In this paper we provide frame definability results for weak versions of classical modal axioms that can be expressed in Fitting's many-valued modal languages. These languages were introduced by M. Fitting in the early '90s and are built on Heyting algebras which serve as the space of truth values. The possible-worlds frames interpreting these languages are directed graphs whose edges are labelled with an element of the underlying Heyting algebra, providing us a form of many-valued accessibility relation. Weak axioms of (...) the form we treat here have been examined from the completeness perspective and further explored for applications in non-monotonic reasoning. Here, we introduce more weak many-valued modal axioms and prove a frame correspondence result for all of them. The classes of corresponding labelled frames possess algebraic properties which are strongly reminiscent of many classical ones, such as the Church-Rosser property, reflexivity, transitivity, partial functionality, etc. (shrink)

We prove frame determination results for the family of many-valued modal logics introduced by M. Fitting in the early '90s. Each modal language of this family is based on a Heyting algebra, which serves as the space of truth values, and is interpreted on an interesting version of possible-worlds semantics: the modal frames are directed graphs whose edges are labelled with an element of the underlying Heyting algebra. We introduce interesting generalized forms of the classical axioms D, T, B, 4, (...) and 5 and prove that they are canonical for certain algebraic frame properties, which generalize seriality, reflexivity, symmetry, transitivity and euclideanness. Our results are quite general as they hold for any modal language built on a complete Heyting algebra. (shrink)

Defeasible conditionals are statements of the form ‘if A then normally B’. One plausible interpretation introduced in nonmonotonic reasoning dictates that ) is true iff B is true in ‘most’ A-worlds. In this paper, we investigate defeasible conditionals constructed upon a notion of ‘overwhelming majority’, defined as ‘truth in a cofinite subset of \’, the first infinite ordinal. One approach employs the modal logic of the frame \\), used in the temporal logic of discrete linear time. We introduce and investigate (...) conditionals, defined modally over \\); several modal definitions of the conditional connective are examined, with an emphasis on the nonmonotonic ones. An alternative interpretation of ‘majority’ as sets cofinal ) rather than cofinite ) is examined. For these modal approaches over \\), a decision procedure readily emerges, as the modal logic \ of this frame is well-known and a translation of the conditional sentences can be mechanically checked for validity; this allows also for a quick proof of \-completeness of the satisfiability problem for these logics. A second approach employs the conditional version of Scott-Montague semantics, in the form of \-many possible worlds, endowed with neighborhoods populated by collections of cofinite subsets of \. This approach gives rise to weak conditional logics, as expected. The relative strength of the conditionals introduced is compared to KLM logics and other conditional logics in the literature. (shrink)

Weak filters were introduced by K. Schlechta in the ’90s with the aim of interpreting defaults via a generalized ‘most’ quantifier in first-order logic. They arguably represent the largest class of structures that qualify as a ‘collection of large subsets’ of a given index set |$I$|⁠, in the sense that it is difficult to think of a weaker, but still plausible, definition of the concept. The notion of weak ultrafilter naturally emerges and has been used in epistemic logic and other (...) knowledge representation (KR) applications. We provide a comprehensive exposition of weak filters and ultrafilters, comparing them with their classical counterparts that have found very important applications in logic, set theory and topology. Weak (ultra)filters capture the ‘majorities’ of social choice theory (which coincide with the commonsense understanding of a ‘large subset’) and in that respect, they outperform classical (ultra)filters in their role as ‘collections of large subsets’. Yet, they lack some of the elegant properties of classical (ultra)filters that make them an almost perfect match for logical theories. We investigate the extent to which some important classical results carry through in this new setting, and we focus on genuinely weak filters and genuinely weak ultrafilters. For weak ultrafilters, we proceed to provide concrete examples, answer questions of existence and characterize their construction. The class of weak (ultra)filters represents a genuine contribution of KR to set theory that might be of some interest to set theorists too and we initiate this study by providing a glimpse on natural set-theoretic questions. (shrink)

We introduce a bimodal epistemic logic intended to capture knowledge as truth in all epistemically alternative states and belief as a generalised ‘majority’ quantifier, interpreted as truth in most of the epistemically alternative states. This doxastic interpretation is of interest in knowledge-representation applications and it also holds an independent philosophical and technical appeal. The logic comprises an epistemic modal operator, a doxastic modal operator of consistent and complete belief and ‘bridge’ axioms which relate knowledge to belief. To capture the notion (...) of a ‘majority’ we use the ‘large sets’ introduced independently by K. Schlechta and V. Jauregui, augmented with a requirement of completeness, which furnishes a ‘weak ultrafilter’ concept. We provide semantics in the form of possible-worlds frames, properly blending relational semantics with a version of general Scott–Montague frames and we obtain soundness and completeness results. We examine the validity of certain epistemic principles discussed in the literature, in particular some of the ‘bridge’ axioms discussed by W. Lenzen and R. Stalnaker, as well as the ‘paradox of the perfect believer’, which is not a theorem of. (shrink)

In this paper we define and examine frame constructions for the family of manyvalued modal logics introduced by M. Fitting in the '90s. Every language of this family is built on an underlying space of truth values, a Heyting algebra H. We generalize Fitting's original work by considering complete Heyting algebras as truth spaces and proceed to define a suitable notion of H-indexed families of generated subframes, disjoint unions and bounded morphisms. Then, we provide an algebraic generalization of the canonical (...) extension of a frame and model, and prove a preservation result inspired from Fitting's canonical model argument in [FIT 92a]. The analog of a complex algebra and of a principal ultrafilter is defined and the embedding of a frame into its canonical extension is presented. (shrink)

A new methodology for developing theories of action has recently emerged which provides means for formally evaluating the correctness of such theories. Yet, for a theory of action to qualify as a solution to the frame problem, not only does it need to produce correct inferences, but moreover, it needs to derive these inferences from a concise representation of the domain at hand. The new methodology however offers no means for assessing conciseness. Such a formal account of conciseness is developed (...) in this paper. Combined with the existing criterion for correctness, our account of conciseness offers a framework where proposed solutions to the frame problem can be formally evaluated. (shrink)

S4.2 is the modal logic of directed partial pre-orders and/or the modal logic of reflexive and transitive relational frames with a final cluster. It holds a distinguished position in philosophical...

