Abstract
An erotetic calculus for a given logic constitutes a sequent-style proof-theoretical formalization of the logic grounded in Inferential Erotetic Logic (\({\mathsf{IEL}}\)). In this paper, a new erotetic calculus for Classical Propositional Logic (\({\mathsf{CPL}}\)), dual with respect to the existing ones, is given. We modify the calculus to obtain complete proof systems for the propositional part of paraconsistent logic \({\mathsf{CLuN}}\) and its extensions \({\mathsf{CLuNs}}\) and \({\mathsf{mbC}}\). The method is based on dual resolution. Moreover, the resolution rule is non-clausal. According to the authors knowledge, this is the first account of resolution for \({\mathsf{mbC}}\). Last but not least, as the method is grounded in \({\mathsf{IEL}}\), it constitutes an important tool for the so-called question-processing.
Highlights
The considerations presented in this paper join two issues, each of which is of indepedendent interest
In this paper we have presented an original account of the resolution system for the paraconsistent logic mbC, and similar systems for the propositional parts of paraconsistent logics CLuN and CLuNs
The resolution rule of our calculi is dual with respect to the standard one and is non-clausal
Summary
The considerations presented in this paper join two issues, each of which is of indepedendent interest. The method of transforming questions (of a certain formal language) concerning some chosen properties of an underlying logic L in accordance with the rules of an erotetic calculus is called the method of Socratic proofs for L (the “Socratic” aspect of the method is concerned with the fact that one aims at questions to which an answer is obvious). A proof of a sequent ‘ A’ in an erotetic calculus is a sequence of questions, called Socratic transformation, with the following properties It starts with a question of the form: ?( A), intuitively interpreted as concerning the validity or theoremhood of formula A. There is no resolution-account of mbC known to us It seems that erotetic inferences may be paraconsistent as well, the philosophical reason for the construction presented in this paper is that embedding paraconsistent logics into the erotetic framework results in a. A similar technique is used in [6] in the context of embedding logic CLuN in CPL, where the normal form of a formula is expressed in a language with a new kind of variables
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