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Review of Heinrich Wansing, Displaying Modal Logic, Kluwer Academic Publishers, 1998 Trends in Logic: Studia Logica Library
"... disjunction of the material on the right. Sequents feature a single kind of punctuation, here the comma, which is interpreted as conjunction on the left and disjunction on the right. Belnap saw (with others, such as Dunn [2] and Mints [4]) that to model interesting intensional logics such as the lo ..."
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disjunction of the material on the right. Sequents feature a single kind of punctuation, here the comma, which is interpreted as conjunction on the left and disjunction on the right. Belnap saw (with others, such as Dunn [2] and Mints [4]) that to model interesting intensional logics such as the logic R of relevant implication, more punctuation was necessary. In particular, it seems necessary to have an intensional form of conjunction, along with the extensional conjunction of standard Gentzen systems. The addition of more `punctuation' in a Gentzen system brings with it a corresponding complexity in proving that the Gentzen system has desirable properties, such as the admissibility of the Cut rule. If sequents can contain a combination of intensional and extensional punctuation on both the left and the right, then it seems like a cut rule will have to reason from premises: X(A)<F17.28
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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Cited by 7 (0 self)
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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
Partial Logics With Two Kinds of Negation as a Foundation for KnowledgeBased Reasoning
 What Is Negation
, 1995
"... We show how to use model classes of partial logic to define semantics of general knowledgebased reasoning. Its essential benefit is that partial logics allow us to distinguish two sorts of negative information: the absence of information and the explicit rejection or falsification of information. ..."
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Cited by 37 (26 self)
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.4. Keyword and Phrases: Partial logic, semantics of knowledgebased reasoning. Note: To appear in D. Gabbay and H. Wansing (Eds.), What is Negation?, Kluwer, 1996. Jan Jaspars was sponsored by CECproject LRE6201 (FraCaS). 1.
Intuitionistic Logic Redisplayed
, 1995
"... We continue the study of Belnap's Display Logic. Specifically, we show that the booleantensemodal setting of Wansing and Kracht not only allows us to "redisplay" intuitionistic logic but also allows us to display superintuitionistic (intermediate) logics by using the underlying Krip ..."
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Cited by 11 (9 self)
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We continue the study of Belnap's Display Logic. Specifically, we show that the booleantensemodal setting of Wansing and Kracht not only allows us to "redisplay" intuitionistic logic but also allows us to display superintuitionistic (intermediate) logics by using the underlying
Oleg Grigoriev RELEVANT GENERALIZATION STARTS HERE
, 2010
"... Abstract. There is a productive and suggestive approach in philosophical logic based on the idea of generalized truth values. This idea, which stems essentially from the pioneering works by J.M. Dunn, N. Belnap, and which has recently been developed further by Y. Shramko and H. Wansing, is closely ..."
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Abstract. There is a productive and suggestive approach in philosophical logic based on the idea of generalized truth values. This idea, which stems essentially from the pioneering works by J.M. Dunn, N. Belnap, and which has recently been developed further by Y. Shramko and H. Wansing
Solving the Display Problem via Residuation
, 1995
"... The "display problem" of Belnap is an attempt to compare and contrast the Pscheme of Belnap and the Ascheme of Wansing, each of which have the display property. Restall has recenly shown that relevant logics can be better displayed using a third scheme. We show that the Cscheme presente ..."
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Cited by 3 (1 self)
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The "display problem" of Belnap is an attempt to compare and contrast the Pscheme of Belnap and the Ascheme of Wansing, each of which have the display property. Restall has recenly shown that relevant logics can be better displayed using a third scheme. We show that the C
Power and weakness of the modal display calculus
 In Proof theory of modal logic
, 1996
"... The present paper explores applications of Display Logic as defined in [Belnap, 1982] to modal logic. Acquaintance with that paper is presupposed, although we will give all necessary definitions. Display Logic is a rather elegant prooftheoretic system that was developed to explore in depth the poss ..."
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Cited by 24 (0 self)
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The present paper explores applications of Display Logic as defined in [Belnap, 1982] to modal logic. Acquaintance with that paper is presupposed, although we will give all necessary definitions. Display Logic is a rather elegant prooftheoretic system that was developed to explore in depth the possibility of total Gentzenization
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"... Abstract. The paper is a study of properties of quasiconsequence operation which is a key notion of the socalled inferential approach in the theory of sentential calculi established in [5]. The principal motivation behind the quasiconsequence, qconsequence for short, stems from the mathematical ..."
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Abstract. The paper is a study of properties of quasiconsequence operation which is a key notion of the socalled inferential approach in the theory of sentential calculi established in [5]. The principal motivation behind the quasiconsequence, qconsequence for short, stems from the mathematical practice which treats some auxiliary assumptions as mere hypotheses rather than axioms and their further occurrence in place of conclusions may be justified or not. The main semantic feature of the qconsequence reflecting the idea is that its rules lead from the nonrejected assumptions to the accepted conclusions. First, we focus on the syntactic features of the framework and present the qconsequence as related to the notion of proof. Such a presentation uncovers the reasons for which the adjective ”inferential ” is used to characterize the approach and, possibly, the term ”inference operation ” replaces ”qconsequence”. It also shows that the inferential approach is a generalisation of the Tarski setting and, therefore, it may potentially absorb several concepts from the theory of sentential calculi, cf. [10]. However, as some concrete applications show, see e.g. [4], the new approach opens perspectives for further exploration. The main part of the paper is devoted to some notions absent, in Tarski approach. We show that for a given qconsequence operation W instead of one Wequivalence established by the properties of W we may consider two congruence relations. For one of them the current name is kept preserved and for the other the term ”Wequality ” is adopted. While the two relations coincide for any W which is a consequence operation, for an arbitrary W the inferential equality and the inferential equivalence may differ. Further to this we introduce the concepts of inferential extensionality and intensionality for qconsequence operations and connectives. Some general results obtained in Section 2 sufficiently confirm the importance of these notions. To complete a view, in Section 4 we apply the new intensionalityextensionality distinction to inferential extensions of a version of the ̷Lukasiewicz four valued modal logic.
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