power for the decisions that were made during the project. (shrink)

[español] En primer lugar, el texto ofrece un acercamiento al papel que amor y nostalgia cumplen en la poesía de Emilio Prados, así como a su íntimo nexo con la muerte como aniquilación mística. Como herramienta interpetativa, recurriré a la razón poética de María Zambrano, autora profundamente emparentada, vital y teóricamente, con la poesía pradiana. Este enfoque permitirá una visión de conjunto sobre la obra del poeta español y en segundo lugar, trazar una comparativa con el saudosismo de Teixeira de (...) Pascoaes. Así, indicaré las numerosas coincidencias que existen entre ambos y me detendré en la cuestión de la muerte mística, ámbito más problemático, donde sin embargo, puede apreciarse una comunión de espíritu entre el español y el portugués. ****************** [english] Firstly, the text offers an approach to the function of love and nostalgia in the poetry of Emilio Prados, as much as its intimate connection with death as mystical annihilation. As interpretive tool, I will use the poetic reason of María Zambrano, an author deeply linked, vital and theoretically, with pradian poetry. This focus will provide an overall view of Prado's work and the possibility of a comparison with Teixeira de Pascoaes's saudosism. Thus, I will point same coincidences between them and I will consider the question of mystical death. This sphere, although it is problematic, can show some kind of community of spirit between both. (shrink)

El presente artículo trata la presentación que Henry Corbin hace del sufismo de Ibn ' Arabī. Pretende mostrar cómo el proyecto filosófico del pensador francés (atravesado de protestantismo, heideggerianismo y fenomenología) produce una obturación de la doctrina akbarí, que denota cierta falta de amor o desinterésen la alteridad en tanto alteridad. El itinerario constará de cinco pasos. Primero, nos acercaremos a los años de formación de Corbin. Segundo, presentaremo salgunos puntos esenciales de su obra más célebre, La imaginación creadora en (...) el sufismo de Ibn ‘Arabî. Tercero, se mostrarán aquellos aspectos de la doctrinade Ibn ' Arabī allí obturados. Cuarto, expondremos algunas conclusiones a partir de estas ausencias. Quinto, a modo de epílogo, y ya en el ámbito de la filosofía latinoamericana, ofreceremos una mirada al proyecto de la transmodernidad de Enrique Dussel, desde el paradigma del amor akbarí. (shrink)

Goodstein’s principle is arguably the first purely number-theoretic statement known to be independent of Peano arithmetic. It involves sequences of natural numbers which at first appear to diverge, but eventually decrease to zero. These sequences are defined relative to a notation system based on exponentiation for the natural numbers. In this article, we provide a self-contained and modern analysis of Goodstein’s principle, obtaining some variations and improvements. We explore notions of optimality for notation systems and apply them to the classical (...) Goodstein process and to a weaker variant based on multiplication rather than exponentiation. In particular, we introduce the notion of base-change maximality, and show how it leads to far-reaching extensions of Goodstein’s result. We moreover show that by varying the initial base of the Goodstein process, one readily obtains independence results for each of the fragments $\mathsf {I}\Sigma _n$ of Peano arithmetic. (shrink)

Dynamic Topological Logic (DFH) is a multimodal system for reasoning about dynamical systems. It is defined semantically and, as such, most of the work done in the field has been model-theoretic. In particular, the problem of finding a complete axiomatization for the full language of DFH over the class of all dynamical systems has proven to be quite elusive. Here we propose to enrich the language to include a polyadic topological modality, originally introduced by Dawar and Otto in a different (...) context. We then provide a sound axiomatization for DFH over this extended language, and prove that it is complete. The polyadic modality is used in an essential way in our proof. (shrink)

The aim of the present study was to determine statistical differences in a set of badminton competition matches in five different modalities with regard to competition level (Group Phase versus Eliminatory Phase). Data from 453 sets (125 in men’s singles; 108 sets in women’s singles; 77 sets in men’s doubles; 73 in women’s doubles and 70 in mixed doubles) from the RIO 2016 Olympics Games were recorded and classified in two groups of variables to analyse variables related to match (5) (...) and set (15). A descriptive analysis and univariate test (Mann Whitney U) for non-parametric data were conducted. The results show in men’s and women’s singles all the variables related to match were higher in the Elimination Phase than in the Group Phase (p<0.01). In Sets 1 and 3, the longest set duration, rally and average rally were found in the Elimination Phase than Group Stage (p<0.05). In women’s singles, these differences were also recorded in Set 2. For doubles, the results are more stable among groups. Men’s doubles had a longer duration of the match and set (set 1 and set 2) (p<0.01), and also scored highest for average rally strokes (set 1 and set 3) (p<0.05) and shuttles used in the Elimination Phase versus the Group Phase along the match (p<0.01). In women’s doubles, more shuttles were used in a match in the Elimination than in the Group Phase. Moreover, the same results are established for Set 2, including for average rally. Mixed doubles saw no match going to three sets. However, the greatest differences showed a longer rally and average rally being registered in the Elimination than in the Group Phase. In conclusion, the timing factors of the badminton singles and doubles games were different in the Elimination and Group Phases. This information may help players and coaches prepare and administer different types of workouts or, more specifically, competition schedules adapted to the characteristics of modern badminton. (shrink)

