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Diamonds are a Philosopher's Best Friends. The Knowability Paradox and Modal Epistemic Relevance Logic (Extended Abstract)
 Journal of Philosophical Logic
, 2002
"... Heinrich Wansing Dresden University of Technology The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the ..."
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Heinrich Wansing Dresden University of Technology The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the unwanted disappearance of the diamond may be escaped. The emphasis is not laid on a discussion of the contentious premise of the knowability paradox, namely that all truths are possibly known, but on how from this assumption the conclusion is derived that all truths are, in fact, known. Nevertheless, the solution o#ered is in the spirit of the constructivist attitude usually maintained by defenders of the antirealist premise. In order to avoid the paradoxical reasoning, a paraconsistent constructive relevant modal epistemic logic with strong negation is defined semantically. The system is axiomatized and shown to be complete.
Intuitionistic Logic with a "Definitely" Operator
, 1997
"... This paper introduces a logic ILED derived from standard intuitionistic sentence logic by adding two operators Dj for "Definitely j" and ~j for "Experience rejects j". A further negation j = def (j®^) Ú ~j , which we call real negation, is introduced. Real negation is like intuitionistic negation ..."
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This paper introduces a logic ILED derived from standard intuitionistic sentence logic by adding two operators Dj for "Definitely j" and ~j for "Experience rejects j". A further negation j = def (j®^) Ú ~j , which we call real negation, is introduced. Real negation is like intuitionistic negation when there are no Doperators but deviates when there are. We see that Dj j is valid but Dj ® j is not and hence that contraposition fails for real negation. We give a semantics for this logic, axiomatise it and prove the axiomatisation complete. Finally we show that real negation behaves as standard intuitionistic negation within Dfree contexts. The logic ILED is proposed as an extension of intuitionistic logic apt for use as a general logic. Introduction The use of intuitionistic logic as a general logic is made difficult by the usual interpretation of intuitionistic negation: to assert notj is to assert that j derives absurdity. This is constrained by the definition of j by j®^ and the...