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Bridge principles and combined reasoning
"... Hume’s wellknown objection on the purported connections between ‘is’ and ‘ought ’ in philosophical argumentation gave rise to a quarrel about the legitimacy of statements that bind factualities to norms. The idea of bridge principle has been inaugurated as statements which precisely crystallize pri ..."
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Hume’s wellknown objection on the purported connections between ‘is’ and ‘ought ’ in philosophical argumentation gave rise to a quarrel about the legitimacy of statements that bind factualities to norms. The idea of bridge principle has been inaugurated as statements which precisely crystallize principles of mixed reasoning. We critically examine the role of bridge principles within the context of combination of logics, emphasizing situations where such principles spontaneously arise with desirable and undesirable consequences for combined reasoning. 1 Bridge principles and combined logics As wittily put in [17], nobody knows how many times the passage from David Hume’s “A Treatise of Human Nature ” (cf. [16], Book 3, Part 1, Section 1, paragraph 27) has been quoted. This passage that generated a neverending controversy and so many quotations attests that many times people (philosophers, perhaps) draw conclusions involving imperative
CDD: 511.3 TOWARDS A STRONGER NOTION OF TRANSLATION BETWEEN LOGICS 1
"... Abstract: The concept of translation between logics was originally introduced in order to prove the consistency of a logic system in terms of the consistency of another logic system. The idea behind this is to interpret (or to encode) a logic into another one. In this survey we address the following ..."
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Abstract: The concept of translation between logics was originally introduced in order to prove the consistency of a logic system in terms of the consistency of another logic system. The idea behind this is to interpret (or to encode) a logic into another one. In this survey we address the following question: Which logical properties a (strong) logic translation should preserve? Several approaches to the concept of translation between logics are discussed and analyzed. Keywords: Translations between logics. Abstract logics. Combination of logics. 1.
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"... In this paper we address some central problems of combination of logics through the study of a very simple but highly informative case, the combination of the logics of disjunction and conjunction. At first it seems that it would be very easy to combine such logics, but the following problem arises: ..."
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In this paper we address some central problems of combination of logics through the study of a very simple but highly informative case, the combination of the logics of disjunction and conjunction. At first it seems that it would be very easy to combine such logics, but the following problem arises: if we combine these logics in a straightforward way, distributivity holds. On the other hand, distributivity does not arise if we use the usual notion of extension between consequence relations. A detailed discussion