Our aim in this paper is to clarify the distinctions and the relationships among several phenomena, each of which has certain characteristics of what is generally called “deference”. We distinguish linguistic deference, which concerns the use of language and the meaning of the words we use, from epistemic deference, which concerns our reasons and evidence for making the claims we make. In our in-depth study of linguistic deference, we distinguish two subcategories: default deference, and deliberate deference. We also discuss the (...) phenomenon of im-perfect mastery, often associated with deference, and which we show to be independent both of linguistic deference and of epistemic deference. If our analysis is correct, then some recent debates on deference can be shown to result from a failure to appreciate all the distinctions that we draw here. (shrink)

The European Union’s Artificial Intelligence Act (AI Act) is a groundbreaking regulatory framework that integrates technical concepts and terminology from the rapidly evolving ecosystems of AI research and innovation into the legal domain. Precise definitions accessible to both AI experts and lawyers are crucial for the legislation to be effective. This paper provides an interdisciplinary analysis of the concepts of AI system, general purpose AI system, foundation model and generative AI across the different versions of the legal text (Commission proposal, (...) Parliament position and Council General Approach) before the final political agreement. The goal is to help bridge the understanding of these key terms between the technical and legal communities and contribute to a proper implementation of the AI Act. We provide an analysis of the concept of AI system considering its scientific foundation and the crucial role that it plays in the regulation, which requires a sound definition both from legal and technical standpoints. We connect the outcomes of this discussion with the analysis of the concept of general purpose AI system and its evolution during the negotiations. We also address the distinct conceptual meanings of AI system vs AI model and explore the technical nuances of the term foundation model. We conclude that rooting the definition of foundation model to its general purpose capabilities following standardised evaluation methodologies appears to be most appropriate approach. Lastly, we tackle the concept of generative AI, arguing that definitions of AI system that include “content” as one of the system’s outputs already captures it, and concluding that not all generative AI is based on foundation models. (shrink)

Goodstein’s theorem states that certain sequences based on exponential notation for the natural numbers are always finite. The result is independent of Peano arithmetic and is a prototypical example of a proof of termination by transfinite induction. A variant based instead on the Ackermann function has more recently been proposed by Arai, Fernández-Duque, Wainer, and Weiermann, and instead is independent of the more powerful theory ATR0. However, this result is contingent on rather elaborate normal forms for natural numbers based (...) on a “sandwiching” procedure. This leaves open both the question of whether the sandwiching procedure can be eliminated while retaining the full strength of the Ackermannian Goodstein principle, and whether other normal forms can lead to nontermination. In this article we settle these questions by showing that any Goodstein process based on the Ackermann function is terminating, and indeed the sandwiching procedure gives rise to Goodstein principles of maximal length. We thus obtain an equivalent principle which does not involve normal forms at all and immediately implies all Ackermannian Goodstein principles that have been considered. Our techniques provide a new approach to termination proofs, where terms in a sequence do not necessarily decrease in complexity, but instead are majorized by some “master” process, already known to be terminating. (shrink)

For any ordinal $\Lambda$, we can define a polymodal logic $\mathsf{GLP}_\Lambda$, with a modality $[\xi]$ for each $\xi < \Lambda$. These represent provability predicates of increasing strength. Although $\mathsf{GLP}_\Lambda$ has no Kripke models, Ignatiev showed that indeed one can construct a Kripke model of the variable-free fragment with natural number modalities, denoted $\mathsf{GLP}^0_\omega$. Later, Icard defined a topological model for $\mathsf{GLP}^0_\omega$ which is very closely related to Ignatiev's. In this paper we show how to extend these constructions for arbitrary $\Lambda$. (...) More generally, for each $\Theta,\Lambda$ we build a Kripke model $\mathfrak I^\Theta_\Lambda$ and a topological model $\mathfrak T^\Theta_\Lambda$, and show that $\mathsf{GLP}^0_\Lambda$ is sound for both of these structures, as well as complete, provided $\Theta$ is large enough. (shrink)

This article describes the progress and impact of the King’s College London Centre for Military Ethics since its collaboration with the Colombian military forces’ educational institutions. More specifically, the article focusses on expanding the military ethics course across different educational facilities of the Colombian Army and the Colombian Navy and Air Force. The impact of the education delivered using an online course designed to be completed without a tutor is analysed and presented. The final part of the article describes a (...) way forward as far as the Colombian project is concerned, as well as the refinement of the course materials and launch of new tools. (shrink)

