Definitional Reasoning in Proof-Theoretic Semantics and the Square of Opposition

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Dokumentart: Article
Date: 2012
Source: Jean-Yves Béziau and Gillman Payette (eds.), The Square of Opposition: A General Framework for Cognition. Bern: Peter Lang 2012, pp. 323-349
Language: English
Faculty: 7 Mathematisch-Naturwissenschaftliche Fakultät
Department: Informatik
DDC Classifikation: 004 - Data processing and computer science
100 - Philosophy
Keywords: Logik , Logisches Quadrat , Negation
Other Keywords: Beweistheoretische Semantik
Definitorische Reflexion
Square of Opposition
Proof-theoretic Semantics
Definitional Reflection
ISBN: 978-3-0343-0537-2
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Within a framework of clausal definitions of atoms, four forms of judgement are distinguished: Direct and indirect assertion, and direct and indirect denial. Whereas direct assertion and direct denial are established by directly applying a definitional clause (“definitional closure”), indirect assertion and indirect denial result from showing that all possible premisses of the opposite judgement can be refuted (“definitional reflection”). The deductive relationships between these four forms of judgement correspond to those represented in the square of opposition, if direct assertion and direct denial are placed in the A and E corners, and indirect assertion and indirect denial in the I and O corners of the square.

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