This paper contains a logic enabling us to reason in the presence of vague- ness phenomena. We consider an epistemological vagueness of concepts caused by the unavailability of total information about a continuous world which we describe in observational terms. Lack of information is manifested by the existence of borderline cases for concepts. Since we are unable to perceive concepts exactly, we cannot establish a sharp boundary between an extension of a concept and its complement. Some results for reasoning about (...) vague concepts are already known in the literature [1], [2], [3], [4], [10]. Usually, a semantics of vague concepts is developed within the theory of fuzzy sets or the theory of supertruth [9]. Following the idea that reasoning about vague concepts requires a special logic, we introduce a propositional language with sentential operators en- abling us to dene positive, negative, and borderline regions of any vague concept. A semantics of the language is rened within a framework of the theory of rough sets . The admitted semantics provides means for dening extensions of concepts in a formal way. We show that these extensions re ect properly our intuition connected with vagueness. For ex- ample, the law of excluded middle is not valid on the level of extensions. Moreover, for any concept, the extensions of formulas representing its pos- itive, negative, and borderline regions provide a partition of a universe of discourse. (shrink)

One of the generalizations of R. W´ojcicki’s concept of referential matrix is so-called pseudo-referential matrix . G. Malinowski, who introduced that concept, also considers a particular case of pseudo-referential matrices called discrete pseudo-referential matrices . In this note we want to show how any generalized matrix determines a semantically equivalent discrete pseudo-referential matrix.

In this paper a unified framework for dealing with a broad family of propositional multimodal logics is developed. The key tools for presentation of the logics are the notions of closure relation operation and monotonous relation operation. The two classes of logics: FiRe-logics (finitely reducible logics) and LaFiRe-logics (FiRe-logics with local agreement of accessibility relations) are introduced within the proposed framework. Further classes of logics can be handled indirectly by means of suitable translations. It is shown that the logics from (...) these classes have the finite model property with respect to the class of -formulae, i.e. each -formula has a -model iff it has a finite -model. Roughly speaking, a -formula is logically equivalent to a formula in negative normal form without occurrences of modal operators with necessity force. In the proof we introduce a substantial modification of Claudio Cerrato's filtration technique that has been originally designed for graded modal logics. The main core of the proof consists in building adequate restrictions of models while preserving the semantics of the operators used to build terms indexing the modal operators. (shrink)

One staple of living in our information society is having access to the web. Web-connected devices interpret our queries and retrieve information from the web in response. Today’s web devices even purport to answer our queries directly without requiring us to comb through search results in order to find the information we want. How do we know whether a web device is trustworthy? One way to know is to learn why the device is trustworthy by inspecting its inner workings, 156–170 (...) 1995; Humphreys 2004, Episteme, 6, 221–229 2009). But ordinary users of web devices cannot inspect their inner workings because of their scale, complexity, and the corporate secrecy which enshrouds both the procedures by which the devices operate and the companies that make them. Further piling on this predicament, authors have criticized web technology on the grounds that the invisibility of the web devices’ inner workings prevents users from critically assessing the procedures that produce a given output, in some cases, barring users from fulfilling their epistemic responsibilities, 343–355 2010; Miller and Record Episteme, 10, 117–134 2013). I consider four broad kinds of reasons which we can acquire without inspecting the inner workings of black-boxed technology: individual understanding, expert testimony, testing through experience, and social vetting; and show how each is a viable method of appraising black-boxed technology. By deploying these methods, we can remain responsible inquirers while nonetheless benefitting from today’s epistemic resources on the web. (shrink)

This book assesses how Vatican II opened up the Catholic Church to encounter, dialogue, and engagement with other world religions. Opening with a contribution from the President of the Pontifical Council for Interreligious Dialogue, Cardinal Jean-Louis Tauran, it next explores the impact, relevance, and promise of the Declaration Nostra Aetate before turning to consider how Vatican II in general has influenced interfaith dialogue and the intellectual and comparative study of world religions in the postconciliar decades, as well as the contribution (...) of particular past and present thinkers to the formation of current interreligious and comparative theological methods. Additionally, chapters consider interreligious dialogue vis-à-vis theological anthropology in conciliar documents; openness to the spiritual practices of other faith traditions as a way of encouraging positive interreligious encounter; the role of lay and new ecclesial movements in interreligious dialogue; and the development of Monastic Interreligious Dialogue. Finally, it includes a range of perspectives on the fruits and future of Vatican’s II’s opening to particular faiths such as Judaism, Islam, Hinduism, and Buddhism. (shrink)

A survey of works on automatic theorem-proving in the ussr 1964-1970. the philosophical problems are not touched.

Upshot: Albeit mostly supportive of our work, the commentaries we received highlighted a few points that deserve additional explanation, with regard to the notion of learning in our model, the relationship between our model and the brain, as well as the notion of anticipation. This open discussion emphasizes the need for toy computer models, to fuel theoretical discussion and prevent business-as-usual from getting in the way of new ideas.

(No abstract is available for this citation).

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This study explored possible deficits in selective attention brought about by Dementia of Alzheimer Type (DAT). In three experiments, we tested patients with early DAT, healthy elderly, and young adults under low memory demands to assess perceptual filtering, conflict resolution, and set switching abilities. We found no evidence of impaired perceptual filtering nor evidence of impaired conflict resolution in early DAT. In contrast, early DAT patients did exhibit a global cost in set switching consistent with an inability to maintain the (...) goals of the task (mental set). We discuss these findings in relation to the DAT literature on executive attention, dual-tasking, and working memory. Ó 2007 Elsevier Inc. All rights reserved. (shrink)

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