Socratic Proofs for Quantifiers★

Wiśniewski, Andrzej; Shangin, Vasilyi

doi:10.1007/s10992-005-9000-0

Cited by 16 publications

(11 citation statements)

References 8 publications

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“…Certain types of phenomenon described in the quote may be successfully modelled by means of erotetic calculi. These are basically calculi of questions, where each rule of inference (erotetic rule of inference) processes a question into another question [26,28,30]. From a proof-theoretical perspective erotetic calculi are based on inverted sequent calculi, 1 which may be also viewed as hypersequent systems (with hypersequents joined conjunctively, cf.…”

Section: ]mentioning

confidence: 99%

“…If the questions are constructed in such a way that they concern the consequence relation in L, then the method becomes in fact a proof-method for L. The method has been adjusted to CPL [26], to First-Order Logic [28], to the propositional parts of CLuN and CLuNs [30], to a large class of propositional modal logics [13][14][15], and to propositional intuitionistic logic [21]. Yet still, an erotetic calculus remains a calculus of questions.…”

Section: ]mentioning

confidence: 99%

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Dual Erotetic Calculi and the Minimal $${\mathsf{LFI}}$$ LFI

Chlebowski

Leszczyńska-Jasion

2015

Stud Logica

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Abstract.An erotetic calculus for a given logic constitutes a sequent-style prooftheoretical formalization of the logic grounded in Inferential Erotetic Logic (IEL). In this paper, a new erotetic calculus for Classical Propositional Logic (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 CLuN and its extensions CLuNs and 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 mbC. Last but not least, as the method is grounded in IEL, it constitutes an important tool for the so-called question-processing.

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Section: ]mentioning

confidence: 99%

Section: ]mentioning

confidence: 99%

Dual Erotetic Calculi and the Minimal $${\mathsf{LFI}}$$ LFI

Chlebowski

Leszczyńska-Jasion

2015

Stud Logica

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“…A survey of signed dual tableaux systems can be found in [6]. Some other proof systems for F with semantically invertible rules can be found in [8] and [14].…”

Section: Rasiowa-sikorski System For Fmentioning

confidence: 99%

Tableaux and Dual Tableaux: Transformation of Proofs

Golińska-Pilarek

Orłowska

2007

Stud Logica

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We present two proof systems for first-order logic with identity and without function symbols. The first one is an extension of the Rasiowa-Sikorski system with the rules for identity. This system is a validity checker. The rules of this system preserve and reflect validity of disjunctions of their premises and conclusions. The other is a Tableau system, which is an unsatisfiability checker. Its rules preserve and reflect unsatisfiability of conjunctions of their premises and conclusions. We show that the two systems are dual to each other. The duality is expressed in a formal way which enables us to define a transformation of proofs in one of the systems into the proofs of the other.

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“…The answer is "yes" with regard to Classical Logic (cf. [18] and [19]). In this paper we address this question with regard to some paraconsistent logics, and come to the affirmative answer.…”

Section: Introductionmentioning

confidence: 98%