Ordinal functions may be iterated transfinitely in a natural way by taking pointwise limits at limit stages. However, this has disadvantages, especially when working in the class of normal functions, as pointwise limits do not preserve normality. To this end we present an alternative method to assign to each normal function f a family of normal functions Hyp[f]=〈fξ〉ξ∈OnHyp[f]=〈fξ〉ξ∈On, called its hyperation, in such a way that f0=idf0=id, f1=ff1=f and fα+β=fα∘fβfα+β=fα∘fβ for all α, β.Hyperations are a refinement of the Veblen hierarchy (...) of f. Moreover, if f is normal and has a well-behaved left-inverse g called a left adjoint, then g can be assigned a cohyperationcoH[g]=〈gξ〉ξ∈OncoH[g]=〈gξ〉ξ∈On, which is a family of initial functions such that gξgξ is a left adjoint to fξfξ for all ξ. (shrink)

Provability logics are modal or polymodal systems designed for modeling the behavior of Gödel’s provability predicate and its natural extensions. If Λ is any ordinal, the Gödel-Löb calculus GLPΛ contains one modality [λ] for each λ < Λ, representing provability predicates of increasing strength. GLPω has no non-trivial Kripke frames, but it is sound and complete for its topological semantics, as was shown by Icard for the variable-free fragment and more recently by Beklemishev and Gabelaia for the full logic. In (...) this paper we generalize Beklemishev and Gabelaia’s result to GLPΛ for countable Λ. We also introduce provability ambiances, which are topological models where valuations of formulas are restricted. With this we show completeness of GLPΛ for the class of provability ambiances based on Icard polytopologies. (shrink)

Se ofrece una interpretación de la filosofía política de María Zambrano desde el sufismo deIbnʿArabī. Primero, explicaremos tres nociones centrales en la obra del Šayḫ, como la doble fidelidad a la dimensión de la «incomparabilidad» (tanzīh) y de la «similaridad» (tašbīh), la «nueva creación» (ḫalq al-ǧadīd) y el «hombre perfecto» (insān al-kāmil). Después, trataremos algunos de los textos más políticos de Zambrano, como Horizonte del liberalismo(1929), Isla de Puerto Rico (1940), «Martí, camino de su muerte» (1953) y Persona y democracia (...) (1958). Según veremos, el marco ontológico, epistemológico y antropológicodel maestro andalusí permite ahondar en el sentido místico del discurso político zambraniano. (shrink)

Dynamic Topological Logic () is a combination of , under its topological interpretation, and the temporal logic interpreted over the natural numbers. is used to reason about properties of dynamical systems based on topological spaces. Semantics are given by dynamic topological models, which are tuples , where is a topological space, f a function on X and V a truth valuation assigning subsets of X to propositional variables. Our main result is that the set of valid formulas of over spaces (...) with continuous functions is recursively enumerable. We show this by defining alternative semantics for . Under standard semantics, is not complete for Kripke frames. However, we introduce the notion of a non-deterministic quasimodel, where the function f is replaced by a binary relation g assigning to each world multiple temporal successors. We place restrictions on the successors so that the logic remains unchanged; under these alternative semantics, becomes Kripke-complete. We then apply model-search techniques to enumerate the set of all valid formulas. (shrink)

The paper presents a new logic for reasoning about the formation of beliefs through perception or through inference in non-omniscient resource-bounded agents. The logic distinguishes the concept of explicit belief from the concept of background knowledge. This distinction is reflected in its formal semantics and axiomatics: we use a non-standard semantics putting together a neighborhood semantics for explicit beliefs and relational semantics for background knowledge, and we have specific axioms in the logic highlighting the relationship between the two concepts. Mental (...) operations of perceptive type and inferential type, having effects on epistemic states of agents, are primitives in the object language of the logic. At the semantic level, they are modelled as special kinds of model-update operations, in the style of dynamic epistemic logic. Results about axiomatization, decidability and complexity for the logic are given in the paper. (shrink)

We introduce the logics GLP Λ, a generalization of Japaridze’s polymodal provability logic GLP ω where Λ is any linearly ordered set representing a hierarchy of provability operators of increasing strength. We shall provide a reduction of these logics to GLP ω yielding among other things a finitary proof of the normal form theorem for the variable-free fragment of GLP Λ and the decidability of GLP Λ for recursive orderings Λ. Further, we give a restricted axiomatization of the variable-free fragment (...) of GLP Λ. (shrink)

Dynamic Topological Logic ( $\mathcal{DTL}$ ) is a modal framework for reasoning about dynamical systems, that is, pairs 〈X, f〉 where X is a topological space and f: X → X a continuous function. In this paper we consider the case where X is a metric space. We first show that any formula which can be satisfied on an arbitrary dynamic topological system can be satisfied on one based on a metric space; in fact, this space can be taken to (...) be countable and have no isolated points. Since any metric space with these properties is homeomorphic to the set of rational numbers, it follows that any satisfiable formula can be satisfied on a system based on $\mathbb{Q}$ . We then show that the situation changes when considering complete metric spaces, by exhibiting a formula which is not valid in general but is valid on the class of systems based on a complete metric space. While we do not attempt to give a full characterization of the set of valid formulas on this class we do give a relative completeness result; any formula which is satisfiable on a dynamical system based on a complete metric space is also satisfied on one based on the Cantor space. (shrink)