Building on the long-standing tradition of challenging oppression and questioning whose interests are being served in the field of language education, we report on a study that involved a group of U.S.-based graduate students who collaborated with a ninth-grade English teacher in Nepal. The study comes out of a larger project that sought to internationalize the curriculum of a graduate educational linguistics course at a U.S. university. At the heart of this internationalizing curriculum endeavour was a commitment to expose graduate (...) students in the U.S. to the issues of language teaching outside of the U.S. This was done through co-designing of a unit of lessons, with six graduate students meeting virtually with their teacher partner, Ditya, in Nepal over the course of a semester. The graduate students and Ditya constitute our research participants. The graduate student participants learned about the need to develop pedagogical materials that were relevant to the local context in Nepali classroom, and not attempt to transplant a Western-centric curriculum onto the Nepali classroom. In keeping with recent calls to decolonize higher education, we illustrate how critical theory in general and decolonizing pedagogy in particular can be infused into a U.S. graduate curriculum by drawing on the rich, indigenous knowledge and resources of a teacher collaborator from the Global South. We do this by reporting how this critical, decolonizing goal was realized through collaborative professionalism, which is characterized by the sharing of knowledge, skills, and experience to improve student achievement, reflection, dialogue and collective responsibility. (shrink)

Le traité Περὶ θείων ὀνομάτων de l’élève de Proclus dissimulé sous le nom de ‘Denys l’Aréopagite’— traité qui a été récemment édité en qualité de premier titre de la série Corpus Dionysiacum— est subdivisé en deux grandes parties par un excursus fameux sur le problème de la substantialité des maux. Dans la première partie, contenant les chapitres I-III, l’auteur discute la possibilité des prédications dont l’objet est le premier principe. Dans la deuxième, contenant les chapitres V-XIII, il en présente les (...) ‘noms’. Les deux parties sont séparées par le long excursus sur la nature du mal, qui forme l’objet du chapitre IV. Ce dernier s’ouvre, il est vrai, sur le propos d’examiner la dénomination de ‘Bien’ attribuée au premier principe , si bien que l’on rangerait volontiers ce chapitre dans la deuxième partie, consacrée à la présentation des ‘noms’ de Dieu et à leur commentaire. Il se trouve pourtant que l’auteur a explicitement placé la charnière principale de son traité après l’excursus sur la nature du mal. Au début du chapitre V, en effet, il déclare aborder la question de l’οὑσιωνυμία divine, en démontrant par là concevoir le ‘Bien’ comme une dénomination différente de toute autre, voire antérieure à tous les noms qui sont en relation avec l’οὑσία, et dont l’examen occupe les chapitres V-XIII. (shrink)

Automated classification of legal documents has been the subject of extensive research in recent years. However, this is still a challenging task for long documents, since it is difficult for a model to identify the most relevant information for classification. In this paper, we propose a two-stage supervised learning approach for the classification of petitions, a type of legal document that requests a court order. The proposed approach is based on a word-level encoder–decoder Seq2Seq deep neural network, such as a (...) Bidirectional Long Short-Term Memory (BiLSTM) or a Bidirectional Encoder Representations from Transformers (BERT) model, and a document-level Support Vector Machine classifier. To address the challenges posed by the lengthy legal documents, the approach introduces a human-in-the-loop approach, whose task is to localize and tag relevant segments of text in the word-level training part, which dramatically reduces the dimension of the document classifier input vector. We performed experiments to validate our approach using a real-world dataset comprised of 270 intermediate petitions, which were carefully annotated by specialists from the 15th civil unit of the State of Alagoas, Brazil. Our results revealed that both BiLSTM and BERT-Convolutional Neural Networks variants achieved an accuracy of up to 95.49%, and also outperformed baseline classifiers based on the Term Frequency–Inverse Document Frequency test vectorizer. The proposed approach is currently being utilized to automate the aforementioned justice unit, thereby increasing its efficiency in handling repetitive tasks. (shrink)

A translation of fourteen of Lucian's dialogues, offering a cross-section of his styles and satirical targets, from serious polemic to lighter squibs and character-portrayals. Also included are How to Write History and his most famous piece, A True History, a parody of the popular vogue for fabulous traveller's tales. Each piece has a summary introduction, and notes to clarify obscure allusions in the text. The Introduction examines in some detail Lucian's importance as a dominant Atticizer in the period of the (...) Second Sophistic, as well as his extraordinarily widespread influence on later European literature. (shrink)

L'A. se base sur deux oeuvres artistiques sur la Trinité qui se correspondent et qui soulèvent des questions sérieuses au sujet de la négociation chrétienne avec les autres religions. Ces deux oeuvres traitent de la Trinité en relation avec les autres traditions religieuses. Il s'agit de l'icône intitulée la Trinité de l'orthodoxe russe André Roublev qui date du 15siècle et de l'oeuvre contemporaine de l'artiste indien catholique romain Jyoti Sahi intitulée Abraham et Sarah recevant les trois anges. Par cette étude (...) comparative, l'A. souligne la richesse du Dieu trinitaire dans l'ouverture à la multiplicité des représentations du mystère infini. Ces représentations, visibles dans les créations, sont parfois le fruit de l'imagination des artistes et des théologiens, imagination qui est nécessaire. (shrink)